Journal of Theoretical Biology 477 (2019) 108–126 Contents lists available at ScienceDirect Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/jtb Is the cell really a machine? Daniel J. Nicholson a , b , ∗ a Konrad Lorenz Institute for Evolution and Cognition Research, Martinstrasse 12, Klosterneuburg, 3400, Austria b Centre for the Study of Life Sciences (Egenis), University of Exeter, Byrne House, St. German's Road, Exeter, EX4 4PJ, United Kingdom a r t i c l e i n f o Article history: Received 27 October 2018 Revised 6 May 2019 Accepted 3 June 2019 Available online 4 June 2019 Keywords: Stochasticity Self-organization Pleomorphic ensembles Brownian ratchet Non-genetic heterogeneity a b s t r a c t It has become customary to conceptualize the living cell as an intricate piece of machinery, different to a man-made machine only in terms of its superior complexity. This familiar understanding grounds the conviction that a cell's organization can be explained reductionistically, as well as the idea that its molecular pathways can be construed as deterministic circuits. The machine conception of the cell owes a great deal of its success to the methods traditionally used in molecular biology. However, the recent introduction of novel experimental techniques capable of tracking individual molecules within cells in real time is leading to the rapid accumulation of data that are inconsistent with an engineering view of the cell. This paper examines four major domains of current research in which the challenges to the machine conception of the cell are particularly pronounced: cellular architecture, protein complexes, intracellular transport, and cellular behaviour. It argues that a new theoretical understanding of the cell is emerging from the study of these phenomena which emphasizes the dynamic, self-organizing nature of its constitution, the fluidity and plasticity of its components, and the stochasticity and non-linearity of its underlying processes. © 2019 Elsevier Ltd. All rights reserved. p t c o c a n ( m e t e p r o t fi e Through its properties, by the microscopic clockwork function that establishes between DNA and protein, as between organism and medium, an entirely one-way relationship, this system obviously defies any 'dialectical' description. It is not Hegelian at all, but thoroughly Cartesian: the cell is indeed a machine. ( Monod, 1972 , pp. 110–111) 1. Introduction: The Machine Conception of the Cell Over the past half a century, molecular biology has generated vast amounts of knowledge at a rate that is surely unprecedented in the history of science. However, our progress in translating this ever-growing repository of information into a deeper theoretical understanding of what living systems are and how they function as coordinated wholes has been far less impressive. Now it may be that this is simply a reflection of the extraordinary complexity of the cell, and that it is only a matter of time before all cellular components are characterized and all of their interconnections are fully mapped out, at which point we will finally have a total grasp of the internal workings of the cell. Alternatively, it is possible that the∗ Correspondence to: Konrad Lorenz Institute for Evolution and Cognition Research , Martinstrasse 12, Klosterneuburg, 3400, Austria. E-mail address: dan.j.nicholson@gmail.com v 2 https://doi.org/10.1016/j.jtbi.2019.06.002 0022-5193/© 2019 Elsevier Ltd. All rights reserved. roblem lies not so much in the complexity of the cell as in the inerpretive framework-the theoretical presuppositions, conceptual ategories, and explanatory models-routinely used to make sense f this complexity. This paper explores this second possibility. The main interpretive framework in molecular biology is mehanicism , a highly influential research program with many forms nd incarnations that can be traced all the way back to the atural philosophy that gave rise to the Scientific Revolution Hall, 1969; Nicholson, 2012; Loison, 2015 ) 1 . Modern proponents of echanicism conceive of the cell as an intricate piece of machinry whose organization reflects a pre-existing design, whose strucure is wholly intelligible in reductionistic terms, and whose opration is governed by deterministic laws, rendering its behaviour redictable and controllable-at least in principle. I shall hereafter efer to this pivotal mechanicist notion as the machine conception f the cell (MCC). The MCC long predates the rise of molecular biology-its hisory runs parallel to that of mechanicism, which is why one can nd rudimentary expressions of the MCC dating back to the sevnteenth century, when analogies between machines and organ-1 Since Descartes, biological theory has oscillated between the mechanicist view of the organism as a complex machine and a vitalist-and more recently organicist - iew of the organism (inspired by Kant among others) as an agential, nonmechanical , intrinsically purposive system ( Allen, 2005; Normandin and Wolfe, 013 ; Esposito, 2013 ; Nicholson and Gawne, 2015 ). D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 109 i o m o t s a e c p ( i a p i o e t ( o l b i w g 1 t b s ( p w s t o i e t ( i g o t e c g ' ( ( t f t g s f o a n c a F a s i t c a t t t s o a t f i t o v o a l h t t t W K M L s b p p t e c t l s o e 2 For complementary critiques of the machine conception of living systems in other areas of biology-such as physiology, development, and evolution-see Nicholson (2013, 2014, 2018 ). sms first began to acquire currency. Malpighi, one of the founders f microscopical anatomy, attributed the bodily functions of anials and plants to "a very large number of machines, which are f necessity made up of extremely minute parts [...] invisible to he naked eye" (Malpighi, quoted in Piccolino, 20 0 0 , p. 149). In a imilar vein, Leibniz, the early modern natural philosopher, charcterized organisms as machines of divine origin, which are hirarchically composed of ever-smaller machines ad infinitum . He ontrasted organisms to machines of human origin, whose comonent parts are not themselves also machines in their own right Smith, 2011 ). By the turn of the twentieth century, the cell was beng variously characterized as "a little engine with admirably dapted parts" ( Conn, 1899 , p. 126), a "chemical machine" caable of "automatically developing, preserving, and reproducng [itself]" ( Loeb, 1906 , p. 1), and "a battery, with a series f resistances and condensers, made up of conductors and dilectrics" ( Matthews, 1924 , p. 15). But most influential of all was he understanding of the cell as a "small chemical laboratory" Hertwig, 1895 , p. 126) or a miniature factory, with proteins and ther macromolecules arranged like machine tools on an assembly ine ( Reynolds, 2007, 2018 ). Following the Second World War, the pioneering ideas of cyernetics, information theory, and computer science captured the magination of biologists, providing a new vision of the MCC that as translated into a highly successful experimental research proram, which came to be known as 'molecular biology' ( Keller, 995; Morange, 1998; Kay, 20 0 0 ). At its core was the idea of he computer, which, by introducing the conceptual distinction etween 'software' and 'hardware', directed the attention of reearchers to the nature and coding of the genetic instructions the software) and to the mechanisms by which these are imlemented by the cell's macromolecular components (the hardare). Early molecular biologists openly conjectured about the tructure and function of the cell along these lines, deliberately ransgressing the boundaries between the technological and the bilogical, as the following excerpt from a paper published in 1962 llustrates: Taking then, as an engineering definition of a living cell, 'A completely automatic factory for fabricating automatic factories like itself', we may profitably consider what components might be found in such a system. Passing over such trivia as a power station for utilizing whatever energy source might be available, it is clear that a large computer would be the control mechanism at the centre of our design. In its store would be an encyclopaedia of programmes which would give the proper response to all possible sets of external circumstances, and these would be activated by input devices which would record the external conditions and the supply position. Other input channels would monitor the progress of the various factory processes, forming the feedback loops which are essential to control mechanisms. Output from the computer would go [...] to a set of automatic machine tools which would perform the various operations required for construction of a duplicate factory. Here the complex task of converting the information stored in the computer into solid matter would be performed. ( Blow, 1962 , p. 177) It is quite remarkable to observe that, despite the enormous mpirical advances that have been made since 1962, our basic heoretical picture of the cell has remained essentially unchanged see, e.g., Bray, 20 09; Danchin, 20 09 ). The standard view nowadays s that the cell coordinates its functions by virtue of a 'genetic proram' encoded in the DNA that directs and controls the expression f a specific set of RNAs and proteins, which assemble determinisically into stable 'molecular machines' that reliably and efficientlyxecute predetermined operations according to the mechanisms of ell division, endocytosis, signal transduction, etc. Machine analoies and metaphorical references to 'locks', 'keys', 'gates', 'pumps', motors', and 'engines' continue to pervade the technical literature e.g. Piccolino, 20 0 0; Frank, 2011 ), as does talk of the 'machinery' e.g. Goodsell, 2009 ) and 'circuitry' (e.g. Alon, 2007 ) that underlies he cellular organization. The MCC itself is seldom explicitly deended; it has become so engrained in our minds that we simply ake it for granted. But why have we relied so heavily on machine metaphors to round our theoretical understanding of living systems? What is so pecial about machines that make them such apposite analogues or thinking about cells? Although there are many different kinds f machines, a machine can be characterized in very general terms s a device with fixed interacting parts that operate in a coordiated fashion to produce a predetermined outcome. More specifially, one can identify four distinctive properties of machines that re particularly relevant in contemporary formulations of the MCC. irst, machines can be described in terms of a list of parts and blueprint indicating how those parts fit together, meaning that omeone who has never seen a particular kind of machine should n principle be able to assemble any number of copies-each virually identical in appearance and performance-provided they can onsult the machine's design specifications. Second, as machines re designed to perform highly specific functions, their operation is ightly constrained, which is why it is possible to predict and conrol their behaviour. Third, machines are highly efficient in what hey do because they always follow the exact same sequence of teps in every cycle of their operation. And fourth, the operation f machines is not continuous; their functioning can be interrupted nd their parts examined without thereby jeopardizing their strucural integrity. The first and fourth of these characteristics account or why the MCC justifies the belief in the sufficiency of reductionstic explanations of cellular phenomena, whereas the second and hird show why the MCC provides support for a deterministic view f cellular processes. In recent years, however, the MCC has come under attack from arious fronts. Ironically, the very successes of molecular biolgy that were instigated by mechanicism have resulted in the ccumulation of experimental data that are difficult to assimiate within its interpretive framework. As a result, critical reviews ave begun to appear that explicitly challenge the reductionisic and deterministic presuppositions of mechanicism and quesion the coherence of the familiar clockwork image of the cell. Noable examples include Kirschner et al. (20 0 0) , Astumian (20 01) , oese (2004) , Cornish-Bowden (2006) , Longo and Tendero (2007) , arsenti (20 08) , Huang (20 09) , Mayer et al. (2009) , Kupiec (2010) , oore (2012) , Bizzarri et al. (2013) , Talbott (2013) , Heams (2014) , ongo and Montévil (2014) , Soto and Sonnenschein (2018) , and a eries of articles by Kurakin (20 05, 20 06, 20 09, 2010 ). Drawing and uilding on this burgeoning body of literature, the aim of this paer is to establish the inadequacy of the MCC. From a theoretical erspective, the MCC offers a poor and rather misleading represenation of biological reality-or so I will argue 2 . The MCC fails to make appropriate sense of cellular phenomna for two basic reasons. The first has to do with the fact that ells, unlike machines, are self-organizing, fluid systems that mainain themselves in a steady state far from thermodynamic equiibrium by continuously exchanging energy and matter with their urroundings. And the second has to do with the fact that by virtue f their microscopic size, cells (and their molecular constituents, ven more so) are subject to very different physical conditions 110 D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 2 f o e a a p p s c c t d f i ( S s s a t t g b p s ( c m ( S w e w e w t t t i h s s N u t s S t t r t d e i h s f m p compared to macroscopic objects, like machines. Although both of these facts are incontrovertible-indeed, they may strike some readers as painfully obvious-the theoretical implications they have for our understanding of life are far from familiar, and it is these implications that shall be concerning me here. What I will contend is that they lead to a conception of the cell that is completely at odds with the mechanicist, reductionistic, and deterministic view that was championed by the founding fathers of molecular biology, such as Monod in his hugely influential Chance and Necessity ( Monod, 1972 ), quoted in the epigraph of this paper. If the facts that underlie the inadequacy of the MCC really are indisputable, why has it taken us so long to start taking serious notice of them? I suspect that part of the answer has to do with the resistance that many biologists intuitively feel towards denunciations of mechanicism. Perceived inconsistencies and contradictions in the established paradigm are often downplayed-or dismissed altogether-in order to safeguard the familiar assumptions that the research community works under. But an even more important factor, I believe, is that we have been blinded by traditional biochemical and biophysical methods. Until relatively recently, it was only possible to examine the cell's interior with crude in vitro techniques, looking at average behaviours of large populations of macromolecules under conditions usually remote from those existing in