Over many years, it has been assumed that enzymes work either in an isolated way, or organized in small catalytic groups. Several studies performed using “metabolic networks models” are helping to understand the degree of functional complexity that characterizes enzymatic dynamic systems. In a previous work, we used “dissipative metabolic networks” (DMNs) to show that enzymes can present a self-organized global functional structure, in which several sets of enzymes are always in an active state, whereas the rest of molecular catalytic sets exhibit dynamics of on-off changing states. We suggested that this kind of global metabolic dynamics might be a genuine and universal functional configuration of the cellular metabolic structure, common to all living cells. Later, a different group has shown experimentally that this kind of functional structure does, indeed, exist in several microorganisms.Here we have analyzed around 2.500.000 different DMNs in order to investigate the underlying mechanism of this dynamic global configuration. The numerical analyses that we have performed show that this global configuration is an emergent property inherent to the cellular metabolic dynamics. Concretely, we have found that the existence of a high number of enzymatic subsystems belonging to the DMNs is the fundamental element for the spontaneous emergence of a functional reactive structure characterized by a metabolic core formed by several sets of enzymes always in an active state.This self-organized dynamic structure seems to be an intrinsic characteristic of metabolism, common to all living cellular organisms. To better understand cellular functionality, it will be crucial to structurally characterize these enzymatic self-organized global structures. One of the most important goals of contemporary biology is to understand the elemental principles governing metabolic structure as a whole which underlie the common design of all microorganisms and cells.This global metabolic structure, conformed by the reactive interactions of thousands of biochemical species densely integrated through a labyrinthine web, represents one of the most complex dynamic systems in nature During the preceding two decades, different metabolic models have been studied intensively. Traditional models have focused on the kinetics of multi-enzyme systems by solving systems of differential equations and algebraic equations In an attempt to get a more accurate comprehension of the metabolic dynamic phenomena, we have proposed a dynamical system called “dissipative metabolic networks” or DMNs, which is basically formed by groups of enzymatic associations dissipatively structured and interconnected by fluxes and regulatory signals .Our model takes into account the fact that the cellular organization at the molecular level presents two relevant dynamic characteristics: the presence of enzymes aggregated in clusters and the emergence of dissipative catalytic patterns.Experimental observations have shown that enzymes operate within metabolic pathways, may form functional catalytic associations and, thus, do not function in isolation of one another. Some of the first experimentally isolated enzymatic associations were, among others, the glycolytic subsystem Association of various enzymes in large complexes (supramolecular organization) allows the direct transfer of their common intermediate metabolites (metabolic channelling). In addition, reversible interactions of enzymes with structural proteins and membranes are a common occurrence. This results in the existence of microcompartments within the soluble phases of cells. The microcompartmentation provides biophysical and biochemical mechanisms of physiological importance for the control of metabolic pathways The second consideration in our model is the presence of dissipative catalytic patterns. Each functional enzymatic association conforms a catalytic entity as a whole, in which spontaneously organized molecular oscillations may emerge.far from equilibrium conditions prevailing inside the cell, the catalytic dynamics of enzymatic sets may present transitions between different stationary and oscillatory molecular patterns. When the enzymatic sets exhibit a rhythmic behavior, all the metabolic intermediaries oscillate with the same frequency but different amplitudes In the It is well known that these biochemical rhythms constitute a new type of supramolecular organization that may emerge in open systems far from equilibrium and was called dissipative structure by Prigogine It has been found experimentally that many enzymatic associations may cause oscillatory processes. The first systematic classification of cellular oscillatory behaviors gathered about 450 different kinds of biochemical rhythms 2+Nowadays, numerous experimental observations have contributed towards a better understanding of metabolic rhythms. For instance, it can be cited, among others: intracellular CaLikewise, numerous works have