one of the fundamental achievements that established neuroscience as a viable and distinct discipline was the development of the _ neuron doctrine _ , which states that neurons are anatomically distinct cells that serve as the basic computational units in the brain . in truth , this was not the original statement of the doctrine , which was originally more concerned with the discrete versus continuous character of the brain s neural network , but this is how it is generally regarded in its present form .still , it is a concept that continues to evolve .  folded into the current interpretation of the neuron doctrine is what i will call the _ spike doctrine _ , which is something so firmly ingrained in current neuroscientific theory that one often finds some version of it on or near the first page of any text on the subject . a rather poetic statement of this doctrine is given by rieke , _ et al . , who write :  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ [ our ] perception of the world is constructed out of the raw data sent to our brains by our sensory nerves , and in each case these data come in the same standard form as sequences of identical voltage pulses called action potentials or `` spikes . '' spike sequences are the language for which the brain is listening , the language the brain uses for its internal musings , and the language it speaks as it talks to the outside world ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  a somewhat more prosaic treatment comes from gerstner and kistler , who write :  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ we think of a neuron primarily as a dynamic element that emits output pulses whenever the excitation exceeds some threshold .the resulting sequence of pulses or `` spikes '' contains all the information that is transmitted from one neuron to the next ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  a second part of the doctrine concerns the assumptions that are made regarding _ how _these spikes encode information about the world . again , from gerstner and kistler :  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ since all spikes of a given neuron look alike , the form of the action potential does not carry any information . rather , it is the number and the timing of spikes which matter ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  they go on to summarize the doctrine quite explicitly : `` the action potential is the elementary unit of signal transmission . ''almost without exception , every theoretical effort to consider cognition and information processing in the brain is built upon this doctrine .it is the aim of this paper to examine this long - held belief in neuroscience and , ultimately , to begin building a case for overturning it .with the proper equipment , it would not take one long to determine that something peculiar is going on inside the brain .indeed , the brain is the exemplar structure of the body electric . although one does find steady electrical signals issuing from the heart , the brain is unique in its level of galvanic chatter .it is perhaps no wonder that the prevailing belief is that crackling inside this tangle of electrical activity is the very language of thought .in addition to seeming very special and _ brain - like _ , this electrical activity also has the advantage of being relatively easy to measure , at least at a coarse level .monitoring the activity of an _ individual _ cell is much more difficult , however .it currently requires getting into the skull and placing an electrode in or near the cell of interest , a procedure typically reserved for certain surgical patients and hapless laboratory animals .  that neurons produce any measurable electrical activity at all seems a minor miracle in itself .neurons do not use electricity the same way a household appliance does .rather , neurons regulate the flow and concentration of charged ions on either side of their cell membranes .the difference in charge between the inside of the cell and the outside is known as a _ membrane potential _ , and a spike is a rapid shift in this potential that propagates down the length of the nerve .the arrival of a spike at the end of the neuron triggers the release of stored chemical _neurotransmitters_.  the most immediate effect these chemicals have is to open gated ion channels on the postsynaptic neuron , thereby changing its membrane potential . causing the influx of positive ions increases the cell s chance of firing a spike ( in which case the responsible neurotransmitteris called _ excitatory _ ) , and causing the influx of negative ions decreases it ( in which case the transmitter is called _ inhibitory _ ) . in short , by releasing neurotransmitters , one cell can influence whether the cells it is signaling fire spikes of their own .this easy - to - state relationship , highly influenced by the early work of mcculloch and pitts , is at the core of artificial neural network ( ann ) research , much of the theory for which can be summarized in the single equation here the `` state '' of neuron is determined by applying some ( often nonlinear ) function to the collected states , of the neurons connected to it multiplied by the `` strength '' of those connections , represented by the _ weight _term the term describes the _ threshold _ for the neuron  . would be an input , to some other neuron unless it was the member of the network s _ output layer_. ] an example of a general network although not an ann is shown in figure 1 .image generated from code found in . ]  in some models , the state of the neuron may simply be 1 or 0 , which could be considered to correspond to whether it is firing or not .the state can also be a firing _rate _ or even a membrane potential . a considerable portion of ann research , which we will refer to by the more general term _ connectionism _ , does not concern itself too much with biological realism , so the `` neuron '' states do not have to correspond to anything an actual cell has to deal with . even in these cases ,though , some of the biological language is preserved .so , if a neuron is considered to be inhibitory , its connection weight to postsynaptic cells will generally be negative ; it will be positive in the excitatory case .artificial neural networks are interesting objects , and they can be `` trained '' to perform a variety of important tasks , from pattern recognition and classification to function approximation .further , it has been shown that certain finite neural networks in fact , neural networks with less than one - millionth the number of neurons in the human brain can simulate a universal turing machine .in essence , this means that such a network given enough time can compute anything that _ can _ be computed .other research has suggested enormous computational potential for spiking neural network models .artificial neural networks `` learn '' to perform certain functions through a training regimen whose purpose is to alter the values of the synaptic weights , until the inputs to the network produce outputs that are as close as possible to _ target _ outputs .this is one example of many where an ann deviates from biological realism , since a _ real _neural network can not be expected to have access to whatever the `` target '' outputs are supposed to be .even so , the basic principle of learning for an ann seems to apply in the brain ._ synaptic plasticity _ , a molecularly and genetically mediated process that adjusts the strength of connections between neurons ,is thought to be the chief component behind learning and memory .current theory states that spikes pulsing through the nerve network in the brain represent and convey information , and the adjustment of the connections between nerves gives rise to memory , learning , problem solving , and everything else that makes us intelligent .the manner in which this information is represented by spike sequences is often referred to as the _neural code_. there is considerable debate as to the exact form of this code , especially with regard to whether the precise _ timing _ of individual spikes or the average _ rate _ of spikes carries the necessary information .temporal coding , rate coding , and population coding ( which takes into account the collective activity of multiple neurons ) are the prevailing theories for how information is encoded in the brain . indeed , if information is conveyed by _ spikes _ , then the neural code _ must _ be described by at least one of these methods .but , as there is at least some evidence to support each of these methods , deciding among them is difficult .it is worth pointing out that rate and population coding have enjoyed considerable success , particularly in vision research and the study of perception and action .for instance , the `` preferences '' of individual neurons for highly specific visual features seem to be indicated by their firing rate , and calculations using the concerted activity of a small population of neurons in a monkey s motor cortex can predict its arm movements with high accuracy .  