the cell. However, the introduction of novel methods capable of tracking and manipulating individual molecules within cells has allowed us to observe for the first time the real-time dynamics of biological macromolecules and the surprisingly wide range of behavioural repertoires they exhibit in in vivo conditions ( Zlatanova and van Holde, 2006; Xie et al., 2008; Tinoco and Gonzalez, 2011 ). As I will discuss in more detail later, single-molecule studies are yielding results not anticipated by the use of populationaveraged methods. These results are bringing about a radical shift in how we think about the cell, replacing a mechanical, neatly ordered, rigid picture with one that is inherently stochastic, more plastic, and less predictable. What we are witnessing, in effect, is a conceptual revolution being triggered by a methodological revolution. Despite the historical predominance of mechanicism, a new interpretive framework is now required to understand what our recent findings are telling us about the nature of the cell. This framework is already arising, as more molecular biologists are becoming aware of the numerous problems plaguing the MCC. This paper will examine in detail four specific domains of research where the incompatibilities with the MCC are becoming particularly pronounced. The first is the study of the cellular architecture, which in line with the MCC has long been construed as a static, highly ordered structure. The second is the study of protein complexes, which have generally been characterized as remarkably specialized, exquisitely designed molecular machines. The third is the study of intracellular transport, which has tended to be explained in terms of miniature engines propelled by mechanical forces. And the fourth is the study of cellular behaviour, which has long been assumed to be governed by a deterministic program encoded in the genome. Increasingly, all of these mechanicist interpretations are being called into question, and a fundamentally different conception of the cell is emerging. As I will show, according to this alternative view, the cellular architecture is regarded as a fluid, self-organizing process; protein complexes are considered to be transient, pleomorphic ensembles; intracellular transport is deemed to result from the harnessing of Brownian motion; and cellular behaviour is viewed as a probabilistic affair, subject to constant stochastic fluctuations. Taken together, these four case studies will illustrate how a rejection of the MCC-along with the mechanicist assumptions that underlie it-is contributing to the development of a more theoretically compelling picture of the cell. . Cellular Architecture: Static Structure or Stabilized Process? Much of what we know about the cell's organization derives rom snapshots of fixed, stained, or desiccated biological samples btained by conventional microscopy techniques. A representative xample is shown in Fig. 1 . Historically, the interpretation of imges of this kind naturally led to an understanding of the internal rchitecture of the cell in terms of clearly delineated, neatly comartmentalized structures that closely resemble machineries. These ermanent structures were eventually assigned functions to make ense of their role in the overall economy of the cell, which in acordance with the MCC was viewed as a factory with highly speialized compartments. But how are these structures that constitute the cellular archiecture formed and maintained? What is it that determines their ifferent shapes and sizes, as well as their respective locations and unctions in the cell? For decades, the basis for our understandng of macromolecular order was the principle of self-assembly Kushner, 1969; Inouie, 1982; Whitesides and Grzybowski, 2002 ). elf-assembly involves the physical association of molecules into a tatic equilibrium structure in the absence of an external energy ource. It is driven by local stereospecific interactions between the ggregating 'building blocks', which remain unchanged throughout he process. As the properties of the resulting structure are deermined by the properties of its parts, self-assembly can be rearded as "an extension of the central dogma of molecular biology, ringing us from the realm of linear information to the realm of rotein assemblies" ( Kirschner et al., 20 0 0 , p. 80). Classical, welltudied examples of self-assembly include viral capsid formation Caspar and Klug, 1962 ) and ribosome biogenesis ( Nomura, 1973 ). However, self-assembly is not the only theoretical principle that an be invoked to explain the spontaneous generation of macroolecular order. There is also the principle of self-organization Nicolis and Prigogine, 1977; Kauffman, 1993; Karsenti, 2008 ). elf-organization refers to the collective behaviour of molecules hen these interact nonlinearly to generate a dynamic far-fromquilibrium structure (sometimes called a 'dissipative structure'), hich maintains itself in a low-entropic 'steady state' by constantly xpending energy and exchanging matter with its surroundings. So, hile self-assembled systems are closed, as their material constiution is conserved, self-organizing ones are open, as they rely for heir preservation on the continuous replenishment of the material hat composes them. Of course, we have known for a long time that self-organization s essential for living systems, given that the cell as a whole- ow ever else one may wish to describe it-is, thermodynamically peaking, a far-from-equilibrium dissipative structure: in the abence of a steady supply of energy, it reaches equilibrium and dies. evertheless, it has proven surprisingly difficult to identify particlar instances of self-organization inside the cell. This is due to he fact that self-assembly and self-organization tend to lead to imilar observable patterns, albeit through totally different means. pecifically, both generate stable structures; the difference being hat those generated by the former exhibit static stability whereas hose generated by the latter exhibit dynamic stability (sometimes eferred to as 'meta-stability'). The problem remained that convenional microscopy methods prevented us from distinguishing them. Recent technological innovations have changed all of this. The evelopment of in vivo microscopy techniques using geneticallyncoded fluorescent tags of individual molecules has provided new nsights into the spatiotemporal configuration of the cell. Peraps the most surprising discovery that has emerged from these tudies is the unexpectedly high degree of dynamism observed or a wide range of macromolecular structures. It appears that any-perhaps most-subcellular compartments are more approriately described as dynamic self-organizing steady states than D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 111 Fig. 1. Electron micrograph of a longitudinal section of the unicellular green alga Chlamydomonas , which conveys a static, clearly compartmentalized impression of the cell's interior. (Image courtesy of J. D. Jamieson and the Department of Cell Biology, Yale University School of Medicine; reproduced under a Creative Commons License.) a o o t m e p t n a c T t d w c t p b t i i A t p s i b fl a t c s w s m t a c t t p f 2 d o a o k l w i m t w L o M s static self-assembling machineries. The molecular constituents f the cell, it turns out, have a tendency to spontaneously selfrganize into morphologically and functionally distinct organizaions through inherently stochastic interactions. These transient eta-stable systems are sustained by the incessant flow of enrgy and matter passing through them, with their respective comonents displaying different recruitment probabilities, residence imes, and turnover rates ( Misteli, 2001a; Kurakin, 2009 ). Let me ow discuss some specific examples of intracellular entities that re currently being completely reconceptualized as a result of reent empirical findings (prompted by the use of new methods). The mitotic spindle of eukaryotic cells is one such example. he spindle is an ordered array of microtubules, associated proeins, and chromosomes that forms during cell division, and which istributes the duplicated genetic material to the daughter cells ith stunning precision. Owing to its remarkably stable-almost rystalline-appearance in cross-sections of cells undergoing miosis, the mitotic spindle is often characterized as "a fascinating rotein machine" ( Mogilner et al., 2006 , p. 88) capable of assemling and disassembling according to genetically encoded instrucions. However, recent research has shown that the mitotic spindle s actually a self-organizing system, displaying high degrees of flexbility and robustness ( Nédélec et al., 2003; Pavin and Toli c, 2016 ). rchitecturally speaking, the microtubules that compose the miotic spindle are constantly polymerizing and depolymerizing, reeatedly undergoing cycles of GTP hydrolysis to maintain it in a teady state far from equilibrium. As a consequence of these findngs, The traditional view of the mitotic spindle apparatus as a molecular machine which is built through a defined irreversible set of instructions is gradually being replaced. It can instead be envisaged as a self-regulating dynamic structure where multiple pathways of MT [microtubule] generation are spatially and temporally controlled and integrated, constantly 'talking' to one another and modifying the behaviour of their MTs in order to s maintain a flexible yet robust steady-state spindle. ( Duncan and Wakefield, 2011 , p. 330) It has further been suggested that not only the mitotic spindle, ut the entire cytoskeleton is better characterized as a meta-stable ux dynamically responding to changes in its environment than as static macromolecular construction. "Despite the connotations of he word 'skeleton'", Fletcher and Mullins (2010, p. 485) write, "the ytoskeleton is not a fixed structure whose function can be undertood in isolation. Rather, it is a dynamic and adaptive structure hose component polymers and regulatory proteins are in contant flux". Self-organization appears to be similarly crucial for intracellular embrane compartments, such as those involved in the secretory ransport pathway, in which proteins targeted to the cell's exterior re transported from the endoplasmic reticulum through the Golgi omplex to the plasma membrane. Although the compartments of his pathway have traditionally been regarded as static structures, he recent tracking of resident and cargo molecules through the athway using in vivo microscopy has revealed that they are in act constantly exchanging material ( Lippincott-Schwartz et al., 0 0 0 ). The Golgi complex, for instance, resembles the mitotic spinle in that its stability is a consequence of the balanced turnover f the molecules that flow through it. Given its fluid nature, its rchitecture can be modified by manipulating the influx and efflux f material passing through its component cisternae. We now now that inhibition of traffic from the endoplasmic reticulum eads to the dispersion of the Golgi complex into small vesicles, hereas blocking the transport of vesicles that bud from it results n its enlargement. Although there is still considerable disagreeent over how the actual traffic occurs-specifically over whether he Golgi cisternae themselves progress or mature along the pathay or if it is only their cargo that gets transported (see Glick and uini, 2011 )-what seems clear is that the Golgi complex is a selfrganizing steady-state organelle ( Tachikawa and Mochizuki, 2017 ). ore broadly, live imaging techniques are unveiling the triking dynamicity that underlies the stability of intracellular 112 D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 i d c t m t t m c i s a g c a t t w p t t t a d p t t t s h l c s s a p v a a r t a m d t e a w l i Table 1 Key differences between the two conceptions of cellular architecture . On the left, the standard view derived from the MCC. On the right, the alternative view suggested by recent research. Static structure Stabilized process Self-assembling Self-organizing Closed system Open system At equilibrium Far from equilibrium Genetically encoded Emergently generated Economical but inflexible Costly but flexible Temporally abstractable Temporally non-abstractable Amenable to reductionism Not amenable to reductionism membrane compartments of both exocytotic and endocytotic pathways ( Kerr and Teasdale, 2014 ). Our understanding of the eukaryotic cell nucleus is also becoming radically transformed. Far from being the static, crowded, gel-like structure described in textbooks, the nucleus is extremely dynamic and surprisingly fluid. Most of its proteins are highly mobile, stochastically moving about the nucleoplasmic space contingently interacting with one another and participating in different nuclear functions, such as chromatin remodelling, transcriptional activation, ribosomal RNA processing, and DNA repair. The dynamic interplay between nuclear proteins results in an everchanging, yet globally stable architecture within which nuclear processes take place ( Misteli, 2001b; Janicki and Spector, 2003 ). The nuclear architecture includes a number of morphologically and functionally distinct compartments, such as nucleoli, Cajal bodies, and perinuclear specks, that are maintained in a state of "perpetual flux" ( Misteli, 2001b , p. 844) by the constant exchange of their resident proteins, which also transiently associate with the chromatin. The latest research on these subnuclear, membraneless organelles strongly suggests that they are better conceived as liquid-like droplets than as solid, core-shell structures: they have a spherical shape, they fuse together, and their molecular constituents are constantly undergoing fluid internal rearrangements ( Brangwynne et al., 2011; Shin and Brangwynne, 2017 ). In addition to its instrumental role in generating and maintaining many organelles, recent studies suggest that self-organization is involved in some of the cell's most essential processes, including metabolism ( De la Fuente et al., 2008 ), genome organization ( Misteli, 2009 ), cell division ( Loose et al., 2008 ), and cell differentiation ( Woodford and Zandstra, 2012 ). The self-organizing nature of the cellular architecture has far reaching theoretical consequences. Most fundamentally, it leads to a view of the cell that is completely at odds with the MCC. For one thing, it dispels the notion that the 'information' that specifies the spatial organization of the cell is somehow encoded in the genome. Strictly speaking, there is no genetic blueprint for the cellular architecture. Self-organization generates order in the absence of an external template or global plan. Genes specify only the primary sequence of macromolecules; the architecture of the cell, for the most part, arises from the interactions of numerous gene products with other cellular components. Genes are