been carried out on the mathematical modelization of metabolic rhythms Due to the importance of cellular enzymatic rhythms, we have taken into account this aspect in our model of DMNs, so that the simulated catalytic processes can present both stationary and oscillatory activity regimes.In the dissipatively structured enzymatic associations, the existence of allosteric enzymes permits the interconnection among them. The catalytic activity of the allosteric enzymes is modulated through the noncovalent binding of a specific metabolite at a place of the protein different from the catalytic site, provoking alterations of the metabolic state in an interval of seconds. Such types of modulation may be both positive  and negative (inhibitory modulators). The regulation by means of the covalent interactions can originate “all-or-nothing” type answers In agreement with all these considerations, our DMNs model is composed of a set of catalytic elements , which are connected by substrate fluxes and regulatory signals . The metabolic subsystems may present oscillatory and stationary activity patterns.on-off changing states .In a previous work Escherichia coli, Helicobacter pylori, and Saccharomyces cerevisiaeThis type of functional metabolic structure has recently been shown by Almaas and colleagues for In this paper, we have analyzed around 2.500.000 different metabolic networks in order to investigate the conditions in which this global configuration emerges. We have found that this functional metabolic structure is an emergent property of all dissipative metabolic networks with a high number of enzymatic subsystems.Experimental observations have shown that the enzymes may form functional catalytic associations in which a new type of supramolecular self-organization may emerge . These catalytic associations that operate within far from equilibrium conditions were called dissipative structures by Prigogine “Dissipative metabolic networks” (DMNs) are dynamical systems basically formed by a given number of groups of dissipatively structured enzymatic associations  interconnected by fluxes of substrates and regulatory signals .The metabolic subsystems receive distinct input fluxes of substrates and three possible types of regulatory signals: activatory, inhibitory (graduated) and total inhibitory . Each MSb transforms the input fluxes and regulatory signals into one or several output activities.In agreement with experimental observations, the output activity of the MSbs may be oscillatory or steady state In our model, when the set of dissipatively structured enzymes shows an activity with rhythmic behavior the output activities present nonlinear oscillations with different levels of complexity, as could be expected in the cellular conditions “in vivo”.In order to be able to effect these different oscillatory or steady state patterns in each metabolic subsystem, the input-output conversion is made in two stages. First, the input fluxes are transformed into an intermediary activity by means of flux integration functions. In a second phase, the “intermediary activity” is modified by means of the “regulatory signals integration”, which depends on the combination of the received regulatory signals. Each regulatory signal has an associated regulatory coefficient which defines the intensity of its influence.i,jq, called “influence coefficients”, that will be described in the The parameters If the signal is of total inhibition , then we will use a parameter δ called threshold value . When a given threshold value is reached it inhibits completely the activity of the MSb.On the other hand, biological processes with long-term correlations are of notable interest in the study of complex dynamics.e.g., the quantification of DNA patchiness K+ channel activity Long-term correlations have been observed in, In a previous work with DMNs In particular, we have characterized the behavior of several large complex transitions series generated in metabolic subsystems by means of the Hurst exponent H, which has been shown to be a robust and reliable test to detect the presence of long-term correlations For a random series with independent increments, it can be shown that H should be equal to 0.5. If H≠0.5 this is indicative of the presence of “persistence” in the data, which means that the present state of the system is affected by previous states.The studied time series generated by DMNs demonstrate complex transitions between the activities of the metabolic subsystems and we have found values for the Hurst exponent of 0.07<H<0.4, indicative of long term persistence over all the studied ranges. Values of H<0.5 are interpreted as characteristic of “trend-reversing” or “antipersistence” (a type of “persistence”). The behavior of the time series tends to reverse itself, for instance, a decreasing trend in the past usually implies an increasing trend in the future and conversely, an increase in the past is likely to be followed by a