researchers who believe that spike sequences encode information in the brain have a fair amount of encouraging evidence on their side . as we have covered earlier , neural spikingis mediated by various neuroactive chemicals . clearly , then, if the information is encoded in action potentials , then it must be the case that these chemicals function in the _ service _ of the spikes .we will soon examine the possibility that it is the other way around .most experiments that investigate the neural code do so by monitoring the response of a certain cell to a controlled stimulus . let us say that over some interval of time , we make a note of the times at which the cell fires a spike . we can denote this sequence by this gives us information not only about the precise timing of each spike but also about the average firing rate , which we can obtain by counting all the elements in the sequence and dividing by the amount of time we were monitoring the cell .scientists looking for the neural code would like to identify , ] which describes the probability of a certain _ stimulus _ given the spike train .these probabilities are related by a classic result known as bayes s theorem , which takes the form = \frac{p [ \ { t_i \ } | s(t ) ] p[s(t)]}{p [ \ { t_i \}]}. \label{bayes}\ ] ] this result states that the probability of a particular stimulus _ given _ a specific observation ( the spike train , ) is proportional to the probability of the observation given the stimulus which makes intuitive sense but it is controlled by the ratio of the probability of the stimulus , , ]  now , while a neuron may conceivably know what its own response history is , which would allow it to evaluate the response probability , where does its knowledge of the _ stimulus _ probability come from ? the implication is that even if one has complete knowledge of the scheme for _ encoding _ , anything short of an _ exact _ prescription for this encoding results in uncertainty when _ decoding _ , that is , when interpreting an observation .much current theory seeks to address this uncertainty .the vast majority of neural network models assume that when a neuron fires , the message that it has fired is sent faithfully .this is not the same as saying that some models do not assume there to be _ noise _ in the system .the difference is that the noise in those models is phrased in terms of random nerve activity that does not encode anything meaningful .but there is another form of `` noise '' in real neural systems that may prove more troublesome .  before we develop this point , however , let us return to the connectionist paradigm for a moment .a neuron s spiking pattern is influenced_caused _ , we might say by the spiking patterns of `` upstream '' neurons that connect to it based on how strong those connections are . with this in mind , another way of writing equation is = \frac{p [ s(t ) , \{ t_i \ } ] } { \sum_{\mathbf{x}(t ) } p [ \ { t_i \}| \mathbf{x}(t ) ] p[\mathbf{x}(t ) ] } , \label{prob_2}\ ] ] where is a time - varying vector that collects all the spike sequences of the upstream neurons .it looks considerably different from the expression in equation , especially since it now invokes the joint probability , ] the output of the upstream neurons , is _ itself _ uncertain .this turns out to be the case .although there is some evidence to suggest that changes in one neuron s membrane potential can have _ direct _ influence on a neighboring neuron s potential , this can not be employed as a general method for neural signaling .after all , neurons routinely communicate with other neurons far outside the influence of the extraordinarily weak electric and magnetic fields that they generate . the only way for one neuron to know that another neuron has fired is to receive a chemical signal from it .neurons do not reliably release neurotransmitter with each spike . not only does the transmitter release probability vary widely _ among _ neurons , this probability is also variable for _ each _ neuron and can change over time .one estimate is that , on average , synapses have a transmitter release probability of about 30 percent .if we replace the upstream spiking record , with the firing indications that our neuron actually _ receives _ , then equation becomes = \frac{p [ s(t ) , \ { t_i \ } ] } { \sum_{\mathbf{x}(t ) } \sum_{\mathbf{\xi}(t ) } p [ \ { t_i \}| \mathbf{x}(t ) ] p[\mathbf{x}(t)|\mathbf{\xi}(t ) ] p[\mathbf{\xi}(t ) ] } , \label{prob_3}\ ] ] which introduces a tremendous amount of additional uncertainty ( and effort ) into the problem . indeed , establishing the new term ,$ ] which can be interpreted as a complete description of the release probabilities of all cells in a neural circuit , is itself a task almost on par with the difficulty of the original signal - interpretation problem stated in equation .the variability in transmitter release would seem to force us to discard _ temporal _ coding as a viable general method for representing information in the brain . and ,although _ rate _ coding remains a possibility since each input neuron s average observed spiking rate would be scaled by its transmitter - release probability it would seem to require that each neuron have a complete and up - to - date account of the release probabilities for the synapses it shares with upstream neurons .our neuron s signal - identification problem has become fraught with ambiguity .we have already discussed one role of neurotransmitters in signaling among cells , namely the manner in which they influence the downstream firing of action potentials .neurotransmitters lie within a broader class of neuroactive chemicals that include chemicals known as _neuromodulators _ , which , as the name implies , modulate a cell s response to other chemical signals .neuromodulators include neuropeptides , which are chains of amino acids ; certain gasses dissolved in the intercellular medium , such as nitric oxide ; and some products of fatty - acid metabolism .  for a chemical to be classified as a neurotransmitter, it must satisfy certain criteria :  1 .it must be manufactured by the neuron and released into the synapse in response to an action potential .2 .  it must induce effects on the postsynaptic cell , mediated by transmitter - specific receptors .there must be a mechanism for inactivating or removing the substance from the synapse after release .4 .  experimental application of the substance to nervous tissue must produce effects similar to those induced by the naturally occurring transmitter .we are familiar with some of the effects described in the second point , as we know that some neurotransmitters are excitatory ( the most common of which is glutamate ) and some are inhibitory ( the most common of which is -amino butyric acid , or gaba ) . the receptors for these chemicals control gates that regulate ion flow , and such receptors are collectively called _there is a second class of receptors , however , known as _ metabotropic_ receptors .once triggered , these receptors initiate complex chemical cascades that generate additional signals _ within _ the neuron .the ultimate recipient of these intracellular signals is the neural genome , as genes are selectively expressed via transcription factors assembled and activated in response to the cascade .   like almost all cells in the body ,every neuron has a complete copy of the genome in its nucleus . and , also like other cells ,only a small fraction of the genes within each neuron s copy of the genome are expressed at any time .it is well known that during development , cells differentiate by expressing a specific subset of genes , regulated by a chemical process that is not completely understood .one pattern of gene expression leads a young cell toward a fate of bone , for instance , while another pattern leads to brain .as gene expression controls not only certain housekeeping duties of the cell but also the _ products _ it makes , we would expect neurons that manufacture , say , dopamine to show a different pattern of gene expression than a neuron that manufactures acetylcholine .this is indeed true , but the differences among neural gene - expression patterns do not end there .selective gene expression does not stop after development , after all .perhaps the most interesting example in neurons is known as the _ immediate - early gene _ ( ieg ) response .this is a specific pattern of gene expression in the neural genome in response to a stimulus , a reaction so specific as to have been referred to as the `` genomic action potential '' in the literature .much recent work has demonstrated this effect in the zebra finch in response to the vocalizations of its fellow finches .further , this genomic response ceases once the vocalization becomes familiar .a number of theories suggest that this response is necessary for memory consolidation of specific events , but it has also been proposed that the response instead improves the efficiency of memory formation by altering the cell s state to better encode transient , but similar , experiences into long - term memory .  it is known that gene expression and subsequent protein synthesis play a role in memory formation , and inhibiting protein synthesis has been shown to greatly interfere with learning .one could interpret the role of protein synthesis in memory formation from a strict connectionist viewpoint and insist that it be in the service of the _ long - term potentiation _( ltp ) , or strengthening , of excitatory synapses namely , adjusting the `` weights '' among interacting cells .this strict interpretation is challenged , however , by the finding that inhibiting ltp at -methyl - d - aspartate ( nmda ) receptors for glutamate does not prevent experimental animals from learning certain tasks .as is often the case in biology , the reality appears to be far more complex .particularly interesting is the way in which the ieg response appears to be independent of spike activity .for instance , as reviewed in , we find the following phenomena in zebra finches : songs that have become habituated by repitition cease to induce a gene response , but this cessation of the gene response occurs _ despite _ continuing spike activity induced by the stimulus .songs of heterospecific and conspecific birds induce similar spiking behavior in the caudomedial neostriatum , but heterospecific songs induce the ieg only _ half as effectively_. and singing induces considerable gene activation in a song - control nucleus in the basal ganglia , but those cells firing rates show _ little to no increase _ during singing .  