important, to be sure, but they do not set in motion a unique chain of events that produces the organization of the cell, as the use of the term 'information' sometimes misleadingly suggests. Rather, gene products are released into a cellular milieu that already possesses spatial structure, and they exert their influence under the physical constraints of the existing order-much of which is shaped by pre-existing self-organizing processes ( Harold, 2005; Rafelski and Marshall, 2008 ). In contrast to a machine, in which a fixed architecture performs a predetermined function, a cell is continuously transforming its internal architecture (by modifying the exquisitely regulated balance between the inflow and outflow of its molecular constituents) in order to keep up with its ever-changing functional needs. Cellular structures showcase what Dumont and Prakash (2014) appropriately refer to as 'emergent mechanics', which cannot be predicted from knowledge of their parts. The disparity with the mechanics of machines is all too evident, as the authors themselves explicitly acknowledge: Unlike the engineered macroscopic structures that we commonly build, biological structures are dynamic and selforganize: they sculpt themselves and change their own architecture, and they have structural building blocks that [...] constantly come on and off. A description of such structures defies current traditional mechanical frameworks. ( Dumont and Prakash, 2014 , p. 3461) Indeed, no machine self-organizes by autonomously exchanging ts material constitution in order to maintain its architecture in a ynamic steady state, yet this is precisely what happens in every ell. But why do cells favour self-organization over self-assembly as he main mechanism for creating their architecture? Would it not ake more sense for a cell to build static, equilibrium structures hat do not require a constant expenditure of energy to maintain hem? Although self-assembly is a more economical and efficient eans of producing durable macromolecular structures of great omplexity (the viral capsid is a conspicuous example), the resultng structures lack morphological flexibility and do not lend themelves easily to modifications. The advantage of a self-organizing rchitecture, despite its huge energetic cost, is that it confers a reat deal of plasticity without compromising on stability. It allows ells to respond rapidly and adaptively to external perturbations nd other critical events that would otherwise jeopardize their sysemic integrity. Overall, recent research on the cellular architecture demands hat we look more carefully at what we have previously assumed ere well-defined structures and reconsider them as stabilized rocesses . Because processes are temporally extended, it follows hat they can only be understood by giving time due consideraion. And herein lies the problem: the methods traditionally used o probe the interior of the cell conceal the dynamic nature of its rchitecture because they have to incapacitate it in order to rener it visible. Yet to study a cell frozen in time is already to aproach it artificially as a static, machine-like object, rather than as he fluid system that it is in reality ( Nicholson, 2018 ). The strucure of a machine, after all, can be grasped in abstraction from ime (as it is not constantly changing), whereas the structure of, ay, a whirlpool or a stream cannot. This explains why, when we ave started using techniques that allow us to examine the celluar architecture in real time, we have found that many of the cell's ompartments and organelles are not fixed machineries at all, but table macromolecular fluxes. More broadly, the transition from a structural to a procesual conception of the cellular architecture implies shifting our ttention from matter to form. Due to its dynamic nature, what ersists in a cell over time is its form, not its matter: the indiidual molecules that make up a cell come and go, but its overrching organization remains. Accordingly, if we are to grasp how cell operates, mapping out the network of spatial and tempoal relations that exist between its parts is as, if not more, imporant than characterizing the parts themselves. The need to adopt non-reductionist stance is further intensified when we bear in ind that self-organizing processes-which, as I have shown, unerlie much of the cellular architecture-force us to focus on sysemic patterns and collective behaviours, rather than on the proprties and structures of single molecules (which would suffice as n approach if the cell was primarily self-assembling and its order as ultimately encoded in the DNA). The main differences between the two conceptions of the celular architecture I have discussed in this section are summarized n Table 1 . D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 113 3 E g a c M g m a t c c o t N h l w a a o o h t s p 2 c t l s fi n l t f 1 m m c t o b t t t t C e r t s d I m t o s t F t b d a s m l i n i p m p i b c i i i v c o o fi w p t r a s r S t t t c c f c p t m . Protein Complexes: Molecular Machines or Pleomorphic nsembles? The mechanicist foundations of molecular biology have not only uided our inquiries into the cell's internal organization, they have lso shaped our theoretical understanding of its basic molecular omponents, especially proteins. As well as championing the MCC, onod also declared in his Chance and Necessity that "[w]ith the lobular protein we already have, at the molecular level, a veritable achine" ( Monod, 1972 , p. 98). In subsequent years, as it became pparent that most proteins in the cell associate with one another o form larger complexes comprised of different subunits, a new oncept began to acquire currency, namely that of a molecular mahine . In 1998, Alberts (then president of the National Academy f Sciences) published a brief but highly influential manifesto tiled 'The Cell as a Collection of Protein Machines: Preparing the ext Generation of Molecular Biologists' ( Alberts, 1998 ), in which e urged aspiring molecular biologists to embrace the MCC and earn to view the cell as "a factory that contains an elaborate netork of interlocking assembly lines, each of which is composed of set of large protein machines" (ibid., p. 291). At the end of the rticle, Alberts prophesized that "much of the great future in biolgy lies in gaining a detailed understanding of the inner workings f the cell's many marvelous protein machines" (ibid., p. 293). It is difficult to overestimate the impact that Alberts' paper has ad on molecular biology. It has been so successful in popularizing he molecular machine concept that this term is now used to decribe virtually any functionally specialized macromolecular comlex found in the cell (e.g. Nogales and Grigorieff, 2001; Neupert, 005 : Frank, 2011 ), as the following quotation illustrates: Molecular machines are the basis of life. [...] The cell's nanometer-scale machines are mostly protein molecules, although a few are made from RNA, and they are capable of surprisingly complex manipulations. They perform almost all the important active tasks in the cell: metabolism, reproduction, response to changes in the environment, and so forth. They are incredibly sophisticated, and they, not their manmade counterparts, represent the pinnacle of nanotechnology. ( Phillips and Quake, 2006 , p. 38) Some have gone as far as to regard the molecular machine coneption of protein complexes as "one of the most important conributions that biology has made to our understanding of how the iving cell works" ( Ji, 2012 , p. 86). The reason this idea has been so uccessful, as I will argue below, is because it addresses in a unied way the two classical concerns of molecular biology research, amely structure and specificity . Historically, molecular biology represents the confluence of two argely autonomous research programs, both of which can be raced back to the 1930s: one focusing on structure and another ocusing on specificity, or information (cf. Kendrew, 1967; Stent, 968; Hess, 1970 ). The structural school of molecular biology (prooted by the likes of Astbury, Bernal, and Pauling) employed ethods such as X-ray crystallography to determine the atomic onfiguration of key biological molecules, and used those findings o make sense of their physiological role. The informational school f molecular biology (led by the so-called 'phage group' of Delrück, Luria, and Hershey) used bacteriophages as model systems o investigate the molecular basis of heredity and its likely mode of ransmission. The former had ties with biochemistry, while the later had ties with genetics. The two schools came together in specacular fashion in 1953 with the famous elucidation by Watson and rick of the double-helical structure of DNA-a momentous discovry which notably combined structural determination with genetic easoning ( Watson and Crick, 1953 ). Nevertheless, during the later half of the twentieth century, the structural and informationaltrands of molecular biology continued to develop more or less inependently of one other, and it is in the context of this schism, believe, that one can understand the appeal and success of the olecular machine concept, serving as it does to reconcile the disinct explanatory concerns of each school. Conceiving of protein complexes as molecular machines draws ur attention to their structure. When a mechanic or an engineer tudies a machine, they examine its structure carefully because hey know that this will enable them to understand its operation. unction is a direct consequence of structure, and so they elucidate he former by scrutinizing the latter. Accordingly, if as molecular iologists we want to work out what a particular protein assembly oes, modelling it as a molecular machine gives us a clear plan of ction. It tells us that "we must foremost know the structure of the tatic molecular machine at the atomic level as a precondition for aking sense of its behaviour and going beyond mere phenomenoogical description" ( Frank, 2011 , p. 1). For many researchers, it s this privileging of structure when investigating cellular compoents that justifies seeing them as molecular machines. As Piccolno puts it, "[g]iven the importance of structure , modern biological athways fully deserve the names 'molecular and supramolecular achines'" ( Piccolino, 20 0 0 , p. 152, emphasis added). In addition to emphasizing its structure, viewing a protein comlex as a molecular machine serves to highlight the specificity of ts operation. It leads us to view it as an intricately ordered assemly of subunits-each with a clearly defined role-which mechanially interlock with one another in a particular temporal sequence nto a unique configuration that allows it to perform its function n an effective and predictable way. Reading Alberts' manifesto, it s clear that this concern with specificity is one of his main motiations for embracing the machine metaphor: Why do we call the large protein assemblies that underlie cell function protein machines ? Precisely because, like the machines invented by humans to deal efficiently with the macroscopic world, these protein assemblies contain highly coordinated moving parts. Within each protein assembly, intermolecular collisions are not only restricted to a small set of possibilities, but reaction C depends on reaction B, which in turn depends on reaction A-just as it would in a machine of our common experience. ( Alberts, 1998 , p. 291) Despite the popularity of the molecular machine concept, reent research is casting serious doubts on the theoretical adequacy f this notion. Some of its problems pertain to its undue emphasis n structure, and others pertain to its undue emphasis on specicity. I shall examine each of these in turn. With regards to structure, it has become apparent that the idespread use of X-ray crystallography has biased our view of roteins. In the last fifty years, crystallographers have deduced he tertiary structure of a very large number of proteins by puifying them into homogeneous, solid-state crystals and then exmining the ordered array of their atoms. Although the inferred tructural reconstructions are of an extremely high resolution, they epresent only snapshots of incapacitated proteins frozen in time. till, we have relied on this technique so much and for so long hat it has come to shape the way we think about protein strucure and its relation to protein function. Specifically, it has led o the view that each protein has a unique three-dimensional onformation-corresponding to its most thermodynamically stable onfiguration-that it must adopt in order to carry out its intended unction. This deeply-entrenched assumption has been called "the entral dogma of structural biology" ( Wright and Dyson, 1999 , . 322), and, as I have noted above, it reflects precisely how we hink about the relationship between structure and function in a achine. 