decrease. The high reliability of these results was tested with exhaustive Monte Carlo simulations. All the series studied presented persistence and these results showed clearly that the complex transitions in the DMNs exhibit long-term memory phenomena.In an attempt to study a possible influence of the past activity on the enzymatic self-organized global structures we have considered the β parameter (the past influence coefficient) in some of the DMNs, in the sense that the present activity of each metabolic subsystem may be affected by its previous activities .2- Dynamic transitions between steady states and periodic behaviors.3- Global configurations that the DMNs may adopt:on state.All the subsystems are always in an All the metabolic subsystems always present cycles of activity-inactivity.on state conforming a metabolic core, while the rest of the subsystems are in an on-off switching state.A certain number of subsystems are always locked in an In our first study, we have considered the simplest situation, which corresponds to a metabolic network formed only by two subsystems . For 0.17<δ≤0.67 the second subsystem presents cycles of activity-inactivity with different patterns of transitions between steady states and periodic behaviors. For 0.68≤δ≤1 the MSb2 is locked in an active state. The same as with the first subsystem, for 0.837≤δ≤1 deterministic chaotic transitions between steady states and periodic behaviors can be observed, that is, the MSb2 spontaneously exhibits infinite transitions between different oscillatory periodic behaviors and steady states.0 and the corresponding periodic and stationary patterns developed by the two subsystems are shown.In The mechanism that determines these behaviors in both subsystems is not prefixed in any of the parts of the system. There is no feedback with oscillatory properties nor any other rules that determine the system to present complex transitions in the output activities of the metabolic subsystems. The dynamic behaviors which emerge spontaneously in the network have their origin in the regulatory structure of the feedback loops, and in the non-linearity of the constitutive equations of the system , the threshold values δ do not provoke qualitative changes in the network. So, for 0≤δ≤1 the first subsystem is always on and chaos emerges in two parametric regions: for δ = 0.3 and for 0.7<δ≤1. The second subsystem also presents, as the MSb1, chaotic behaviors under these conditions, however, for δ = 0.3 the MSb2 exhibits an on-off state, and when 0.7≤δ≤1 its state is on.When β = 0.2 the MSb1 is always on and MSb2 is on-off in the first range and is on in the second one.As β increases, the regions of chaotic behavior augment in correlation with δ. For instance, when β = 0.5 and either 0.1<δ≤0.6 or 0.8<δ≤1 chaos emerge in the metabolic net, the first subsystem is always on, and chaotic transitions emerges when 0.2<δ≤0.8. The second subsystem exhibits two different behaviors: for 0≤δ≤0.2 and 0.7≤δ≤1 its state is off, and when 0.2<δ≤0.7 its state is on-off; as occurs in the MSb1, chaotic transitions between steady state and periodic behaviors emerges for 0.2<δ≤0.7.If β = 1 the net presents only one chaotic parametric region. The first subsystem is always If we take δ as the first reference parameter, it can be observed in on, always off, or an on-off changing dynamics. Thus, for low values of δ (0≤δ≤0.2) the metabolic subsystem 2 is always inactive (off) independently of the values of β. For high values of δ the MSb2 shows a behavior in which it is always active (on) . Finally, the MSb2 presents dynamics of change active-inactive (on-off) for medium values of δ [0.3–0.6], with 0.2≤δ≤1 as the maximum range for β = 0.8.On the other hand, it can be observed that the MSb1 is always active for all values of δ and β. However, the MSb2 may present one of three general states: always More interesting situations appear in the DMNs with more than one flux and one regulatory signal associated to each subsystem. In on, always off and an on-off changing dynamic. If we take into account the dynamics followed by these subsystems, interesting functional configurations in the whole net can be observed.Each subsystem may present three states: always on-off changeable state  never emerge DMNs characterized by presenting a metabolic core.In on-off changing dynamic emerge . Last, the DMNs with low levels of β and high values of δ present all their metabolic subsystems always active (on).It can be observed also that in this kind of networks, for high covalent regulatory activity (0.1≤δ≤0.4) nets with all metabolic subsystems in an In order to better understand the influence of the control parameters δ and β on the global self-organizations in the DMNs, we have made a first study of different nets constituted by twelve metabolic subsystems with three regulatory signals and two input fluxes by subsystem. In this study all networks present the same flux configuration described in