here , then , we have distinct cellular responses to stimuli that are _ not_ distinguished by their spiking behavior .it is not at all clear how a strict connectionist viewpoint could account for these phenomena .imagine that you are given a printout of a neural spike train and are asked to identify the stimulus that provoked it . what might your answer be ?if you are a cognitive neuroscientist , you may try to get some additional information out of your interlocutor .if you learn , for instance , that the cell is in the occipital lobe , then you can be fairly sure that the stimulus was a _visual _ signal of some sort .but `` a visual signal '' is unlikely to be a winning response in this game , so you still need to know more . if you learn that the cell is from area v1 , then you know a bit more , but still not enough to unequivocally identify the specific feature of the stimulus that the cell is responding to .  cognitive neuroscience researchis concerned with identifying the neural correlates of behavior , perception , action , emotion , and cognition in general .much of that research involves locating specific parts of the brain that appear to be involved in producing or influencing these phenomena .this research has shown consistently that certain parts of the brain are specialized for dealing with certain types of information .it has also been shown that the activity of individual cells can be highly preferential , responding strongly to very specific types of stimuli and hardly at all to others .could identifying a stimulus from a spike train be made possible by identifying the cell that produced the spikes ?could we identify a single cell in the human brain in a game of 20 questions ? if we are restricted to_ yes_-or-_no _questions , then we can not .it would take , on average , such questions to identify an individual cell among the 100 billion in the human brain .  what is the point of considering such a game ?recall from section 3.2 that experimental research into the neural code often takes the form of monitoring a cell s response to a given stimulus . from the discussion that followed , we know that during an experiment , we researchers have more information than the cell does , since we know the stimulus the cell is tasked with identifying .but we also know something else , namely the specific _ location _ of the cell being monitored .this may seem to be a trivial point , but we must keep in mind that the additional context we would need for trying to make sense out of a spike train should also be required by a _ neuron _ trying to make sense of a spike train .after all , although a neuron s activity can be highly variable , it is limited to a relatively narrow range , almost never exceeding 1000 hz ( spikes per second ) but usually topping out at about 400 hz .as harvey writes :  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the origin and targets of nerve fibers establish information and meaning because signals are similar in all nerve cells .that is , meaning has to do with the particular neural group , while frequency coding conveys information about the stimulus intensity . __ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  in other words , even if spikes do encode crucial information , neurons should need to know what neurons are _ sending _ them in order to properly interpret the incoming signals .the question becomes how one neuron might tell other neurons apart .the brain is a three - pound biochemical laboratory . to date , well over 100 neuroactive chemicals have been identified , and the list continues to grow .neurochemicals are often found in well - defined circuits in the brain , such that detecting a certain chemical in a signal gives you considerable information as to the part of the brain from which the signal originated .we could imagine , then , that the presence or absence of a certain chemical in a signal could be interpreted as the answer to a _ yes_-or-_no _ question . as we saw above , it would take about 37 such questions to specify a single cell among 100 billion , meaning that the brain would require the selective , combinatorial expression of 37 neuroactive chemicals in neurons if it wished to chemically encode signal provenance .clearly , with over 100 neurochemicals and counting , _ specificity _ regarding neural signals is a problem the brain need not face.  anatomical location may not be the main variable of interest to the brain .but it is clear that the brain possesses a _ chemical _ means for providing additional information or context for a signal .since the chemical `` messages '' associated with this additional information would undoubtedly outnumber the distinct types of neurochemicals in the brain , we would expect to see individual cells express _ multiple _transmitters if specific information is to be encoded chemically .indeed , this is the case .not only is it true that neurons express multiple transmitters , but they also do so in highly specific patterns .cotransmission of neurochemicals is now known to be `` the rule rather than the exception '' , but the physiological purpose of such cotransmission is not understood and is currently regarded as an open question .for an example of how chemical context is provided in neural signals , consider replacing the cholinergic neurons in the spinal cord with dopaminergic cells .a moment s thought should convince the reader that the behavioral differences would be obvious , even if the spiking of the impostor cells were experimentally manipulated to exhibit the _ same _ spiking behavior of the original cells .although this example is a thought experiment , _ actual _ transplantation of neurons from one brain region to another has produced astounding results .in one study , serotonergic cells from the mesencephalic raph nucleus expressed substance p after transplantation to the hippocampus and striatum , but this effect was not seen upon transplantation to the spinal cord .it is apparent that a specific region of the brain can be indicated by a chemical signature , one that is so influential as to impose itself on foreign cells when they are introduced .but the brain is not a device running a fixed program .if specific information is actually encoded by the chemical signature of neural signals , then it should be necessary that a neuron s transmitter phenotype be allowed to change over time .this is also true , and it has been shown that neurotransmitter phenotypes are highly plastic and can change in response to activity or environmental signals .chemical signaling is an ancient technique , and it is still employed as the sole means of communication by our distant , nerveless cousins .interestingly , `` neurotransmitters '' such as epinephrine , norepinephrine , and serotonin are contained in sponges , in which there is nary a neuron to be found .these putatively subordinate chemicals actually evolutionarily _ predate _ the cells they are assumed to serve !chemical signaling in the cell is a complex process often referred to as _ signal transduction_. the interactions in these transduction networks have the appearance of complex `` neural '' networks , so the question of their computational potential is a natural one .indeed , recent opinion has advocated the investigation of the contribution of these chemical networks to neural computation .specific studies have indicated that neural biochemical networks are capable of decoding complex temporal patterns of input .the kinetics of chemical reactions has also been shown to enjoy the same turing universality demonstrated for certain neural networks .further , it is becoming evident that microrna plays an important role in these complex intracellular chemical - genetic networks .this is particularly remarkable , since microrna is produced from _ noncoding _ dna , which makes up well over 90 percent of the human genome but was once regarded as `` junk '' .although the computational complexity of the individual neuron is being increasingly appreciated by researchers , it remains unorthodox to suggest a role for biochemical and genetic components in cognitive computation in a manner that challenges the spike doctrine .that is , the prevailing view still assumes the basic unit of information signaling to be the action potential , in whose service the chemical and genetic components are still assumed to function . : `` neural - network computational models typically treat neuronal processing as an electrical phenomenon in which the firing of one neuron affects the firing of all neurons connected to it by excitatory and inhibitory links . the role of neurotransmitters and other molecules _ in determining this electrical activity _ is rarely discussed '' . on the other hand , a recent example of the rare , `` unorthodox '' view i promote is due to emanuel diamant , who discusses the inadequacy of spike trains as the sole means of information transfer , favoring a biochemical alphabet instead . ]it is only the expanding repertoire of this servile function that appears to be appreciated .it has never been claimed in the neuroscience literature that neuroactive chemicals are unimportant or meaningless .but we are beginning to get some indication of the deeper role they may play in the representation of information in the brain indeed , a _central _ role .earlier we considered the function of