114 D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 a s m h ( f m l t A t I o o a b u c s p s e ( s m g t H t w h p m e t t i t o j a a d a t t i ( d g r E a c t a n ( The problem, of course, is that proteins do not naturally exist in crystallized form. In fact, in their native environments, they behave more like liquids than like solids. Proteins are really "dense liquids", or "melted-solids", consisting of a "near-solid interior" and a "full-liquid exterior" ( Rueda et al., 2007 , p. 798; see also Zhou et al., 1999 ). In this context, the investigation of protein structure using nuclear magnetic resonance (NMR) spectroscopy, which probes proteins as they twist and turn in solution, has proved more revealing. Although this technique is almost as old as X-ray crystallography, for decades its applicability was severely limited. Only recently has it become possible to employ it in largescale studies of protein structure determination 3 . What we have found by introducing the temporal dimension into our study of protein structure is that proteins are highly dynamic entities that display very high degrees of flexibility, ranging from simple side chain rotations to complete rearrangements of their secondary structure ( Henzler-Wildman and Kern, 2007; Teilum et al., 2009 ). The structure of a protein is soft and fluid, not hard and rigid-like that of a machine. Another important discovery, prompted by the introduction of single-molecule methods, is that proteins in vivo seldom exhibit a single ordered conformation. What is commonly referred to as the conformation of a protein actually comprises a range of well-defined configurations separated by low-energy barriers that a protein molecule continuously samples by means of stochastic fluctuations ( Yang et al., 2003 ). Any population of seemingly identical proteins is really a heterogeneous mixture of molecules with slightly different conformations in equilibrium. It is just that classical structure determination methods identify only the predominant conformation in the population, averaging out the differences that exist between individual molecules (a problem that I shall discuss in more detail later on). This difficulty is compounded when faced with proteins that do not have a predominant conformation. For example, the globular protein lymphotactin adopts two completely distinct alternative conformations, and it undergoes major structural changes as it flickers from one to the other ( Tuinstra et al., 2008; Murzin, 2008 ). More generally, it is important to realize that the conformational landscape of a protein is not fixed. The binding of ligands, post-translational modifications, temperature, pressure, and solvent concentration can all alter a protein's conformational landscape by changing the heights of the energy barriers that separate its alternative conformational states. Lastly, and perhaps most surprisingly, many proteins do not have an ordered conformation at all , but instead roam the cell as unfolded polypeptide chains. This major class of proteins, which have only recently come to the attention of researchers, are called intrinsically disordered proteins (IDPs), and they are found in all domains of life. In mammals, it has been estimated that approximately 75% of signalling proteins and about 50% of all proteins contain at least one disordered region of more than 30 amino acids, and as many as 25% of all proteins are completely disordered ( Dunker et al., 2008 ). It is possible to make such calculations because IDPs differ from ordered proteins already at the level of their amino acid sequence; peculiarities in this sequence define both the ability of ordered proteins to fold, and the ability of IDPs to stay unfolded. While the former have funnel-like conformational landscapes with a well-defined energy minimum, the latter have flatter conformational landscapes with numerous local energy minima, allowing IDPs to adopt a far wider spectrum of conformations- albeit less energetically stable ones ( Uversky, 2013 ). Ordered3 Increasingly, NMR is used in tandem with X-ray crystallography (see, e.g., Fenwick et al., 2014 ). b t a o p nd disordered proteins play different roles in the cell. While ome functions (e.g. enzyme catalysis, immunological recognition, olecular discrimination by receptors, etc.) require proteins to ave clearly-defined three-dimensional structures, other functions e.g. cell signalling and regulation) can be accomplished by unolded chains, sequence patterns, or isolated secondary structural otifs ( Wright and Dyson, 2015 ). From a structural perspective, IDPs pose an interesting chalenge. The old idea that a protein binds to its substrate because heir shapes match like a lock and a key seems totally inadequate. s Chouard (2011, p. 152) playfully remarks, "[y]ou might as well ry to open the door with cooked spaghetti". In the case of an DP, "the spaghetti uses the lock to mould itself into the shape f the key, rather than forming the key beforehand" (ibid.). IDPs nly acquire stable functional conformations when they bind to ppropriate targets. Some, however, remain disordered even after inding, such as the signalling protein Sic1, which stays unfolded pon binding to Cfc4 ( Mittag et al., 2010 ). IDPs thus disprove the entral dogma of structural biology, as they empirically demontrate that an ordered conformation is not, in fact, required for rotein function. It appears, moreover, that this lack of a definite tructure confers a considerable functional advantage on IDPs, as it nables them to interact with a broad range of binding partners including other proteins, membranes, nucleic acids, and various maller molecules) by adopting different configurations. Macroolecular aggregates containing IDPs also tend to display high derees of conformational ambiguity-a phenomenon which has been ermed 'fuzziness' ( Fuxreiter, 2012; Fuxreiter and Tompa, 2012 ). ere we are once again far away from how we think about strucure and its relation to function in a machine. Indeed, the more e learn about the structure of proteins in their native state, the arder it is to uphold the mechanicist notion that protein comlexes can be conceptualized, and effectively studied, as molecular achines. Turning now to specificity, it is also becoming apparent that arlier generations of molecular biologists grossly overestimated he specificity of proteins (cf. Kupiec, 2010 ). This is partially due o the fact that for most of the twentieth century, methodologcal limitations required proteins to be studied in isolation from he cellular milieu in which they are embedded. Undoubtedly, one f the great appeals of the molecular machine concept is that it ustifies ignoring this context, allowing researchers to focus their ttention on the structure of the mechanical device and the 'mechnism' of its operation. The problem is that, when it comes to unerstanding what happens in a cell, context is everything! What particular protein does-we no w kno w-is largely defined by he environment it finds itself in and the interactions it has with he molecules around it; trying to acquire a complete picture of ts behaviour while overlooking these factors is a futile exercise Barabási and Oltvai, 2004; Gierasch and Gershenson, 2009 ). I have already indicated that in the case of IDPs, function is etermined not by structure, but by context. This lesson can be eneralized to all proteins. Functional promiscuity seems to be the ule rather than the exception for proteins ( Nobeli et al., 2009 ). ven enzymes, which have traditionally been regarded as remarkbly specific catalysts, exhibit varying degrees of catalytic promisuity owing to the inherent conformational flexibility of their acive sites, among other factors ( Babtie et al., 2010; Khersonsky nd Tawfik, 2010 ). A rather extreme case is methane monooxygease, which can hydroxylate 150 substrates in addition to methane Copley, 2003 ). Not only are enzymes catalytically promiscuous, ut many of them also perform a range of non-catalytic funcions, such as cell motility, membrane trafficking, chaperoning, ctivation and inhibition of metabolic pathways, and chromatin rganization. This exciting discovery has come as such a surrise (given that it conflicts with the mechanicist expectation of D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 115 s ( e d i i p c i o f i p i a i n a s a ( d w w i fi m g a c c n s t t m S p l c u p t s o l o t f o s s t f p c q c n s S p s u w m fi k u s c r r t s t c p w c t d d i w t s e h t w fi a n d t s m fl i a d c T pecificity) that the phenomenon has been called 'moonlighting' Jeffery, 1999, 2003 ). A protein can have very different functions- ven if it does not undergo any post-translational modifications- epending on where it is located in the cell, on the cell type n which it is expressed, on the nature and number of proteins t binds to, and on the amount of ligand, substrate, cofactor, or roduct available to it. As the multifunctional (or moonlighting) apacities of proteins are not coded in their genomic sequences, t is very difficult to predict them. Indeed, it is likely that many f the proteins that we think we know quite well actually perorm additional functions that have not yet been experimentally dentified. It is also worth mentioning that large-scale studies of proteinrotein interactions have revealed that the typical number of nteractors for a given protein is far greater than was previously ssumed ( Cusick et al., 2005 ). This discovery becomes less surprisng when we remember that the interior of a cell is a highly dyamic environment: most proteins within it are rapidly moving bout, continuously interacting with ever-changing partners. Asociations among proteins tend to be stochastic and short-lived, nd are usually characterized by relatively low binding affinities Misteli, 2001b ). Clearly, the ambiguity, contingency, and contextependence of protein-protein interactions are hard to reconcile ith the exquisite specificity and tightly constrained operation that e would come to expect from a genuine molecular machine. Simlarly, the transient nature of protein associations conflicts with the xity and durability that we intuitively associate with the arrangeent of parts in a machine. Overall, the various findings I have discussed in this section rearding the structure and specificity of proteins (or lack thereof) re prompting a basic shift in how protein complexes are coneptualized. The potentially innumerable ways in which proteins an come together to form functional aggregates, the extraordiarily wide range of factors that can change their conformational tate, and the dynamic and ephemeral nature of these associaions has led some researchers to argue that many of the proein complexes found in the cell are better understood as pleoorphic ensembles than as molecular machines ( Mayer et al., 2009; uderman and Deeds, 2013; Falkenberg et al., 2013 ). Drawing esecially on studies of protein complexes involved in intracelluar signalling, these authors draw attention to the fact that these omplexes are extremely diverse in size and composition, and ndergo numerous reversible post-translational modifications (e.g. hosphorylations) in ways that drastically alter their conformaion and activity. Receptor complexes, adhesion complexes, mRNA plicing complexes, trafficking intermediates, and many other kinds f protein associations do not exist in the cell as clearly deineated, structurally stable assemblies of fixed and highly cordinated subunits exhibiting a discrete number of conformaions (in accordance with the molecular machine model), but as uzzy and transient ensembles-with half-lives in the order of secnds or less-composed of weakly interacting and ever-changing ubunits constantly flickering between alternative conformational tates. As Mayer et al. put it, after considering the vast range of potenial configurations that a single transmembrane receptor complex or platelet-derived growth factor (PDGF) can adopt, the activated receptor looks less like a machine and more like a pleiomorphic ensemble or probability cloud of an almost infinite number of possible states, each of which may differ in its biological activity. ( Mayer, 2009 , p. 81.2) Rejecting the molecular machine model has wide ranging imlications for how we study, represent, and explain protein assoiations and interactions. Importantly, it compels us to call intouestion the widespread appeal to wiring diagrams and design harts (akin to those found in mechanical and electronic engieering) in schematic representations of metabolic, regulatory, and ignalling pathways. An emblematic example is shown in Fig. 2 . uch engineering-based diagrams present compact summaries of rotein-protein interactions, and by deliberately imitating the deign of electronic circuit boards, they convey the impression of nderstanding and control. Visualizing cellular pathways in this ay gives us confidence and it emboldens us to speak optiistically about the current state of research in our particular elds. A good illustration of this last point can be found in a wellnown paper by Hanahan and Weinberg (20 0 0) , which made se of circuit-like representations of the cell to reflect on the tate of cancer biology and define its agenda for the twenty-first entury: Progress in dissecting signaling pathways has begun to lay out a circuitry that will likely mimic electronic integrated circuits in complexity and finesse, where transistors are replaced by proteins (e.g., kinases and phosphatases) and the electrons by phosphates and lipids. [...] Two decades from now, having fully charted the wiring diagrams of every cellular signaling pathway, it will be possible to lay out the complete 'integrated circuit of the cell' upon its current outline. We will then be able to apply the tools of mathematical modeling to explain how specific genetic lesions serve to reprogram this integrated circuit in each of the constituent cell types so as to manifest cancer. ( Hanahan and Weinberg, 20 0 0 , p. 59, 67) The problem with these engineering-based descriptions and epresentations is that they do not accurately reflect biological eality. For wiring diagrams such as Fig. 2 to be as useful as he wiring diagrams of electronic engineering, they need to asume a very high degree of specificity in the molecular interacions and chemical conversions that are depicted as links in the ircuits. And although this assumption of extreme specificity is erfectly consistent with the molecular machine model, it is not ell supported empirically, as I have shown in this section. Reent research strongly suggests that most protein-protein interacions are contingent and opportunistic, and do not reflect a preetermined (genetic) design. It is important to realize that wiring iagrams like Fig. 2 illustrate only one of the many-potentially nnumerable-ways in which a given set of proteins may interact ith one another in the cell depending on an eclectic range of facors and circumstances. Engineering-based representations of this ort are undoubtedly interesting to look at, but they are of limited xplanatory value. All things considered, such representations probably do more arm than good, as they wrongly imply that the proteins feaured in them reliably and predictably form the same exact netorks of interactions, which are envisaged (again, misleadingly) as xed, solid-state, molecular circuit boards. In doing so, these digrams prevent us from appreciating the vast spectrum of alterative interaction networks that the same set of proteins can and o form in different cells, and even in the same cell at different imes ( Kurakin, 2010; Talbott, 2013 ). Hence, when it is claimed, ay, that "[s]caffold proteins are analogous to circuit boards- odular platforms that wire together components and direct the ow of information-and can program complex signaling behavors" ( Good et al., 2011 , p. 682), one should take such assertions, nd the representations from which they derive, with a generous ose of scepticism. The main differences between the two conceptions of protein omplexes I have discussed in this section are summarized in able 2 . 