on, off or changing on-off was that the subsystem had the corresponding state between the iterations 200 and 300.A total of 1.210.000 different metabolic nets were built, the results of this study are shown in on or is always off and never is in an on-off changeable state). It can be observed that if β is maximum (β = 1) all the percentages are greater than 50% (between 51.11% for δ = 0 and 70.66% for δ = 0.9). When the covalent regulation is very low (0.9<δ≤1) and 0<β≤0.6, the biggest percentages are reached (between 64% and 97.6%). For 0.3<δ≤0.7 and 0.6<β≤0.9 the lowest percentages are reached .In The maximum percentage of dissipative networks with all its metabolic subsystems unable to change the state (97.6%) is obtained when δ = 1 and β = 0.1, and the minimum (1.39%) is attained for δ = 0.6 and β = 0.7.off state is represented. They constitute a particular case of the DMNs showed in In on-off regime is shown. The biggest percentages are obtained when β = 0.9 and 0.3≤δ≤0.9. The lowest percentages  are found for a value of δ around 0.7 and β≤0.4. The maximum percentage (45.5%) is obtained when β = 0.9 and δ = 0.8, and the minimum (0.001%) is obtained when β = 0.4 and δ = 1.In on-off changeable state. If the covalent regulatory activity is minimum (δ = 1), the percentage of nets presenting these functional configuration varies strongly as a function of β, in fact, the absolute maximum is 87.33% (β = 0.9) and the absolute minimum is 2.39% (β = 0.1). For a maximum covalent regulation (δ = 0) the biggest percentage is 71.37% (β = 0.8) and the minimum percentage is 37.09% (β = 0). When 0<δ<1, the highest percentages (about 80%) are attained for a given value of β between β = 0.5 and β = 0.7 and the minimum values correspond to β = 1. The 64.4% of the pairs  present a percentage over 50% for these kind of metabolic nets.Finally, on-off regime, and the 52.56% are metabolic nets characterized by having a subset of dissipative metabolic elements locked into an active state while the rest exhibit an on-off changeable state. The percentage of networks with all their subsystems in an off state  is 4.95% (this percentage constitutes part of the 33.26% of the nets unable to change its state).A total of 33.26% of the studied DMNs correspond to the case in which all its subsystems are unable to change the state, the 14.09% of the nets present all their elements in an It can be observed that the global configuration characterized by having a metabolic core is the one that presents the maximum percentage when compared with the other two active global configurations.on  and in metabolic subsystems that exhibit an on-off changeable state .In metabolic networks formed by twelve subsystems, complex dynamical transitions in the activities of each MSb are common and we have observed that chaotic transitions between steady states and periodic behaviors may emerge both in subsystems always Under experimental conditions, most of the local dynamic behaviors of the metabolic subsystems present periodical oscillatory patterns or steady states Xenopus laevis oocyte carried out by our group. These chaotic oscillations correspond to a subsystem in an on-off changeable regime.In Cl− channels sensitive to the intracellular The blood serum from many animals contains a factor which activates a membrane receptor that is coupled to the phosphatidylinositol second messenger system and produces oscillatory currents. These currents are elicited by activation of The enzymatic activity bound to the membrane of the oocyte after the external stimulus of the Fetal Bovine Serum causes the dynamic mobilization of the intracellular calcium. This activity ceases soon after the exposure of the cell to the external agent.on-off switching state and both the mean amplitude A0 , similar statistics were also carried out. In this case, networks formed by subsystems with one regulatory signal for each metabolic subsystem and one input flux were considered; likewise the same probability for each regulatory signal was assigned. Each net subsystem can have an outer input flux with a probability of 0.1, so that a metabolic network could have more than one outer input flux but at most one for each subsystem. Again, all parameters, the topology of the regulatory signals and flux interconnections (flux topology) were randomly configured. The β parameter was always taken equal to 0.3. For this study  and is study  1.250.00on or is always off, and never is in an on-off switching state. It can be observed that for a fixed δ there is a remarkable trend towards a decrease in this percentage when the number of subsystems that conforms the net is increased. When n = 2, the mean percentage with respect to δ is 75.5% and for n = 50, it is 29.6%. With respect to the behavior of percentages when the number n of subsystems is fixed, two different clusters are observed.In n up to 35 subsystems, the percentage decreases slightly with δ when δ is less than 0.8, and increases