neuroactive chemicals as being in the service of spikes . sohow might it be the other way around ?if we believe that information is represented in the brain by patterns of neural electrical activity , then we must also consider the implications of that belief .namely , we should convince ourselves that the evolutionary advent of the nerve and the action potential coincided with the abandonment of _ specific _ informational roles for biological molecules , molecules that had served a symbolic , informational purpose in our preneural ancestors .we should also ask why the action - potential paradigm , which clearly must be rich enough to deliver all the complexity of consciousness , is not used exclusively throughout the body as a means of information transfer .the fact is that while all cells in the body communicate chemically and , indeed , also possess the genetic instructions and therefore the potential for electrical communication only the cells that require fast communication outside of their immediate physical neighborhoods employ the action potential .this suggests that the action potential is simply a means for _ delivering _ the message and an expensive one at that  but not the message itself .why , then , do studies of spiking seem to provide so much information ?the answer may come from an example drawn from current events .many news reports in the years since september 11 , 2001 , have reported on `` chatter '' among cells of terrorists , with the suggestion being that the dynamics of this chatter indicates something about the threat posed by these cells .this is , of course , information that is completely independent of the _ content _ of that chatter .the messages , in other words , are unknown ; we simply know that more or fewer are being sent. such may also be the case with the very different but even more mysterious cells that we have been discussing in this paper .what does a neuron _ know _ ? as we have discussed earlier , neural responses to stimuli can be very specific .some neurons respond preferentially to faces , and some respond preferentially to _ specific _ faces . but does this mean that there is a neuron in my brain whose job it is to `` know , '' say , halle berry ?strict connectionists argue against this interpretation . instead , they claim , neurons that seem highly specific toward a stimulus only exhibit this specificity within the context of their networks .progressively higher - level features are extracted at each layer of processing as information about a stimulus percolates through the network .if we take a neuron from an ann and look under the hood , we see only the machinery described in equation . in thisregard , all neurons in such a network are essentially alike and only give the suggestion of meaning by their activity within the complete network .in short , the connectionist story goes , an _ isolated _neuron knows nothing .  [cols="^ " , ]   if membrane potential is the variable of interest in cognitive information exchange , then it should be held to one of the standards that candidate neurotransmitters are : namely , the cell should not really care where the voltage changes are coming from ; it should only care that they are there .consider the two identical networks shown at the top of figure 2 .one is a clone of the other , and we will imagine that every last molecular detail is the same in network i ( ) as in network ii ( ). clearly , as these networks are identical , their responses to the same stimuli will be identical . if we consider the single neuron at the top of the network to be the _ output _, then we can write \implies [ \mathcal o(n_{\text{i } } ) = \mathcal o(n_{\text{ii } } ) ] , \label{logic_1}\ ] ] which simply states symbolically what we have already said .namely , if the information , spread over the network is the same , then the output , will be the same also .now let us perform surgery on the second network by removing the connections leading _ into _ the leftmost neuron in the second layer , which we will call we will make up for this insult , though , by connecting this neuron to its corresponding neuron , in the intact _ first _ network and allow it to copy its membrane potential dynamics .this arrangement is shown at the bottom of figure 2 .if we now present the same stimuli to both networks , it is clear that the purple neuron in network ii should have identical firing behavior to its counterpart in network i. after all , we have set it up that way by `` voltage linking '' the two networks .if the spike doctrine is correct , then all of the information in network i is also present in network ii , since anything that was eliminated by the surgery is being imported into the network via our connecting device .even connection - strength changes , such as one would see in long - term potentiation or depression , only serve to affect the firing behavior and are therefore also accommodated for in this arrangement .we have covered earlier ( section 5.2 ) that a neuron s transmitter phenotype can change over time in response to environmental signals .this process , however , is mediated by intracellular chemical signal transduction and gene expression , processes that are essentially independent of the membrane voltage .if the signal we are feeding the networks produces a shift in transmitter phenotype in then even with an exchange of voltage information , will not show the same shift in transmitter phenotype .since the _ chemical _ output from these corresponding cells no longer matches , there are at least some cases in which measured at the output neuron .returning to the relation in expression , we write its _ contrapositive _ , which is true whenever expression is true , \implies [ \mathcal i(n_{\text{i } } ) \neq \mathcal i(n_{\text{ii } } ) ] , \ ] ] and we must conclude that in the cases where the outputs do not match which is a certainty in at least some cases involving a shift in transmitter phenotype the information distributed over the network is not equivalent . the only difference between the networks is chemical , so the specific _ chemistry _ must account for the missing information .this result holds irrespective of the method for evaluating the `` output '' of the network .that is , one measure could be differences in firing patterns , while another could be the presence or absence of an ieg response within the cell . in this case , however , since we are concerned with evaluating the spike doctrine , we will only look at the spiking behavior of the neuron .unless the outputs of the two networks are _ identical _ in every way in every case , then it must be said that the voltage information can not encode the stimulus but that the chemistry can . andsince we can be confident that changing the chemistry will change the firing behavior of downstream neurons , then we know the output will _ not _ be identical . regardless of whether this network is supposed to respond to halle berry or the song of a zebra finch , it is clear that changing the chemistry changes the information distributed over the network .notice that earlier i said that the information would be different in _ some _ cases instead of making the stronger claim that it would differ in _ all _ cases .that is because we must allow for the case in which a stimulus is such that _ stability _ within the cell is maintained .that is , some stimuli could conceivably be passed along without changing the cell s transmitter phenotype or gene - expression patterns . in such stable cases , one _would _ obtain all the necessary information from observing the spike train , assuming that the _ current state _ of the cell were known .it is the position of this paper that a certain `` electrical chauvinism '' pervades modern cognitive science , an assumption that may have us looking in the wrong place in our search for _ information _ in the brain . if the main claim of this paper is correct , then it is the chemistry of the brain , and not the spiking of neurons , that defines the elementary units of information relevant to cognition .it would hardly mean , however , that connectionism is dead .  rather , the cognitive and computational sciences should look forward to an era of _ superconnectionism _ , in which each node of a turing - universal neural network contains _ another _ turing - universal network a massively interacting chemical - genetic one with vastly different properties and dynamics .although this does make the _ modeling _ landscape considerably more complex , it redefines the problem in a way that allows us to reconsider the variables of computational importance in the cognitive system , variables whose very nature could have profound theoretical implications for the capabilities of the human brain .  despite the appearance of additional complexity, there is an elegant _ simplicity _ inherent in the brain s modern application of a chemical alphabet whose first words were spelled out in primordial pools billions of years ago . to be sure , modeling this molecular language poses a significant challenge .but if the language the brain speaks _ is _ a chemical one indeed , one having many dialects then it is a challenge we must accept .koppell , n. , and ermentrout , b. ( 2004 ) .`` chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks . ''_ proceedings of the national academy of sciences , 101(43 ) _ , 1548215487 .martindale , d. ( 2005 ) .`` one face , one neuron : storing halle berry in a single brain cell . '' _ scientific american , 293(4)_. mcculloch , w.s . , and pitts , w. ( 1943 ) .`` a logical calculus of the ideas immanent in nervous activity . '' _ bulletin of mathematical biophysics , 5 _ , 115133 .