116 D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 Fig. 2. Engineering-based wring diagram depicting the metabolic pathways included in the Kyoto Encyclopedia of Genes and Genomes (KEGG) database (see Kanehisa and Goto, 20 0 0 ). Each node in the circuit corresponds to a protein ( source: http://rest.kegg.jp/get/map01100/image ; reproduced with permission). Table 2 Key differences between the two conceptions of protein complexes. On the left, the standard view derived from the MCC. On the right, the alternative view suggested by recent research. Molecular machine Pleomorphic ensemble Hard and rigid subunits Soft and fluid subunits Fixed size and composition Variable size and composition Few conformational states Multiple conformational states Functional specificity Functional promiscuity Context-insensitive behaviour Context-sensitive behaviour Stable, predefined interactions Transient, opportunistic interactions Amenable to crystallization Not amenable to crystallization s c p l f i i m o c t t r e o s n t c a q m c 1 t m k f m n t 4. Intracellular Transport: Power-Stroke or Brownian Ratchet? In addition to grounding our theoretical understanding of the organization and constitution of the cell, the MCC has also influenced our view of the processes that take place inside it. To illustrate this, consider again the image of the cell as a highly intricate chemical factory-probably the most popular formulation of the MCC. The following extract from a recent textbook offers a typical articulation of this view: Cells act as chemical factories, taking in materials from the environment, processing them, and producing 'finished goods' to be used for the cell's own maintenance and for that of the larger organism of which they may be part. In a complex cell, materials are taken in through specialized receptors ('loading docks'), processed by chemical reactions governed by a central information system ('the front office'), carried around to various locations ('assembly lines') as the work progresses, and finally sent back via those same receptors into the larger organism. The cell is a highly organized, busy place, whose many different parts must work together to keep the whole functioning. ( Hazen and Trefil, 2009 , p. 252) Descriptions of this kind make clear that the cell must posess highly effective means of sorting, packaging, and transporting argo to different destinations. The efficient delivery of molecular roducts to their intended cellular location is known as intracelular transport , and it is of vital importance for the cell's normal unctioning-when it is disrupted, complications and pathologies nevitably ensue. Prima facie, the orderliness and efficacy that is magined in the targeted mobilization of essential cargo inside a iniature factory contrasts rather starkly with the physical reality f the cellular milieu. At the microscopic scale, all entities exhibit onstant stochastic movements as a consequence of thermal agitaion. This phenomenon, traditionally referred to as 'Brownian moion', causes molecules in solution to perform 'random walks' that esult in diffusion . Although diffusion is a passive process, it nevrtheless plays an indispensable role in the intracellular transport f small molecules, especially over short distances. For example, it erves as the primary basis for connectivity in signal transduction etworks. However, diffusion becomes inefficient in the transportaion of large vesicles and macromolecules. In such situations, the ell makes use of active and directional modes of transport, which re made possible by so-called 'motor proteins' that carry cargo uickly and efficiently across cytoskeletal tracks. The discovery of otor proteins has long been assumed to have provided empirial support for the MCC (see, e.g., Pollard, 1992; Urry, 1993; Block, 997 ). Motor proteins convert chemical energy-usually obtained by he hydrolysis of adenosine triphosphate (ATP)-into directional otion and the performance of work. There are many different inds of motor protein, each of which performs a distinct motile unction ( Schliwa, 2003 ). Those that utilize the cytoskeleton for ovement fall into two categories based on their binding parters: actin motors, such as myosin, move along microfilaments hrough interaction with actin, whereas microtubule motors, such D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 117 Fig. 3. Cropped snapshots of the acclaimed computer animation The Inner Life of the Cell , created by XVIVO for Harvard University's Department of Molecular and Cellular Biology. The four consecutive snapshots depict the cycle of orchestrated movements by which a cargo-carrying kinesin 'walks' along a microtubule. ( A ) ATP-binding to the motor domain of the left leg triggers a change in its conformation which generates a power-stroke in the linker region that throws the motor domain of the right leg overhead of the left leg. ( B ) The motor domain of the right leg re-attaches to the microtubule and the products of ATP hydrolysis are released. ( C ) Binding of ATP to the motor domain of the right leg in turn induces a rearrangement of its structure which generates a further power-stroke in the linker region that pushes the motor domain of the left leg above the right leg. ( D ) The motor domain of the left leg re-attaches to the microtubule and the products of ATP hydrolysis are again released, thus completing the cycle ( source: http://www.artofthecell.com/theinnerlifeofthecell ; © 2006 The President and Fellows of Harvard College). a t t t o c h t v X p V m o g e a f s w e p i s t h t W t i w c t m m h l p m f p c t p v fi t s f d c t s e e w r I l A i c e t a m c M o t p s 3 m m a t e f M a s kinesin and dynein, move along microtubules through interacion with tubulin. These proteins also differ in the type of cargo hey transport and in their direction of travel. In accordance with he MCC, motor proteins are conceptualized as miniature versions f macroscopic motors. They are often described as "tiny nanomahines [that] work in many ways just like an automobile on the ighway" ( Shi and Ha, 2011 , p. 4), as they consume fuel to power heir motion, and they move steadily in a directional manner at ariable speeds along 'molecular highways'. Structural studies by -ray crystallography have also been invoked to suggest that these roteins are reminiscent of large-scale machines ( Rayment, 1996; ale and Milligan, 20 0 0 ). But how do motor proteins actually ove? The orthodox approach to explaining the directional movement f motor proteins is to appeal to the mechanical principles that overn the motion of man-made motors. In an internal combustion ngine, for instance, the energy input (delivered by the ignition of combustible gas under pressure) is tightly coupled to the perormance of mechanical work, which manifests itself as a 'powertroke' that results in the movement of the piston. In the same ay, in motor-driven intracellular transport it is argued that the nergy input (delivered by the hydrolysis of a high-energy comound like ATP) induces a large-amplitude conformational change n the motor protein which generates a mechanical force-a powertroke-that drives the molecule forward relative to a polymeric rack. Appropriately, this is called the power-stroke model , and it as dominated our theoretical understanding of how motor proeins work for decades ( Cooke, 1986; Howard, 2001; Tyska and arshaw, 2002 ). Sometimes, the chemically-induced conformaional change in the motor protein that produces the power-stroke s compared to the mechanical release of a viscoelastic spring, hich thrusts the molecule forward (e.g. Howard, 2006 ). In the ase of kinesin, which forms dimeric 'legs' that alternatively attach o tubulin, the repetitive power-strokes result in a 'hand-over-hand' otion that makes the protein appear like it is 'walking' along the icrotubule ( Yildiz et al., 20 04; Asbury, 20 05 ). Fig. 3 illustrates ow the kinesin walk is commonly represented in the technical iterature, as well as in textbooks and other educational materials. Of course, animations such as the one shown in Fig. 3 conform erfectly to what we would expect to find if the cell was indeed a achine, as they portray motor proteins as tiny robotic bipeds perorming sequential cycles of precisely-coordinated, mechanically-owered movements along cytoskeletal tracks. However, upon loser inspection, it becomes apparent that these models of inracellular transport are fraught with problems. For a start, the lasticity, fluidity, and dynamicity that most proteins exhibit in ivo-which I discussed at length in the previous section-are difcult to reconcile with the rigidity, solidity, and stability that moor proteins would need to possess for them to move by powertroke mechanisms. Moreover, these models tend to overlook the act that proteins operate in an environment that is drastically ifferent from the macroscopic one in which we, and our mahines, exist. Motor proteins, like all other molecules, are subject o constant thermal and quantum fluctuations that make carefullyynchronized movements along a desired path challenging in the xtreme. In fact, the energy of ATP hydrolysis responsible for genrating the power-strokes that allegedly propel motor proteins forard is only about an order of magnitude larger than the envionmental stochastic forces that are permanently buffeting them. n such conditions, moving mechanically and deterministically is ike trying to 'swim in molasses' or 'walk in a hurricane' (see stumian, 2007 ). Besides these general worries, a number of surprising empircal findings-made possible by the use of novel methods-have alled into question the theoretical adequacy of power-stroke modls such as the one illustrated in Fig. 3 . For example, although he hand-over-hand mechanism that underlies the walking motion ttributed to kinesin is dependent on the protein's dimeric form, onomeric kinesin motors have been reported which are equally apable of directional movement ( Okada and Hirowaka, 1999 ). ore broadly, there is no obvious correlation between the amount f chemical energy a motor protein consumes and the distance it ravels. Single-molecule measurements of myosin-mediated transort have revealed that a single cycle of ATP hydrolysis can reult in displacements of wildly variable lengths, ranging from 5 to 0 nm ( Kitamura et al., 1999 ). Additional studies of myosin moveent indicate that the structural geometry of a protein's motor doain is not correlated with its step size ( Yu et al., 2012 ). These nd other recent findings suggest that the structure of motor proeins may not be as crucial for their operation as one might have xpected if these proteins were bona fide molecular machines perorming precisely-coordinated, mechanically-powered movements. otor proteins also lack the functional specificity that is typically ssociated with machines, as many of them have been found to be 118 D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 Fig. 4. Schematic representation of the Brownian ratchet model of intracellular transport. The motor protein attached to a cytoskeletal track is hypothesized to display two distinct potential energy landscapes depending on its conformational state. In the 'flip' conformation-( A ) and ( C ), white ball-the energy landscape is flat, so the motor protein slides freely along the track, buffeted by stochastic fluctuations. In the 'flop' conformation-( B ) and ( D ), grey ball-the energy landscape has a sawtooth shape, so the motor protein drifts to the closest energy minimum where it remains until it acquires the 'flip' conformation. By periodically switching between these two conformations upon repeated cycles of ATP hydrolysis, the motor protein is driven by thermal fluctuations to the right. (Figure adapted from Kurakin, 2006 ; reproduced with permission.) a z t a a w t w a a e c a i a i m b i g c ' t p p b h r e t d h p c c i l o t r i m S t t m p p p m d a 4 A ratchet is, of course, a machine, so it might seem odd-even contradictory-to criticize the invocation of mechanical principles in the explanation of intracellular transport and then propose an alternative explanation that explicitly refers to a mechanical device. But there is, in fact, no contradiction involved. The use of the term 'ratchet' in the Brownian ratchet model is merely intended to describe the spiky, non-sinusoidal shape of the energy profile of the motor protein when it adopts a 'flop' conformation (see Fig. 4 ). It does not imply or suggest that the protein structurally resembles a ratchet, or that it works mechanically like a ratchet. In fact, the operation of a Brownian ratchet is decidedly non -mechanical, as I will explain in the remainder of this section. involved in a number of additional, non-motor cellular functions ( Schliwa and Woehlke, 2003 ). In light of these problems, in the last few years a completely different account of motor-driven transport has started to receive widespread attention known as the Brownian ratchet model . Although it is almost as old as the power-stroke model, it has remained relatively unknown until fairly recently-presumably because it does not appeal to our mechanical intuitions in the way that the comfortingly familiar idea of a power-stroke does. The basic contention of the Brownian ratchet model is that the directional motion of a motor protein is primarily driven by stochastic fluctuations and rectified (or biased) by chemical reactions, such as the hydrolysis of ATP. Empirical studies have established that motor proteins use the energy of ATP hydrolysis to flip–flop between two alternative conformations. What the Brownian ratchet model postulates is that the 'flip' and 'flop' conformations of a motor protein are characterized by different potential energy landscapes, as shown in Fig. 4 . In the 'flip' conformation (A and C, white ball), the energy landscape has a flat shape. This means that the motor protein performs a random walk on its track as a result of thermal agitation, exhibiting equal probabilities of moving to the left or to the right of its initial position. In the 'flop' conformation (B and D, grey ball), the energy landscape has a jagged, saw-tooth shape. Consequently, random collisions jostle the motor protein overwhelmingly to the right, where it gets trapped in the nearest potential energy minimum trough. In this way, by stochastically switching between two distinct conformational states as a result of repeated cycles of ATP hydrolysis, the motor protein is able to harness the perturbations of Brownian motion to move in a specific directionlong a cytoskeletal track ( Astumian, 1997; Ait-Haddou and Herog, 2003; Kurakin, 2006 ) 4 . A fundamental difference between the power-stroke model and he Brownian ratchet model is that the former takes chemical rections (such as the hydrolysis of ATP) to be responsible for generting the mechanical forces that drive the motor protein forward, hile the latter assumes that chemical reactions serve to bias he existing Brownian motion in a particular direction. In other ords, a power stroke motor moves despite stochastic fluctuations; Brownian ratchet motor moves because of them. In this respect, very attractive feature of the Brownian ratchet model is that it xplicitly factors in the counterintuitive physical conditions of the ellular milieu in its explanation of how proteins move directionlly, instead of conveniently ignoring them or dismissing them as nconsequential. A further advantage of the Brownian ratchet model is that it is ble to make sense of experimental findings that appear perplexng from the perspective of the power-stroke model. The aforeentioned reports of monomeric motors, the lack of correlation etween the chemical