starting from this value. In this cluster, the maximum percentage (83.31%) is obtained when δ = 0.1 and n = 2, and the minimum percentage (24.81%) is obtained when δ = 0.7 and n = 35.For n = 40, and the minimum percentage (21.65%) is obtained when δ = 0.9 and n = 50.For a number of metabolic subsystems greater than 35, the percentage decreases steadily with respect to δ; this decreasing is very remarked for δ>0.5 . In this second cluster, the maximum percentage (41.92%) is obtained when δ = 0.1 and n = 2, and its minimum (0.32%) is reached when n = 50.The DMNs in which all subsystems are off constitute a particular case of the nets in which all the metabolic subsystems are unable to change their state . It is oon-off switching state is shown. For δ fixed, the percentage increases when the number of subsystems is between 2 and 4, and then it decreases, tending to 0 asymptotically with the number of subsystems. The global maximum (30.9%) is reached for δ = 0.9 and n = 3, and the global minimum (0.11%) is reached for δ = 0.1 and n = 50.In on-off changeable state is shown. When δ is fixed, the percentage grows pronouncedly with the number of subsystems. The rank of growth  is 59.3 for δ = 0.1 and 76.3 for δ = 0.9. For a given n with n>35 the percentage increases notably with δ.In n = 2, and the maximum (77.71%) is obtained when δ = 0.9 and n = 50.The minimum percentage (0.61%) is attained when δ = 0.1 and off) as well as the nets with all their subsystems unable to change state and the nets with all their subsystems changing. Nevertheless, this increment in the number of subsystems suggests an asymptotic trend to reach a percentage of 100% of the nets presenting a global configuration characterized by having a metabolic core of subsystems locked into an active state while the rest of metabolic subsystems exhibit an on-off switching state.It can be observed that an increase in the number of subsystems that constitute the net results in a decrease in the percentage of nets functionally non-viable  connected by substrate fluxes and regulatory signals  we have used a type of dynamic system, which we call “dissipative metabolic networks” or DMNs.Three types of basic emergent behaviors can be distinguished:Dynamic transitions corresponding to the mean amplitude, amplitude and frequency in the activities of each subsystem.Activity patterns developed by the metabolic subsystems.Global functional configurations in the network.Upon the numerical analysis, a number of different qualitative types of transitions among the activity patterns of the subsystems can be observed: steady state-steady state, steady state-periodic regime, changes between different periodic regimes and chaotic transitions.Periodic and chaotic transitions in these activity patterns of the subsystems are common. For the case of periodic cycles of transitions, the subsystems run repeatedly through the same set of states, resulting in a cycle of distinct periodic oscillations and steady states. Chaotic behaviors can be observed even in very simple nets of two or more subsystems with a single flux and a unique regulatory signal sent by a catalytic element in the network.on, always off, or an on-off changing dynamics. If we consider the dynamic behaviors of a metabolic network regarding only these three general states, interesting global functional configurations in the overall of the net can be observed.Each metabolic subsystem may present one of the three general states: always on state. In this situation, the dynamics are restricted to the possible changes in the variables of the active subsystems.In fact, for a specific parameter value  all the subsystems can be in an on-off changeable state.Further modifications in the control parameter may lead to a new global configuration in which all their dissipative subsystems are in an on-off changing dynamics. Besides, all these metabolic subsystems, both those locked in an always active state and those which are permanently in a process of activation and inhibition, exhibit local dynamics with transitions between different steady states and oscillatory behaviors.A new variation in any control parameter may provoke a qualitative change in the metabolic net, resulting in the emergence of a new global configuration, in which a certain number of subsystems are locked in an active state (metabolic core) while the rest of the subsystems remain in an on-off changing state .In the prevailing conditions inside the cell, catalytic dynamics seem to show a similar structure to this kind of metabolic global configuration. The cellular metabolism presents a metabolic core formed by a set of catalytic associations always in active states  while the rest of the catalytic subsystems are in an Since this global metabolic dynamic may be a genuine and universal functional configuration of the cellular metabolic structure common to all living cells, we have focused our efforts on analyzing the elements which may determine