Abstract: in this paper , i examine what i refer to as the _ spike doctrine _ , which is the generally held belief in neuroscience that information in the brain is encoded by sequences of neural action potentials . i present the argument that specific neurochemicals , and _ not _ spikes , are the elementary units of information in the brain . i outline several predictions that arise from this interpretation , relate them to results in the current research literature , and show how they address some open questions .


evolution is one of the most fundamental principles in biology . while organismal genotypes are becoming accessible due to rapid advances in sequencing technology , further understanding of the complicated mapping from sequence to phenotypeis necessary for a richer understanding of evolutionary dynamics .while the terms genotype and phenotype can be flexibly assigned in a biological system , genotypes are generally defined as the genetic material upon which mutations act and phenotypes capture the properties of the organism on which selection can differentiate . as such , the mapping from genotype to phenotype the _ gp map _ links mutations to potentially selectable variation , and is therefore of critical importance in understanding evolutionary systems .gp maps also provide a basis for understanding important biological concepts such as mutational robustness and evolvability , which may profoundly affect evolutionary dynamics , and help determine the fundamental topologies of the landscapes upon which evolutionary processes occur .in general it is intractable to directly model the details of even small parts of a whole organismal gp map , due to both the very large numbers of genotypes , and a lack of knowledge of all possible phenotypes .advances have been made in recent years , however , with the use of simplified models .three particular systems have been modelled with notable success .firstly , genetic regulatory networks have been approximated using a variety of abstract models , including boolean networks . despite their simplicity ,boolean networks have demonstrated a remarkable ability to produce biologically realistic results .for example , they have been shown to reproduce key aspects of the yeast cell cycle . secondly , rna secondary structure can be routinely and accurately predicted via a host of different methods , as a result of which it has become one of the best - known gp maps , particularly for the study of evolutionary dynamics .finally , the complex problem of a protein folding into well defined tertiary structure has been investigated using various models including the highly simplified hp lattice model , where folds are represented as self - avoiding walks on a lattice , and the full sequence is reduced to binary alphabet ( h stands for hydrophobic and p for polar amino acids ) . despite its heavily coarse - grained nature , this model has produced important biological insights and has been shown to accurately model known features of protein tertiary structure . while these models have been successful for specific biological examples , another very important advantage of their tractability is the potential for extracting more general underlying principles of gp maps , building on our understanding of how evolution shapes the natural world .    in this paperwe extend this family of coarse - grained models for biological structure , exploring a very recently introduced model for tile self - assembly which can be viewed as a highly coarse - grained gp map for protein quaternary structure ( protein complexes ) . understanding the formation of protein complexes is important as demonstrated by the fact that most proteins form complexes in the cell ( around in yeast ) andthe function of these complexes is often strongly linked to their physical form .protein complexes are formed by the interaction of multiple individual protein chains to form larger structures .the interaction between two chains is predominantly mediated by hydrophobic forces acting to pack together non - polar amino acids to provide fewer energetically unfavourable interactions with water .invaluable resources for the study of protein complexes are the protein data bank , providing a database containing experimentally known protein quaternary structures , and the 3d complex database categorising pdb structures with a graph representation of the interactions between different subunits and a characterisation of the symmetry in a complex .the relationship between the topology of a protein complex and the individual amino acids that make up its protein chains is highly complex due to the multiple functionality encoded in the protein sequence .for example , correct tertiary structure , folding pathways and other inter - protein interactions are all potential requirements for a single protein chain . given these complexities , a direct and complete gp map of protein quaternary structure is intractable as including all required functionality would be unfeasible . instead ,in the spirit of the highly simplified hp model for protein tertiary structure , we represent the proteins as square tiles on a lattice . interactions between tiles model the protein - protein interactions that lead to self - assembly . in the model ,a genotype is a sequence of characters describing interactions on the edges of the tiles , which , when combined with a self - assembly process on a 2d square lattice , leads to the formation of phenotypes comprising of different square tile building blocks conjoined along interacting edges .these square tile structures are known as polyominoes and thus , we refer to the model as the polyomino model and the resulting gp map as the polyomino gp map .they are closely related to a wider class of lattice tiling models that have a long and important history in mathematics and computer science ( which we discuss further in section [ section : model ] ) .  despite these great simplifications , and in analogy with the highly schematic hp model , rna secondary structure models or boolean network models of grns, we expect the polyomino model to provide insight into the general structure of the full gp map for the formation of protein complexes from folded proteins .in fact , our earlier work has already discussed the evolutionary dynamics of the polyomino model , demonstrating that it can be used to rationalise the preference of dihedral over cyclic symmetries in homomeric protein tetramers .  in fig .[ comparisons ] , we compare coarse - grained representations for rna secondary structure , protein tertiary structure and protein complexes . on the left hand side ,the biological representation is shown and on the right , a given model representation . through this figurewe wish to highlight two points .firstly , that each of the model systems is a dramatically simplified version of the corresponding biological system and that the polyomino model is of a similar order of coarse - graining to previous models . andsecondly , that the polyomino model can provide a concise representation of real protein complexes by capturing features such as the symmetry of the subunit arrangements ( c in this case ) .in contrast to rna secondary structure or protein tertiary structure , where structure forms through the folding of a connected string of individual entities ( nucleotides or amino acids ) , protein complexes are built by joining separate individual entities ( protein chains ) .furthermore , while for string - like self - assembly the final structure size is constrained , proteins can form unbounded structures that can be ordered or disordered . in our work here , we focus on the subset of deterministic , finite sized structures to model protein quaternary structure .but , in principle , the polyomino model can also capture the more general phenomenology of unbounded and non - deterministic assembly .moreover , tiling models have been used to study synthetic self - assembling systems , and a better understanding of the design space of polyominoes may aid in the design of these artificial systems .this article proceeds as follows .we first describe in detail the polyomino model and some of its fundamental properties ( section [ section : model ] ) .we then analyse a wide range of properties of the resultant gp map and compare these properties to those described , for example in , for the hp model and the rna secondary structure map . in particular , we show in sections [ section : redundancy]-[section : components ] that the mapping from sequences to phenotypes for all three models share the following general properties : _ redundancy _ ( there are many more genotypes than phenotypes ) leading to large _ neutral sets _ ( the collection of all genotypes that map to a given phenotype ) and _ phenotype bias _ ( some phenotypes are associated with many more genotypes than others ) .a more fine - grained analysis shows that the neutral sets also exhibit _ component disconnectivity _( not all genomes in a neutral set can be linked with single mutational steps ) .we proceed with a more detailed comparison of the polyomino and rna systems , through considering _ shape space covering _( most phenotypes can be reached from any other phenotype with just a small number of mutations ) , before showing the mean mutational robustness of a phenotype ( the _ phenotypic robustness _ ) scales very roughly logarithmically with the redundancy of a phenotype , and finally that it is positively correlated with the _ evolvability _ ( defined here as the number of other phenotypes _ potentially _ accessible from a phenotype ) , as postulated to hold more generally by . finally , in section[ section : discussion ] we discuss some implications of the remarkable agreement we find between the structure of our polyomino gp map and those of the better studied rna secondary structure and hp maps .the process of tiling and its connection with computer science was first developed by . since then , tiling models have been shown to be capable of computation and , in particular , turing - universal computation under the condition that cooperative binding is allowed between tiles , demonstrating the ability of 2d tiling systems to model computational as well as structure - forming processes . studied the program size complexity necessary to build a structure of a given size .more general considerations of the complexity of tiled structures have since been discussed in , with a more biological slant given by and applications to artificial biological systems discussed by .  