energy used by the motor and the distance t travels, and the independence of step size from the structural eometry of the motor domain can all be straightforwardly acommodated within the Brownian ratchet model. In this model, structure' and 'specificity' do not play the same critical role in deermining how the protein moves as they do in the MCC-derived ower-stroke model. Once it is adopted, the discovery that motor roteins are also involved in other cellular processes ceases to be affling or surprising. Although the Brownian ratchet model is less intuitive and arder to initially grasp than the power-stroke model, it is in many espects the simpler model of the two. As there is no specific refrence to the topological or geometrical configuration of the moor protein (other than to its alternative energy profiles, which o have a structural basis), there is no need to speculate about ow its various structural domains interact with one another in a erfectly synchronized fashion to generate motion. Similarly, beause there is no crucial mechanical step-no power-stroke-that an be identified as the specific moment at which chemical energy s transformed into work, it becomes unnecessary to invoke 'vioent kicks' ( Liphardt, 2012 ), 'judo throws' ( Vale and Milligan, 20 0 0 ), r any other anthropomorphic actions to explain how motor proeins move directionally. But perhaps the greatest theoretical virtue of the Brownian atchet model is that it elegantly demonstrates how stochasticty can be put to good use in the cell. Whereas the power-stroke odel considers motor-driven transport to be an example of what chrödinger (1944) called the 'order-from-order' principle, given hat the complexity of the mechanism it postulates is assumed o derive from a pre-existing genetic design, the Brownian ratchet odel regards it instead as an instance of the 'order-from-disorder' rinciple, which Schrödinger claimed (incorrectly, as it turns out) lays no role in biology. This is because it shows how the couling of two random (or disordered) processes-namely Brownian otion and the binding of ATP-can result in a non-random (or orered) outcome: directional movement. In this way, by providing non-deterministic, design-free conceptualization of intracellular D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 119 t o 1 n t ( i u m t m o t e r t m W t p t e s f i o t w p t n i c a i t d t t i 2 t m l M a t t e c i m T t t w w t i t a w s i Table 3 Key differences between the two conceptions of motor-driven intracellular transport. On the left, the standard view derived from the MCC. On the right, the alternative view suggested by recent research. Power-stroke Brownian ratchet Continuous forward movement Discontinuous forward movement Energy input generates motion Energy input rectifies motion Overpowers stochastic fluctuations Harnesses stochastic fluctuations Motor structure plays critical role Motor structure is secondary Coordinated motor movements No coordinated motor movements Includes crucial mechanical step Lacks crucial mechanical step 'Order-from-order' mechanism 'Order-from-disorder' mechanism t o h a a n G i i o c p t s t d s 5 c n a fl t m m r w b t t b d t b i ransport, the Brownian ratchet model strikingly illustrates how rder can be generated out of chaos (cf. Prigogine and Stengers, 984; Hoffmann, 2012 ). It is undeniable that the growing use of single-molecule techology in experimental studies of motor proteins has greatly conributed to raising the profile of the Brownian ratchet model Yanagida et al., 2007; Karagiannis et al., 2014 ). However, there s still no consensus as to whether motor-driven transport is best nderstood in terms of the increasingly popular Brownian ratchet odel or the more traditional power-stroke model. Advocates of he former maintain that power-strokes are irrelevant in deterining the directionality, stepping force, and optimal efficiency f motor proteins ( Astumian, 2015 ), while supporters of the later insist that motor proteins would not be as fast and powrful as we know them to be if they operated by a Brownian atchet mechanism ( Wagoner and Dill, 2016 ). Some claim that the wo models sit at opposite ends of a continuum within which ost motor proteins actually operate. For example, Oster and ang (2003, p. 208) assert that "[t]here are only a few moors that can be regarded as being pure power stroke motors or ure ratchets; most protein motors employ a combination of the wo strategies". If this is true, then the two models are not necssarily mutually exclusive. At present it is not yet possible to ettle this theoretical dispute. The two models, we should not orget, constitute different attempts to interpret the same empircal data; they are extrapolations from experimental studies-no ne has actually seen a kinesin literally walking along a microubule, as portrayed in Fig. 3 . Nevertheless, what can be asserted ith a reasonable degree of certainty is that the engineering-based ower-stroke model, at least when conceptualized in analogy with he power-stroke mechanism of an internal combustion engine, if ot irretrievably flawed, at best offers only an extremely idealzed interpretation of motor-driven transport as it occurs in the ell. Still, even if the Brownian ratchet model becomes unanimously ccepted as the preferred explanation of how motor proteins work, t could be argued that recognizing that the cell contains real moors is already one concession too many to the MCC. This, however, oes not follow. 'Molecular motors'-if that is how one is to refer o motor proteins-are not miniature versions of macroscopic moors. In fact, they differ from macroscopic motors in almost every mportant respect (cf. Astumian, 2001; Linke et al., 2005; Wang, 008 ). For one thing, they lack rotors, armatures, and all the other rappings of conventional motors. They are made of soft, flexible aterials which exhibit high degrees of freedom, unlike the hard evers, cranks, and hooks that make up most mechanical devices. oreover, due to their minuscule size, the influence of gravity nd inertia on their operation is insignificant compared to that of he raging 'Brownian storm' that permanently engulfs them. This urbulence, combined with the high viscous drag of their fluid nvironment, makes the long-range transmission of precise mehanical forces physically impossible. In addition, as I have already ndicated, whereas in man-made motors energy is used to drive otion, in molecular motors energy is used to restrain motion. he former move directionally by overcoming stochastic perturbaions; the latter do so by exploiting them. A further difference is hat molecular motors convert chemical energy directly into work ithout using heat or electrical energy as intermediates, which is hy their efficiency is much higher than that of macroscopic moors. Overall, because of all of these crucial differences, although t may seem tempting to draw analogies between molecular moors and macroscopic ones, we should keep firmly in mind that "in nswering fundamental questions regarding problems associated ith friction, wear, transmission, efficiency, fuel, motion and work, uch facile comparisons often serve to cloud rather than simplify ssues" ( Browne and Feringa, 2006 , p. 26). Ultimately, the issue boils down to how we choose to define he term 'motor'. We tend to assume that motors constitute a class f machine-hence the objection I have just considered. But peraps we should reverse this relation and consider machines to be class of motor. After all, a motor can be defined very generally s an entity that imparts motion (in fact, this is the first defiition of 'motor' that is listed in the Oxford English Dictionary ). iven that machines are not the only entities capable of impartng motion, it follows that not all motors are machines. As I noted n the introduction, the word 'machine' tends to carry a number f additional connotations, such as a pre-existing design, a tightly onstrained operation, and a deterministic outcome. It is therefore ossible to conclude that motor proteins are indeed genuine moors, even though they are not machines. It is interesting to oberve that some authors are starting to display an awareness of his important distinction, as the following passage suggests: Because they operate inside a cell, [molecular motors] are tiny and operate on a physical scale that makes them very different from the manmade, macroscopic objects we normally imagine when we hear the word 'machine'. Further, their size and soft structure allows them to be much more dynamic and robust than artificial machines. They work needing very little input, as energy levels not far from average thermal energy are sufficient for a given task. This property too contrasts with artificial machines, which work much more rapidly, accurately, and deterministically, but with higher energy demands and less adaptability. ( Karagiannis et al., 2014 , p. 3318) The main differences between the two conceptions of motorriven intracellular transport I have discussed in this section are ummarized in Table 3 . . Cellular Behaviour: Deterministic or Probabilistic? So far, I have shown how the MCC has provided the theoretial foundation for our traditional understanding of the cell's interal architecture, of the macromolecular complexes that compose it, nd of the transport processes that take place within it. But its inuence does not end there. The MCC has also shaped the way we hink about how the cell behaves, as I will argue in this section. What a cell does is largely determined by its internal akeup. This makeup is constituted by a complex network of etabolic, regulatory, and signalling pathways that-as I have aleady discussed-are often misleadingly conceptualized in analogy ith electronic circuit boards. These pathways, when prompted y internal or external cues, generate specific behavioural outputs hat allow the cell to perform its various functions and respond o changes in its environment. As these pathways have a genetic asis, the behavioural outputs they specify are themselves depenent on how and when the pertinent genes become activated and ranscribed in the cell. Consequently, in order to understand the asis of cellular behaviour, it is necessary to consider how the allmportant process of gene expression is initiated. 120 D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 a a a i c t g d 2 b t ( s o p j f n o h t n c r s t p n c o m o a e o ' c e g c r c u p p t s b t e s t a t b e s ( v g n h t Basically, an intracellular or extracellular signal-an 'inducer'- triggers a cascade of biochemical reactions that causes proteins called 'activators' (which are a class of transcription factor) to bind to specific sites in the DNA known as 'enhancers'. Upon binding, the activators interact with other proteins that recruit RNA polymerase and its associated transcription factors, collectively referred to as the 'preinitiation complex', to the 'promoter' region of the target gene, where it begins the process of transcription. Thousands of transcription factors have been identified in the past few decades, as have the enhancer and promoter regions of countless genes. But despite this wealth of information, there has been considerable debate regarding the precise way in which transcription is regulated and modulated. It has long been known from numerous experimental studies that when cells are treated with varying intensities of an inducer and the gene product-mRNA or protein-corresponding to a specific gene is assayed, the level of gene product changes in a smooth, dose-dependent manner. Specifically, a gradual increase in the concentration of the inducer usually results in a proportional increase in the expression of the gene. In order to make sense of this observation, it was generally assumed that cells adjust the rate of expression of a responsive gene progressively and linearly from zero to its maximum output in direct proportion to a rising concentration of an inducer. This came to be known as the graded model of gene expression (it is sometimes alternatively referred to as the 'rate', 'analogue', or 'rheostat' model), and it remained the dominant view of gene expression until the end of the last century ( Ross et al., 1994; Rossi et al., 20 0 0; Pirone and Elston, 2004 ). It is a model that clearly exemplifies the MCC, as it construes the modulation of gene expression as a continuous, linear, mechanical process, "akin to depressing the accelerator on a car" ( Hume, 20 0 0 , p. 2323). It is also a thoroughly deterministic model, as it suggests that gene expression, and by implication most cellular behaviour, can be anticipated, computed, and predicted-in principle, at least-from knowledge of the 'initial conditions' (such as the concentration of the inducer). It therefore fits well with the classic mechanicist idea that the cell is endowed with a genetic program, analogous to a computer program, which controls and reliably executes its operations in a predetermined way ( Jacob, 1973; Bray, 2009 ; Nicholson, 2014 ). When considering this model, it is important to bear in mind that until recently, gene expression-and cellular behaviour more generally-could only be studied by looking at large populations of cells. If one uses conventional molecular biology techniques such as Northern blots, microarrays, and reverse transcriptasepolymerase chain reaction, the only way to gather together enough gene product to reach a detectable threshold is to grind up vast numbers of isogenic (i.e. genetically identical) cells grown under the same conditions and then measure the amounts of the relevant mRNA or protein in the homogenate. What this means is that, although the goal is to understand the behaviour of an individual cell, one proceeds by studying the behaviour of a population of cells. The consequence of doing so is that the specific behavioural patterns of individual cells are averaged out across the entire population, and this can mask differences between members of the population. In the past, this methodological limitation was not considered a problem because "molecular biologists habitually assume uniformity of the cell populations that serve as starting material for experimental analysis" ( Huang, 2009 , p. 3853). If all cells are presumed to be identical and one is therefore dealing with a homogeneous population, then one can confidently infer that the average behaviour of the population as a whole accurately reflects the individual behaviour of each cell in that population. Notice that this assumption-like so much else I have discussed in this paper-is grounded in the MCC: just as cars manufactured in anssembly line according to the same model design will behave lmost identically, cells endowed with the same genetic program nd grown in the same conditions are expected to behave almost dentically. The situation has changed radically in recent years. Technologial advances in the