its emergence.With this purpose, in a first study, we have analyzed 1.210.000 different randomly constructed metabolic nets with only 12 subsystems and with three regulatory signals and two input fluxes subsystem.The numerical results show that more than 50% of the analyzed nets present a global configuration characterized by exhibiting a metabolic core.Regarding the rest of the global metabolic configurations, apart from appearing in smaller percentages than the previous one, it is observed that these percentages diminish even more when the level of covalent regulation is not very high, as could be expected in living cell conditions .In fact, when the nets with all their subsystems unable to change its state are studied (this happens for the 33.26% of the networks), it is noted that the smallest number of these nets is obtained when the level of covalent regulations is intermediate and the influence of the past is high .In the particular case of nets with all their subsystems off , it can also be observed that the percentage of such nets is less than 1% when the level of covalent regulation is intermediate or low and the influence of the past is not very high (β<0.7).As in the previous cases, when nets in which all the subsystems are in an on-off changeable state are considered (this happens for the 14.09% of the nets), it is observed that the lowest percentages are obtained when the level of covalent regulation is not high and the influence of the past is low.The nets characterized by having a metabolic core, appear in the highest percentages, which become particularly high (up to 80%) when the level of covalent regulations is not high and β is low.on-off switching state in any generic metabolic net.In the light of these results, despite the fact that the control parameters β and δ may cause important changes in the dynamic behaviors of the nets, it seems clear that none of these control parameters are determinant in the emergence of a global metabolic configuration characterized by a set of subsystems locked into an active regime while the rest is in an n of subsystems that conform each network and the threshold value δ  as control parameters.In order to better understand which elements could determine the emergence of this global configuration, we have carried out simulations including 1.250.000 randomly constructed nets, using the number The obtained results seem to show that the percentage of nets with all their subsystems unable to change the state decreases remarkably with increased numbers of subsystems. This decrement is more notable when the level of covalent regulation in these nets is not high.off state  their percentage tends asymptotically to zero. In fact, when the number of subsystems is 50, the percentage is negligible.In the particular case of nets with all their subsystems in an An analysis of the nets with all their subsystems in an on-off changeable state shows clearly that this percentage tends also to zero.Finally, the study of the remaining nets (the ones with a metabolic core) shows a rapid increase in their percentage as a function of the number of subsystems. These values are particularly high when the level of covalent regulation is moderate. These results suggest that there is an asymptotic trend leading towards 100% in the percentages of this global functional configuration when the number of subsystems increases.In conclusion, the fundamental element for the emergence of a global metabolic configuration characterized by presenting a metabolic core is the number of subsystems. It seems that this global configuration is an emergent property of all the DMNs with a high number of subsystems.It is possible that the complexity inherent to a biochemical system conformed by a high number of dissipative subsystems provokes the spontaneous emergence of this fundamental aspect of the cellular metabolic structure.Unicellular organisms present a kind of metabolic cellular structure characterized by having a dynamic functional configuration in which a small group of metabolic subsystems are always active whereas the rest present on-off catalytic dynamics. Our numeric analysis seems to show that this global dynamic self-organization of the metabolism emerges spontaneously in the cellular metabolic space, as a consequence of the fact that the cells possess catalytic structures conformed by a big number of metabolic subsystems.All living cellular organisms seem to display some metabolic subsystems that are always active, (these are involved in the permanent production of ATP), whereas the rest of the subsystems present on-off reactive dynamics. Taking all this into account, we can conclude that this global dynamic organization of the reactive cellular processes is possibly a genuine characteristic of the metabolism, common to all living cellular organisms, which could be basic and fundamental in the regulation of the most elementary cellular processes.By means of modelling approaches, such