here , rather than focussing on these tiles as potential computing devices or as models for complexity ,we explore how they can be used to understand the gp map of a specific biological system , namely the self - assembly of finite - sized protein structures . nevertheless , we are aware that some of our conclusions may have applications for a wider class of systems.  we now proceed with a more detailed description of the polyomino model as a gp map .the genotype is modelled as a character string representation of a set of tiles which make up an _assembly kit_. the edges of each tile in the assembly kit is given a number which represents the _ interface type_. interactions between interface types are defined via an _ interface interaction matrix _ . in our work here , we only consider one such interaction matrix type , with a total of interface types .there are no self - interacting interface types and interface types interact in unique pairs ( , , ... ) , with the only fully neutral types being and .defining interface interactions in this way allows the single parameter to control the number of potential unique bond types . as such ,the two parameters that describe a given parameterisation of the polyomino gp map are the tile number and the total number of interface types , allowing a particular polyomino gp map to be labelled as .  below we discuss the genotype , phenotype and map used in the polyomino gp map .the genotype for the set of building blocks in the assembly kit is written as a bit - string of length in base .the base we employ in this paper is the total number of interface types used in a given gp map .this allows each base to mutate to any other base at each site .the procedure of converting a genotype string into the assembly kit is part of the _map_.   in the context of the self - assembly mapping , there are several ways of classifying a polyomino structure .these may include criteria based on its overall shape and the individual tile types making up the final polyomino structure , as well as individual tile orientations .these different possibilities are discussed in .  here, we will classify the phenotype according to the overall shape of the polyomino independent of origin translation and c ( 90 degree ) rotations .note that chiral counterparts of polyominoes represent distinct phenotypes .the map has two stages : conversion of the genotype into the assembly kit , followed by assembly of a polyomino from an assembly process involving the assembly kit and the interface interaction matrix .a diagram representing this process is shown in fig . [ method ] .the characters of the genotype are read from left to right along the string .characters are assigned to the next blank edge of a square tile in the assembly kit .the edges are taken in clockwise order ( from the top side ) with all edges being written before moving on to a new block .the total number of tiles , in terms of the genotype string length , can be expressed as .the assembly of the 2d polyomino takes place on a square lattice where individual tiles from the assembly kit are placed .the interface types on the edges of tiles can form an attractive interaction as determined by the binary interface interaction matrix , with 1 denoting attraction and 0 neutrality .a bond may form between tiles if two adjacent ( interacting ) edges have interface types which attract , as defined by the interaction matrix .the assembly process is initialised by placing ( seeding ) a single tile on the lattice .we will consider only gp maps in which the seed tile corresponds to the first tile described in the genotype .a different protocol where any tile may be used to seed the assembly is also possible and does not significantly effect the results presented here .the assembly then proceeds as follows :  1 ._ available sites _ on the lattice are identified .these are places on the lattice where a tile may be placed in a particular orientation such that it will form a bond to an adjacent tile that has already been placed . in the assembly algorithm ,a list is kept of the position , tile type and orientation for each possible tile placement .a random available site on the lattice is chosen .the chosen site is filled with the associated tile and with the corresponding orientation .these steps are repeated until either :  * there are no available sites for bonding .* the structure grows beyond a certain width or height , which is taken as a proxy for unbounded assembly , so that the resulting phenotype is described as _unbound_. we set here , but our results are not sensitive to this cutoff as , for the polyomino systems we study here , there are no bounded structures larger than this .  at this pointthe assembly process is terminated and the structure produced is recorded . to test whether the structure is _ deterministic _ , the assembly process is repeated times , with each c rotation of the final structure checked against the recorded structure .if there are any differences between any of the assemblies , the phenotype is classified as _ non - deterministic_. phenotypes that are classified as unbound or non - deterministic structures are represented by a single phenotype , which we refer to as the undetermined ( _ und _ ) phenotype and is assumed not to be biologically relevant in this context . a more detailed discussion of the classification of polyomino structures is given in .in this section , we analyse the polyomino gp map by making measurements of redundancy , phenotype bias and component numbers , before moving on to analyse the properties of shape space covering , robustness and the relationship between robustness and evolvability . for each measurement ,comparisons are made with the rna secondary structure model and , for the first three of these properties , an hp lattice protein model .the software used to model rna secondary structure was the well - known vienna package , and for the hp lattice model we used the data from the spaces enumerated by .   .[ cols="<,<,>,>,>",options="header " , ]     robustness and evolvability are two evolutionary properties that have received much recent attention in the literature . as discussed in the previous section , robustness is the ability of an organism to maintain its phenotype if its genotype is mutated .evolvability on the other hand is considered as the capacity for producing phenotypic variation .one might expect that for an individual to be robust it would have to compromise its ability to produce variation ( to be evolvable ) . using the rna gp map , demonstrated that this expected trade - off exists for individual genotypes , but that the two properties are in fact positively correlated at the level of phenotypes .a possible geometric explanation is that phenotypes can become more mutationally robust as a result of increased redundancy ( more neutral neighbours ) .this in turn leads to connected components spreading out further across genotype space and possessing a greater ` surface ' , thus allowing a greater number of phenotypes to be accessible through neutral mutations .wagner s argument is really about the static structure of genotype space and does not account for any dynamical evolutionary effects .other authors have considered further static properties , including a different notion of phenotypic evolvability ( diversity evolvability ) defined as being the probability that two non - neutral mutations lead to different phenotypes .such a definition of evolvability was found to not be correlated with robustness in the rna gp map .a dynamical study by demonstrated that the relationship between robustness and evolvability could also depend on population parameters and mutation rates . in our work here , we simply consider whether the static properties of the polyomino gp map behave in a similar manner to those of the rna gp map as demonstrated by without here commenting on the wider debate of how robustness and evolvability relate .  in the left hand plots of fig .[ re ] , we show fractional evolvability versus fractional robustness , for genotypes and phenotypes in both the rna and polyomino gp maps .the genotype plot is a binned version of randomly sampled genotypes for each phenotype ( apart from the non - deterministic / trivial structure ) in each gp map .the fraction of all phenotypes that can be produced in any 1-mutation to each sampled genotype ( genotypic evolvability , ) is plotted against the fraction of those 1-mutations that produce the same phenotype as that of the genotype being tested ( genotypic robustness , eq.