experimental use of fluorescent reporter proeins and the development of new microscopy techniques have ranted us unprecedented access to the real-time dynamics of inividual molecules in single cells ( van Holde, 1999; Deniz et al., 008 ). As we have begun to monitor biological processes on a celly-cell and molecule-by-molecule basis, it has become apparent hat there exists "a hidden world beneath population averages" Altschuler and Wu, 2010 , p. 559). Being able to precisely meaure the distribution of cellular behaviours across a population, as pposed to merely relying on the average behaviour of the whole opulation, has unexpectedly revealed that even isogenic cells subect to the same environmental conditions behave quite differently rom one another. There is no such thing as a perfectly homogeeous population of cells. All cell populations exhibit some degree f heterogeneity . Gene expression offers perhaps the clearest illustration of this eterogeneity. Single-cell studies strongly suggest that increasing he concentration of an inducer in an isogenic population does ot lead to a gradual increase in the rate of transcription in every ell in the population (as hypothesized by the graded model), but ather results in the recruitment of a rising number of cells that repond in an all-or-nothing fashion once their particular activation hresholds have been reached. In other words, in each cell of the opulation the target gene is either maximally expressed, or it is ot expressed at all, and the probability of its expression in every ell rises as the concentration of the inducer increases. In addition, nce a cell begins to express the gene, the rate of its expression reains largely unaffected by further increases in the concentration f the inducer. With regards to each of the genes it contains, a cell ppears to exist in one of two meta-stable functional states: it is ither 'on' or 'off'. This is generally known as the stochastic model f gene expression (it is also referred to as the 'binary', 'digital', or threshold' model), and it has become very widely accepted in reent years ( Walters et al., 1995; McAdams and Arkin, 1997; Elowitz t al., 2002 ). In direct contrast to the deterministic character of the raded model, the stochastic model is inherently probabilistic . Each ell in the population exhibits a specific and distinct probability to espond to a given concentration of inducer, and this probability an vary widely-even among members of the same isogenic poplation. According to the stochastic model, the regulation of gene exression is accomplished by modifying the probability that the reinitiation complex will come together successfully and bind to he promoter of the target gene. Activators and enhancers are preumed to act by increasing the likelihood that the promoter will e transcriptionally active at a given moment, but do not affect he rate of mRNA production once transcription has begun ( Fiering t al., 20 0 0; Blake et al., 20 03 ). The random switching of the trancriptional apparatus between active and inactive states is deemed o generate short and sharp 'bursts' or 'pulses' of transcriptional ctivity, which result in corresponding bursts of translational acivity. The hypothesis that proteins are synthesized in bursts has een subsequently verified by single-molecule experiments ( Cai t al., 2006; Yu et al., 2006 ). Bursting behaviour in gene expresion has been reported not only in bacteria, but also in yeast Zenklusen et al., 2008 ), mammalian cells ( Raj et al., 2006 ), and deeloping embryos ( Paré et al., 2009 ). Even different nuclei in a sinle multinucleated syncytium such as a muscle fibre, which share ot only a common environment but also a common cytoplasm, ave been found to display disparate bursts of transcriptional acivity ( Newlands et al., 1998 ). D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 121 Fig. 5. Graded versus stochastic models of gene expression. Raising the concentration of an inducer results in a proportional increase in the expression of the relevant gene in an isogenic population of cells. If gene expression is measured by assaying the total amount of mRNA or protein produced by the population, it is not possible to distinguish between stochastic and graded transcriptional responses, as both are consistent with population-level observations. Single-molecule methods, however, have recently enabled gene expression to be studied on a cell-by-cell basis, and this has revealed that most cells exhibit an all-or-nothing stochastic expression pattern. (Figure adapted from Kringstein et al., 1998 ; © 1998 National Academy of Sciences.) m t s i d b t c e b t e t i t o c i r m c i i g s c p s s t o i s a a o p c u t e c g c r d i r t d t c s e c a ( i fi t s o t h h A i c p ' t t c n Given all this evidence in support of the stochastic model, it ay seem difficult to understand why the graded model remained he orthodox view for as long as it did. But the answer is quite traightforward. When the only way to measure gene expression n a cell was to assay the total amount of mRNA or protein prouced by an entire population of cells, it was simply not possile to discriminate between the two competing models. Indeed, he aforementioned observation that progressively raising the conentration of an inducer results in a proportional increase in the xpression of the corresponding gene is perfectly consistent with oth models, as Fig. 5 shows. The level of gene expression in he population as a whole could reflect similar levels of gene xpression in all cells (as postulated by the graded model), or he statistical mean of different subsets of cells either expressng or not expressing the gene (as postulated by the stochasic model). It was not until single-molecule methods were develped that it became possible to examine gene expression on a ell-by-cell basis, and thereby distinguish the two models expermentally ( Kringstein et al., 1998; Pirone and Elston, 2004; Kuakin, 2005 ). The study of gene expression illustrates rather draatically how being forced to average out data across a biologial population due to methodological limitations can lead to critcal losses of information pertaining to the phenomenon under nvestigation. Intriguingly, it has been suggested that the distinction between raded and stochastic models of gene expression "is conceptually imilar to the difference between Newtonian and quantum mehanics, and it offers similar intellectual challenges" ( Hume, 20 0 0 , . 2324). This theoretical comparison is not as far-fetched as it may eem. The stochastic model regards cellular response patterns as tate transitions, which are rather reminiscent of thermal or quanum phase transitions. Moreover, the precise timing and frequency f the switching between active and inactive transcriptional states s impossible to predict, as it is not a mechanical process but a tochastic one. In the absence of deterministic certainties, genes in population cannot be considered to be either active or inactive at ny given instant. Instead, they can only be attributed a probability f being active in a particular cell at a particular time, even if this robability can sometimes be very close to 0 or 1. The variable flickering of transcriptional activity in different ells is one of the major causes of heterogeneity in isogenic poplations. But where exactly does this cell-to-cell variability in ranscriptional activity come from? The answer becomes apparnt when we remember that gene expression is a molecular proess, and like all molecular processes, it is inherently stochastic, iven that it takes place in an environment that is subject to the haotic dynamics of Brownian motion. Each step in the process elies on fortuitous encounters between molecules that are ranomly moving about as a consequence of thermal agitation. Evdently, these molecules must be at the right place and at the ight time-not to mention in the right vibrational state-for them o be able to participate in the appropriate reactions. The unpreictability of the whole process is further amplified by the fact hat the participating molecules in each step are present in the ell in very low copy-numbers, as this decreases the chances of uccessful interactions between them. DNA is the most extreme xample, since there are usually only one or two copies in a ell at any given time, but mRNA and most regulatory proteins nd enzymes are present in remarkably small numbers as well Xie et al., 2008 ). Other contributing factors to cell-to-cell variabilty in gene expression include variations in the topological conguration of the nuclear architecture ( Cremer et al., 2006 ), and he uneven partitioning of cytoplasmic contents during cell diviion ( Huh and Paulsson, 2011 ). Of course, gene expression is only ne of many cellular processes that, due to the inherent stochasicity of the molecular interactions that underpin them, generate eterogeneous responses in isogenic populations. From a theoretical perspective, the discovery of non-genetic eterogeneity in isogenic cell populations came as a huge surprise. t first, molecular biologists struggled to make sense of it, as it s a difficult phenomenon to accommodate within the mechaniist interpretive framework of the MCC. After all, as Kurakin (2005, . 60) vividly puts it, "[n]o computers, no aircrafts, no automobiles, isogenic' as they are built, acquire spontaneously personality of heir own and respond in a probabilistic manner to environmenal cues by all-or-none functional and/or structural transitions". Beause it conflicts with the deterministic assumptions of the MCC, on-genetic heterogeneity was initially viewed with suspicion, as 122 D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 Table 4 Key differences between the two conceptions of cellular behaviour. On the left, the standard view derived from the MCC. On the right, the alternative view suggested by recent research. Deterministic Probabilistic Individually predictable Collectively predictable Graded response patterns Stochastic response patterns Subject to linear dynamics Subject to nonlinear dynamics Produces homogeneous populations Produces heterogeneous populations Population averages are accurate Population averages are misleading Noise is a nuisance that is tolerated Noise is an asset that is exploited Every isogenic cell is the same Every isogenic cell is unique a w c o i c fi s i c l T 6 u o m c w a p c i i e a p c 5 Note that this conclusion does not imply that every entity or process within the cell is being (or needs to be) reconceptualized. To be clear, the thesis I have sought to defend is not that all organelles exist as irreversible steady states, that every protein complex is a pleomorphic ensemble, and so on. It is rather that a a consequence of 'rogue' cell behaviour resulting from so-called 'illegitimate transcription' ( Chelly et al., 1989 ). But as instances of heterogeneity became more widely reported, researchers could no longer afford to dismiss them. As a result, an engineering term began to be used to designate this phenomenon in order to render it theoretically compatible with the MCC. This is the concept of noise , which has since become widely adopted by the community as whole (e.g. Elowitz et al., 2002; Rao et al., 2002; Raser and O'Shea, 2005 ). It is worth reflecting for a moment on the consequences of the biological appropriation of this concept. In engineering contexts, noise refers to an unwanted random disturbance that hampers the perception of a transmitted signal. Noise is therefore regarded as a nuisance which engineers strive to overcome by designing machines that avoid or filter out its detrimental effects. Interestingly, when stochastic cell-to-cell variability began to be referred to as noise in the literature, those very same negative connotations from engineering became associated with this phenomenon. Accordingly, it was claimed that biological "[n]oise is often harmful, as it garbles cell signals, corrupts circadian clocks, and disrupts the fine-tuned process of development" ( Ozbudak et al., 2002 , p. 71). Similarly, it was frequently assumed that "[c]ell signalling pathways and developmental switches have evolved so as to minimize the disruptive effect of such fluctuations" (ibid.). Note that these negative assessments of the effects of stochasticity make perfect sense from the theoretical perspective of the MCC. Stochasticity is perceived to thwart the capacity of biologists to totally control cellular behaviour in the exact same way that noise thwarts the capacity of engineers to design perfectly efficient and predictable machines. More recently, however, there has been a noticeable shift in how biologists speak about noise. Discussions about how cells tolerate noise are gradually giving way to discussions about how cells exploit noise (see, e.g., Huang, 2009; Eldar and Elowitz, 2010; Balázsi et al., 2011 ). The reason for this is that as research into the non-genetic heterogeneity of cells continues, evidence for the biological importance of this phenomenon is mounting ever-rapidly. We now know that non-genetic heterogeneity plays key roles in both microbial and eukaryotic cells, in embryonic development, and in evolution. For one thing, it is a crucial generator of phenotypic diversity, which enables cell populations to adapt rapidly to changing environmental conditions. It does so by permitting the implementation of probabilistic diversification strategies within a population, such as bet-hedging and divisions of labour, which can confer considerable fitness advantages. It also influences cell fate decisions, which facilitates the regulation of differentiation during development. Non-genetic heterogeneity has even been suggested to allow tumours to counteract the effects of chemotherapy, thereby limiting the efficacy of target-selective drugs ( Brock et al., 2009 ). In general, it is clear that highly heterogeneous cell populations are more robust and they adapt, grow, and evolve faster than more homogeneous cell populations. Far from being a nuisance, 'noise', it turns out, is central to many cellular functions. One very important theoretical implication of the probabilistic nature of cellular behaviour and the observed heterogeneity of cell populations is that, quite literally, every cell (in an organism and elsewhere) is a unique entity. No two cells are identical, given that no two cells respond to a stimulus in the exact same way-even if they are genetically the same. As this simple yet profound observation becomes more widely recognized, cell individuality is likely to become an ever-more important area of research. Our traditional dependence on methods that average out responses across populations has inadvertently driven us to rely on what Levsky and Singer (2003) fittingly call the 'average cell': a statistical contrivance for representing biological knowledge beyond the limits of detection. But as