as the constraint-based analysis applied to metabolic networks, E. Almaas, A.L. Barabási and their group of researchers, These studies have been made in Escherichia coli, Helicobacter pylori, and Saccharomyces cerevisiae metabolism, showing also that most current antibiotics may interfere with the metabolic core The global configuration that emerges in the DMNs, characterized by displaying a metabolic core formed by a set of subsystems always active embedded in a set of subsystems in an on-off changeable state, seems to agree remarkably with the observations of E. Almaas, A.L. Barabási and their group of researchers. Our numeric results seem to show that this metabolic global organization is originated by the dissipative dynamics that spontaneously emerge in the cellular reactive structure formed by a network with a high number of enzymatic processes.On the other hand, the emergence of frozen cores in dynamic networks has also been pointed out in Random Boolean networks. This interesting kind of dynamical systems was introduced in 1969 by S. Kauffman Under experimental conditions, most of the local dynamic behaviors of the metabolic subsystems exhibit periodical oscillatory patterns or steady states. However, it has also been observed that some subsystems can present chaotic activities. For example, that occurs in oscillations in citric acid cycle  and in calcium oscillations in oocytes where the membrane receptors are activated.on as well as in metabolic subsystems that exhibit an on-off switching state chaos can be observed.Our results also show that the mean amplitude, amplitude and frequency in the activities of certain subsystems may present chaotic patterns. These dynamic behaviors may emerge in the simplest nets with only two subsystems and in the most complex nets; likewise, in subsystems always The combination of chaotic dynamics in some subsystems with a stable functional configuration which presents a metabolic core may be of biological interest. The stability of this global configuration is necessary to ensure the maintenance of its metabolic structure. The existence of chaotic dynamics in the transitions of the subsystems activity may constitute an advantage in the self-regulatory control of the system, due to the sensitivity of chaotic behaviors to initial conditions; these dissipative metabolic networks with local chaotic patterns may permit fast responses during the cellular adaptation and in the regulation against perturbances.on-off changing dynamics, and able to simultaneously develop steady states, regular oscillations and chaotic transitions, may help to better understand cytological phenomena and to reinterpret them in a closer to reality way.This conception of the cellular metabolic structure as a complex dissipative catalytic network endowed with a stable global configuration in which a core of metabolic subsystems are locked into an active regime, while the rest present complex n interconnected elements, called metabolic subsystems or MSbs. Each subsystem represents a group of enzymes aggregated in clusters and dissipatively structured. This enzymatic set is considered as an individual catalytic entity.DMNs consist of a set with The subsystems receive both input fluxes  and regulatory signals, which may be of three types: activatory, inhibitory and total inhibitory . These interactions correspond with the activity of allosteric enzymes and regulatory enzymes of covalent modulation.Each MSb converts the input fluxes and regulatory signals into a unique or several output activities and sends one or several fluxes and regulatory signals to other subsystems.The output activity can be periodic or stationary  = (A0)i+iAsin(iωt), where (A0)i is the mean amplitude, iA is the amplitude of the oscillation and iω is the frequency. Since iy(t) has to be non-negative, we will take (A0)i≥0 and 0≤iA≤(A0)i. We will also suppose that the values of (A0)i and iω are bounded, that is, there exist constants (A0)max and maxω such that (A0)i≤(A0)max and iω≤maxω for all i. The function iy(t) can be characterized by three variables, ix,1, ix,2 and ix,3, with values between 0 and 1, by taking (A0)i = ix,1(A0)max, iA = ix,2(A0)i and iω = ix,3ωmax . Hereinafter, we will identify the activity of the i-th subsystem during the k – th dynamical regime with the triple i varies from 1 to n, being n the number of subsystems and where j varies between 1 and 3; the superindex k indicates the current iteration.So the activity of the ix,2 = 0 or ix,3 = 0, and the subsystem will be in an inactive state when ix,1 = 0.The activity will be steady when The normalized activity of each MSb is T. During the k-th iteration the time t will vary between (k-1)T and kT.The temporal period during which each oscillation is maintained will be a constant value that we will call k-th iteration will bej in 0A, A and ω when j is 1, 2 and 3, respectively. This matrix describes the state of the whole net in each iteration and