[eq : r_g ] ) . for both polyominoes and rnawe see a significant negative correlation .this expected negative correlation simply represents the trade - off between genotypic evolvability and robustness at the level of the individual genotype  in the right hand plots of fig .[ re ] , we plot phenotypic evolvability against phenotypic robustness. the phenotypic evolvability of phenotype is defined here as the fraction of all phenotypes that can be reached in a single mutation from any genotype with phenotype .we also refer to this as the _ potential _ evolvability because it represents the potential number of phenotypes that could be reached . whether they can be reached depends , of course , on details of the evolutionary dynamics . for example , if only single mutations are available then should really be defined with respect to the relevant component  .phenotypic robustness is defined in the same way as in section [ section : robustness ] , as the average genotypic robustness over all genotypes with phenotype ( eq .[ eq : r_p ] ) . in the plots ,we see strong positive correlations for both the rna and the polyomino gp maps , as expected . in other words , for both maps , phenotypes with a greater redundancy can be generated by a larger number of genotypes and are therefore , on average , more likely to be mutationally robust .furthermore , such phenotypes are also likely to have a larger set of genotypes , and therefore a greater diversity of other phenotypes potentially accessible from this set .thus , phenotypic robustness and potential evolvability are positively correlated .in this paper , we have explored the properties of a gp map for biological self - assembly of the kind exhibited by protein quaternary structure based on a recently introduced polyomino model for tile assembly  .we compared its properties to models of rna secondary structure and the hp model for protein tertiary structure . as is the case for these twowell studied gp maps , we argue that even though our polyomino model is highly schematic and thus misses many details of protein quaternary structure , it may nevertheless provide important biological insight into the structure of the design space for protein complexes .  despite the great complexity in potential phenotypes ,the polyomino model remains tractable as demonstrated in this paper by the ability to perform a wide variety of useful measurements on the gp map .our main results are : firstly , the polyomino model exhibits large - scale redundancy , a strong phenotype bias and the presence of disconnected genotype components across several parameterisations of the polyomino gp map ( section [ section : redundancy]-[section : components ] ) .secondly , that shape space may be covered in only a fraction of mutations that is , all phenotypes are a significantly smaller number of mutations away from each other than the total sequence length ( section [ section : ss_covering ] ) .thirdly , phenotypic robustness scales very roughly with the logarithm of the phenotype frequency ( section [ section : robustness ] ) . and finally , genotypic robustness and genotypic evolvability are negatively correlated , whilst phenotypic robustness and phenotypic ( potential ) evolvability are positively correlated ( section [ section : re ] ) .the polyomino model describes the self - assembly of disconnected units ( proteins ) into finite sized structures ( protein clusters ) that can vary in size .by contrast , for rna secondary structure and the hp model for protein tertiary structure , strings of connected units ( nucleotides or amino acids ) assemble into shapes of a fixed size .given the substantially different class of the phenotypes in our model , it is remarkable that the measured properties of these gp maps turn out to be so similar .this begs the question of whether what we observe is in fact a more general property of self - assembling systems , or even broader , whether a wider class of gp maps will share these properties .this question can be sharpened by looking at the different properties separately .redundancy should be widely shared across gp maps .phenotype bias has been observed in models for gene - regulatory networks and developmental networks  . could it be a more general property of gp maps ?disconnected components have also been observed in a boolean threshold model for gene regulation . to our knowledge shape spacecovering has not been studied for other gp maps , but general considerations based on the high dimensionality of genetic space suggest that something like this may be more widely relevant .finally , the correlation between phenotypic robustness and potential evolvability is deeply connected to the geometry of neutral sets and so is likely to be a much more general property of gp maps .how this correlation plays out for realistic evolutionary dynamics is , of course , a much more complicated question .we are hopeful that more complete answers will be derived through further analysis and comparisons of different model gp maps in a similar manner to the work here and in or .an important related question is whether model gp maps for parts of systems can be combined to achieve a more complete understanding of the evolution of phenotypic traits in the full organismal gp maps .the polyomino model can easily be adapted to study unbounded assembly or the assembly of synthetically produced objects like dna tiles or patchy colloids .thus the perspective gained from viewing polyominoes as a gp map may also shed light on the artificial design process for these systems .  finally ,although we introduce the polyomino model as a coarse - 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Abstract: the mapping between biological genotypes and phenotypes is central to the study of biological evolution . here we introduce a rich , intuitive , and biologically realistic genotype - phenotype ( gp ) map , that serves as a model of self - assembling biological structures , such as protein complexes , and remains computationally and analytically tractable . our gp map arises naturally from the self - assembly of polyomino structures on a 2d lattice and exhibits a number of properties : _ redundancy _ ( genotypes vastly outnumber phenotypes ) , _ phenotype bias _ ( genotypic redundancy varies greatly between phenotypes ) , _ genotype component disconnectivity _ ( phenotypes consist of disconnected mutational networks ) and _ shape space covering _ ( most phenotypes can be reached in a small number of mutations ) . we also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability . although our gp map describes the assembly of disconnected objects , it shares many properties with other popular gp maps for connected units , such as models for rna secondary structure or the hp lattice model for protein tertiary structure . the remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic gp maps . +  * keywords * : genotype - phenotype ( gp ) map , self - assembly , robustness , evolvability , polyomino , protein quaternary structure


the brazilian government classifies the goods it buys according to a particular taxonomy : the catmat ( catalog of materials ) .when the government purchases a new good , the person in charge of classifying it must choose one of the 560 catmat classes .the cognitive load is heavy , especially if the person is new to catmat .the result is misclassification .for instance , of the 30,774 goods classified as wheeled vehicles ( catmat class # 2320 ) between 1999 - 04 - 01 and 2015 - 04 - 02 , 17,469 cost less than r 250 as of 2015 - 12 - 01 ) .that price seems too low for a wheeled vehicle .when we inspect the product descriptions we see that the problem is misclassification : spare parts ( catmat classes # 2510 , # 2520 , # 2530 , and # 2590 ) are often misclassified as wheeled vehicles ( catmat class # 2320 ) .  when the misclassification rate is so high it is hard to audit government expenditures .in particular , it is hard to know whether the price paid for a given item was reasonable ( i.e. , similar to the prices paid for the same item before ) or not . auditing authorities waste resources investigating legitimate purchases , on the one hand , and fail to investigate fraudulent purchases , on the other hand .to reduce misclassification i trained a support vector machine ( svm ) classifier that takes a product description as input and returns the three most likely catmat classes as output .the idea is to semi - automate the process : we want to suggest likely classes to the person classifying the good ( the user of our app ) .he or she may choose among the suggested classes or ignore them and choose a different class .for instance , say some public hospital is buying insulin syringes .the hospital will describe the product in detail on the invitation to bid - say , as disposable insulin syringes with 0.5ml and ultra - thin ( 6 mm ) needle , 50 units " .the user feeds that description to the svm classifier , which then suggests three catmat classes : # 6515 ( medical and surgical equipment and supplies ) , # 6550 ( supplies for medical diagnostic and testing ) , and # 6640 ( laboratory equipment and supplies ) .the user chooses one of these three classes or , alternatively , discards them and chooses a different class.  