these authors point out, the advent of single-molecule methods has demonstrated that theverage cell is a myth. Variability is everywhere in the cellular orld. In fact, as a cellular phenomenon, variability is less diffiult to explain than similarity. Looking to the future, as cell biolgy progressively morphs into 'single-cell biology' and we devote ncreasing attention to carefully characterizing not just individual ells, but also individual molecules in individual cells, we may soon nd ourselves in the position of having to reconsider our undertanding of even the most basic biological processes. The following excerpt, co-authored by one of the leading figures n the field, effectively summarizes the two very different views of ellular behaviour that I have examined: As biologists, we must grapple with, and reconcile, two very different views of cellular behaviour. On the one hand, we frequently think of cellular functions as being determined by 'circuits' of interacting genes and proteins. In a loosely analogous way to electronic circuits, these chemical circuits encode genetic programmes that underlie differentiation, the cell cycle and other behaviours. They accurately respond to stimuli and generate precise behavioural programmes in individual cells. On the other hand, there is the 'noisy' view of the cell we get when we actually look at cells : they exist in squishy, dynamic and heterogeneous populations, the morphologies, geneexpression patterns and differentiated states of which differ from one another, even when environment and genotype are fixed. ( Locke and Elowitz, 2009 , p. 383; emphasis added) The main differences between the two conceptions of celluar behaviour I have discussed in this section are summarized in able 4 . . Conclusions: Towards a New View of the Cell I have argued in this paper that molecular biology is currently ndergoing a fundamental shift in its theoretical conceptualization f the cell. The conventional mechanical, reductionistic, and deterinistic view is gradually giving way to an understanding of the ell that emphasizes its fluidity, plasticity, and stochasticity. Faced ith the formidable task of interpreting the vast and ever-growing mount of experimental data that continues to get published, exlanatory appeals to engineering notions of design, programs, and ircuits are increasingly being replaced by recourses to the physcal principles of non-equilibrium thermodynamics and complexty theory. Cells are empirically revealing themselves to be inherntly dynamic, self-organizing systems that respond stochastically nd nonlinearly to environmental stimuli. The inescapable conclusion that follows from the analysis I have resented is that the cell can no longer be unproblematically coneptualized as a machine 5 . Over the course of the paper, it has D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 123 b o t l i o c s c fi f s i o t k t i b t i a f t p a u t g c p t t m c c f m n p r r w i r p i w p t i c t 1 t v t d a c c t p l h fi t ( t e s t w t i g e 1 i y w p m o t f o m t m p p t i t d u t e m e y f s m c o i ecome apparent that cells lack all four characteristic properties f machines that were identified in the introduction. First, once he crucial role that self-organization plays in shaping the celular architecture is acknowledged, it is difficult to uphold the dea that the spatiotemporal arrangement of the parts of a cell beys a predetermined blueprint or design, as it does in a mahine. Second, the conformational flexibility of most cellular contituents and the functional promiscuity they exhibit shows that a ell's operation is not as tightly constrained by its structural conguration as it is in a machine. Third, whereas a machine perorms its function by precisely following a predefined sequence of teps, a cell can arrive at a particular end in a variety of ways: t can recruit different kinds of molecules to the same function- r the same kind of molecule to different functions-depending on he conditions it finds itself in. And fourth, a cell cannot be broen down into parts without jeopardizing its structural integrity in he way that every machine can. Cellular components form deeply ntertwined, ever-changing networks of interactions that cannot e individually dissected without sacrificing the organization of he whole. "Cells are not engineered systems of discrete, interactng computational components, naturally yielding to compositional nalysis" ( Melham, 2013 , p. 134), which is why they cannot be ully explained reductionistically; and neither do they operate deerministically, which is why their behaviour cannot be perfectly redicted. Monod was wrong. The cell is not a machine, but something ltogether different-something more interesting yet also more nruly. It is a bounded, self-maintaining, steady-state organizaion of interconnected and interdependent processes; an interated, dynamically stable, multi-scale system of conjugated fluxes ollectively displaced from thermodynamic equilibrium. Given its recarious nature, the cell is constantly having to negotiate a rade-off between structural stability and functional flexibility: oo much rigidity compromises physiological adaptability, and too uch promiscuity compromises metabolic efficiency. The cell acomplishes this by continuously turning over and reorganizing its onstituents into different macromolecular complexes with diverse unctional capabilities, which assemble and disassemble in order to eet the ever-changing demands of the environment. The permaent stochastic shuffling of molecules inside the cell and their oportunistic associations to form transient functional ensembles in esponse to intracellular and extracellular cues provides fast and obust solutions to the adaptive problems faced by the cell in a ay that strikes an optimal balance between efficacy and plasticty ( Misteli, 2001b; Kurakin, 2009 ). Although this view of the cell has only come to the fore very ecently, it is rather surprising to find that the theoretical princiles that underlie it, as well as the empirical findings that support t, are not new at all. General denunciations of the MCC go back ell over a century (e.g. Haldane, 1884 ), and even the recent emirical discoveries in each of the four domains I have examined in his paper have unmistakeable historical precedents. For instance, n the first half of the twentieth century it was not unusual for biohemists to describe the cell and its ostensibly solid and rigid conents in terms of streams, fluxes, and other processes (see Gilbert, 982; Nicholson, 2018 ). A particularly visionary characterization of he dynamicity of the cellular architecture was offered by Berta-ery large number of cellular and molecular phenomena that were traditionally inerpreted in terms that support the MCC are now being explained in terms that irectly oppose it. It is also worth mentioning that the various MCC-derived charcterizations and their alternatives I have considered (and which I summarized for ontrastive purposes in the tables included at the end of each section) may in some ases represent idealizations: two opposite extremes of a spectrum of actual posiions . I already hinted that this might be the case for the ongoing dispute between ower-stroke and Brownian ratchet models of intracellular transport. w w h s t t s fi i anffy, who was one of the first theoretical biologists (though today e is better known as the founder of general systems theory): Formations such as the nuclear spindle, the Golgi apparatus, and the like appear as structures when we have them before us in a fixed and stained microscopic preparation. However, if we consider them in their changes in time, they are a manifestation of processes at the chemical and colloidal levels, quasistationary states that last for a while but soon undergo changes or disappear. ( Bertalanffy, 1952 , p. 136) Challenges to the undue emphasis on the structure and specicity of proteins are likewise nothing new. The first reports of proeins with disordered structural domains date back to the 1950s Karush, 1950; Jirgensons, 1958 ), and some hypotheses regarding he substrate ambiguity and catalytic promiscuity of metabolic nzymes are over forty years old ( Jensen, 1976 ). Similarly, the uggestion that a microscopic ratchet might be able to harness he energy of Brownian motion to generate directed movement as carefully explored by Feynman in his physics lectures more han half a century ago ( Feynman et al., 1963 ). Moreover, expermental evidence for the stochastic nature of cellular behaviour oes back six decades ( Novick and Weiner, 1957 ), and the hetrogeneity of isogenic cell populations was already noticed in the 970s ( Spudich and Koshland, 1976 ). Nevertheless, all of these deas and observations remained severely neglected for many ears. Only in the last two decades have they begun to receive idespread attention-mostly because the adoption of novel exerimental methods has served to empirically substantiate them, aking them impossible to ignore. But what is perhaps most surprising of all is that even though ne would be hard-pressed to find a molecular biologist today hat would dispute the fact that the cell is an open system far rom equilibrium, or that because of its microscopic size the effects f stochastic fluctuations on its operation cannot be overlooked, any continue to explain cellular and molecular phenomena in he terms of classical mechanics, equilibrium thermodynamics, and echanical and electronic engineering-that is to say, in terms of rinciples and concepts that are fundamentally at odds with the hysical nature of the cell. This curious refusal of many researchers o accept, or even seriously consider, the new view of the cell that s arising is likely to be due to several factors. One might be that he new view is less intuitive than the MCC. The MCC, after all, raws on our everyday familiarity with machines. It is almost 'natral' for us to interpret everything in mechanical or engineering erms because such interpretations accord well with our experince of the familiar macroscopic physical world that we (and our achines) inhabit. Consequently, confronted with a microscopic ntity such as a cell, "[t]he challenge for researchers is to look beond our usual engineering principles and to appreciate the less amiliar logic of biological organization." ( Glick, 2007 , p. 132). Another factor that may help account for the reluctance of ome researchers to endorse the new view is that it appears to ake the cell a harder object to study than the MCC. Viewing the ell as a machine allows us to think of its organization in terms f modular, solid-state circuits that can be approached reductionstically, and it also gives us the confidence to expect that when e eventually work out how all of the cell's parts fit together, we ill be able to completely predict its behaviour. If, on the other and, we view the cell as a highly integrated, self-organizing, fluid ystem composed of densely interconnected processes ever-subject o stochastic fluctuations, we no longer have reasons to suppose hat achieving such epistemic goals is even possible, let alone feaible. The stark contrast between these two outlooks is exemplied by their strikingly different ways of understanding causation n the cell ( Bizzarri et al., 2019 ), and it serves to explain why some 124 D.J. Nicholson / Journal of Theoretical Biology 477 (2019) 108–126 A A A A A A B B B B B B B B B C C C C C C C C C C D D D D D E E F F F researchers find it easier than others to obtain funding and publish their work. As Mayer et al. point out: It is much easier to write and publish a paper suggesting Protein X is necessary for transmitting a signal from A to B, than one showing that Protein X is one of many potential components of a heterogeneous ensemble of signaling complexes that together couple A to B. ( Mayer et al., 2009 , p. 81.6) A further factor could be that accepting the new view of the cell requires us to adopt, and maybe also develop, concepts that fall outside the remit of the conventional molecular biology toolbox. It requires us-among other things-to seriously consider how the ideas of non-equilibrium thermodynamics and complexity theory, and even those of condensed matter physics and quantum mechanics, may be brought to bear on the interpretation and explanation of the phenomena we investigate, and this might not be agreeable to all researchers, many of whom appear to show little appetite for theoretical considerations-or, worse still, assume that they can proceed in the absence of theory altogether. Despite all of this, the advantages of embracing the new view of the cell are legion. Most importantly, the new view gives us a systematic and internally consistent interpretive framework capable of making theoretical sense of a multitude of empirical findings that appear paradoxical and almost inexplicable when viewed through the traditional lens of the MCC. Reports of self-organizing organelles, liquid-like macromolecular assemblies, fuzzy signalling complexes, moonlighting proteins, non-mechanical motors, orderfrom-disorder processes, non-genetic heterogeneity, and cell individuality seem totally baffling from the perspective of the MCC, but they can all be perfectly accommodated within the interpretive framework that is currently emerging. Findings which are confusing and unexpected within the old view become natural and expected within the new one. Ultimately, the current practice of overlooking some of the principles that govern the internal operation of the cell because they are unfamiliar, and of dismissing many of the cell's distinctive properties because they are difficult to study, is likely to be a mistake. Only by confronting these head on can we hope one day to arrive at a theoretically satisfying understanding of what the cell is and how it functions as an integrated unit. Acknowledgements This paper has been a very long time in the making, and I am grateful for the feedback and encouragement I have received from many biological and philosophical colleagues over the course of its slow gestation. The ideas it presents have also benefitted from the valuable input provided by audiences at All Souls' College, Oxford, the Cohn Institute for the History and Philosophy of Science and Ideas in Tel Aviv, the European School of Molecular Medicine in Milan, the Marine Biological Laboratory in Woods Hole, the École Normale Supérieure in Paris, and the MRC Laboratory for Molecular Cell Biology in London. This work was financially supported by a Senior Research Fellowship at the Konrad Lorenz Institute for Evolution and Cognition Research and by the European Research Council under the European Union's Seventh Framework Program (FP7/2007-2013)/ERC grant agreement no. 324186 . References Ait-Haddou, R. , Herzog, W. , 2003. Brownian ratchet models of molecular motors. 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