we can not fully automate the process ( i.e. , substitute the svm classifier for the human classifier ) , for two reasons . first , in about 16.7% of the cases none of the svm - suggested classes is the correct one ( more on this later ) . hence a human must remain in charge of the final decision .but in the remaining 83.3% of the cases the svm classifier will be correct , which should reduce classification error . and perhaps this is a foundation upon which a fully automated classifier can be created in the future .second , after the user has chosen a catmat class he or she must also choose a subclass and an item .the catmat is a hierarchical taxonomy : it comprises 79 groups , 560 classes , 18,380 subclasses , and 217,907 items ( as of 2015 - 04 - 02 ) .but the svm classifier can not offer any suggestions when it comes to subclasses or items : with 18,380 or 217,907 categories there is just not enough data to train the classifier ; its accuracy would be too low . butreducing misclassification at the catmat level already improves the quality of the data , even if the user chooses the wrong subclass or item - research and auditing done at the class level will be more reliable . and perhaps the user is more likely to choose the correct subclass and item when the catmat class is correct .svm is a well - known classification algorithm first introduced by vapnik and lerner ( 1963 ) and later popularized by boser , guyon and vapnik ( 1992 ) and by cortes and vapnik ( 1995 ) .it learns from manually classified samples ( the training samples ) and then uses that knowledge to classify new samples .here we have a total of 28,420,761 samples , which are all the goods the brazilian government purchased between 1999 - 04 - 01 and 2015 - 04 - 02 .i split the samples into 70% training , 15% validation , and 15% testing .the classifier sees " the description _ and _ the catmat class of each of the training samples and thus learns how to map descriptions onto catmat classes .for instance , the classifier learns that when stapler " appears in the description the good is usually classified under catmat class # 7520 .it learns that when tea " appears in the description the good is usually classified under catmat class # 8955 .and so on .once the classifier is trained we use the validation samples to assess its performance . for each validation sample and each catmat classthe classifier estimates the probability that the sample belongs to that class .hence for each validation sample the classifier estimates 560 probabilities .the estimation is word - based .for instance , having the word stapler " in the description increases the probability that the sample belongs to catmat class # 7520 and decreases the probability that it belongs to catmat class # 8955 .when all estimations are done we check how often the catmat class of highest probability is the correct one .we then go back to the training phase , changing one or more model parameters ( like the learning rate or the regularization term ) .we assess the classifier s performance once more .we train the model again , with new changes in the parameters .and so on and so forth until we are satisfied with the results .when the classifier performs well enough with the validation samples we check how well it performs with the testing samples .that is the final result - once the testing samples are used we can not go back and adjust the parameters again , lest we overfit the classifier ( i.e. , lest we make the classifier too responsive to the idiosyncrasies of our data and thus non - generalizable ) .before we can train the svm classifier we need to collect , clean , and process the data .all the data are in the comprasnet database .the descriptions are in the d_itcp_item_compra table .the catmat classes are in the f_item_compra table .a common key allows joins between these two tables .i discarded the cases whose description and/or class was empty or null we are left .i also discarded the cases that corresponded to services ( about 10% of the total ) , as services are too unique and idiosyncratic for algorithmic classification .the result was a total of 28,420,761 samples ; as mentioned above , they correspond to all the goods the brazilian government purchased between 1999 - 04 - 01 and 2015 - 04 - 02 .i lower - cased all the descriptions and removed all special characters , numbers , and one - character words .i also converted plural words to singular words , using the first step of a portuguese stemmer algorithm ( the rslp algorithm , created by orengo and huyck [ 2001 ] ) .finally , i removed all words that only appeared once in the entire dataset .i transformed each document ( description ) into a vector of word counts and merged all vectors .this resulted in a term - frequency matrix - a matrix whose rows represent words , columns represent documents , and each entry is the frequency of word _i _ on document _ j _ ( i.e. , the term - frequency , ) .next i apply the transformation .the of each entry is given by its term - frequency ( ) multiplied by , where is the total number of documents and is the number of documents in which word appears ( i.e. , the word s document frequency  ; the ratio thus gives us the inverse document frequency ) .what the transformation does is increase the importance of the word the more it appears in the document but the less it appears in the whole corpus .hence it helps us reduce the weights of inane words like ` the ' ( ` o ' , in portuguese ) , ` of ' ( ` de ' ) , etc and increase the weights of discriminant words ( i.e. , words that appear a lot but only in a few documents ) . for more details on manning , raghavan , and schtze ( 2008 ) .the next step is normalization .here we have documents of widely different sizes , ranging from two or three words to dozens of words .longer documents contain more unique words and have larger values , which may skew the results ( manning , raghavan , and schtze 2008 ) . to avoid that we normalize the columns of the matrix , transforming them into unit vectors .the resulting matrix has dimensions 28,420,761 ( descriptions ) by 505,938 ( unique words ) .it is this matrix that we use to train , validate , and test the svm classifier .our svm classifier achieved an accuracy of 83.3% .the errors seem to have two main causes . first , misclassification in the training data. the svm classifier is learning from imperfect examples .as we discussed before , half the goods currently classified as wheeled vehicles ( catmat class # 2320 ) are actually spare parts ( catmat classes # 2510 , # 2520 , # 2530 , and # 2590 ) .second , class frequency .catmat classes that are bought more often tend to be more accurately classified by the svm classifier .this is expected : for these classes there are more training samples , so the classifier has a larger set of descriptions from which to learn .in fact , there is a negative linear correlation between class frequency and misclassification rate ( -0.36 , with p 0.0001 ) .i used the trained classifier to build an open source web app .its interface is very simple : there is a single input form , wherein the user writes or pastes the description of the good being purchased ( as it appears on the invitation to bid , for example ) .the user then clicks submit and is shown the three most likely catmat classes .  in the example below we inputed the description of an air conditioning unit andgot back three catmat classes : # 4120 ( air conditioning equipment ) , with probability 58% ; # 4130 ( air conditioning and cooling components ) , with probability 22% ; and # 6550 ( supplies for medical diagnostic and testing ) , with probability 4% . herethe first class - the one with the highest probability - is the correct one .initially the idea was to put the app up online but the cost was prohibitive .the trained classifier is heavy ( the coefficients take up over 4 gb on disk ) and requires a computer with large ram - at least 16 gb but ideally more . on cloud providers like amazon web services andgoogle compute engine that would cost around us 800 as of 2015 - 12 - 01 ) .the code for the app is available on github though : https://github.com/thiagomarzagao/catmatfinder .i made the code open source so that anyone can use and modify it .bird , steven , edward loper , and ewan klein .2009 . natural language processing with python . "oreilly media inc .boser , bernhard , isabelle guyon and vladimir vapnik .1992 . a training algorithm for optimal margin classifiers . " in d. haussler , editor , _ proceedings of the annual conference on computational learning theory _ , 144 - 152 .platt , john . 2000 .probabilistic outputs for support vector machines and comparison to regularized likelihood methods . in a.j .smola , p.l .bartlett , b. schlkopf , and d. schuurmans , editors , _ advances in large margin classifiers_. mit press .

Abstract: the brazilian government often misclassifies the goods it buys . that makes it hard to audit government expenditures . we can not know whether the price paid for a ballpoint pen ( code # 7510 ) was reasonable if the pen was misclassified as a technical drawing pen ( code # 6675 ) or as any other good . this paper shows how we can use machine learning to reduce misclassification . i trained a support vector machine ( svm ) classifier that takes a product description as input and returns the most likely category codes as output . i trained the classifier using 20 million goods purchased by the brazilian government between 1999 - 04 - 01 and 2015 - 04 - 02 . in 83.3% of the cases the correct category code was one of the three most likely category codes identified by the classifier . i used the trained classifier to develop a web app that might help the government reduce misclassification . i open sourced the code on github ; anyone can use and modify it .