we will call it the state matrix. The integration process that transforms kx in kx+1 consists of two stages that will be fully described in which follows. The first stage is the flux integration, in which F1,F2 and F3. The second one is the regulatory signal integration stage, in which we pass from We proceed now to describe the way the subsystems are interconnected and how the conversion of the input activities into a unique output activity is realized. As we said above, the activity of the whole DMN in the i-th subsystem receives flux from only one subsystem, say the l-th. The input flux will consist of the three values Each subsystem receives an input flux from a subset of the remaining ones. In the simplest case, the F1,F2,F3 defined as follows:p is a parameter associated to each flux integration function.The qualitative behaviors of the amplitude and frequency in the glycolytic subsystem were studied in detail by Goldbeter and Lefever i-th subsystem receives flux from more than one subsystem. We will define the integrated flux as the arithmetic mean of the received integrated fluxes.In the most general case, the F1,F2,F3 that were defined before, but for other parameter values Each subsystem can also have an outer input flux, consisting of three fixed values i-th MSb receives a regulatory signal from the l-th one. Let j-th component  of the activity of the subsystem which regulates at the beginning of the k+1-th iteration, and j-th component of the activity of the regulated MSb after the input flux integration.When the flux integration has been done, we proceed next with the signal regulatory integration. First, we will describe the process in the simple case in which a MSb has only one regulatory signal. Let us suppose that the i,jq when i,jq. Thus, we have If the signal is of inhibitory type , then the activity x in  is equivalent to reducing 1-x to a smaller value x′ in . So, we will define the activatory functions byIf the signal is of activatory type , the function is similar to the one described above, once we take into account that to augment a value i,jq “influence coefficients”; they represent the influence of each modulator on each subsystem.We will call the parameters If the signal is of total inhibition type, then we will use a parameter δ, that will be called threshold. The activity r regulatory signals for each MSb, then we have r intermediary states s,kx, where s varies between 1 and r, (besides of the intermediary state x′k obtained after the flux integration was done). In this case, we replace in the previous formulas In the general case in which a MSb receives regulatory signals from several subsystems, they act sequentially, so that if there are r,kx = kx+1.At the end we obtain Now we will describe some additional rules for the integration of the activities of each subsystem.l-th stage of the signal regulatory integration a total inhibition acts and the threshold is reached then we will ignore the subsequent regulatory signals for that component  and we will take i-th subsystem receives a regulatory signal from the l-th one and When after the flux integration stage off independently of Finally, when The DMNs are discrete and deterministic dynamical systems. Once the parameters of the net are fixed, there is only one solution in the net. In the simplest case, each metabolic subsystem presents a unique dynamic behavior, which can be a steady state or a periodic oscillation. However, the net can self-organize spontaneously in such a way that each metabolic subsystem shows a solution characterised by presenting uninterrupted transitions between various behaviors periodic and/or stationary. In the most complex cases deterministic chaotic solutions can emerge spontaneously, originating infinite transitions between different periodic and/or stationary behaviors. In this situation, each metabolic subsystem modifies uninterruptedly its enzymatic activity in such a way that it changes between different periodic and/or stationary regimes that never repeat its activity along arbitrarily long periods of time.The dynamic behaviors that emerge spontaneously in the DMNs have their origin in the regulatory structure of the feedback loops, in the non-linearity of the constitutive equations of the system and in the complexity of the own dynamics that are generated in the network.N of transitions and, in the k-th stage, we suppose that the oscillation is harmonic, that is, the activity of the subsystem is described by a function of the form y(t) = (A0)+A sin(ωt), where A0max and ωmax are given fixed parameters independent of the stage number and of the subsystem. The duration of the harmonic oscillation is a given parameter hT independent also of the stage and of the subsystem. In between two stages, a mixed transition regime is maintained with a duration trT independent of the stage number and of the subsystem. If the transition goes from the k-th stage to the (k+1)-th stage then, during the trT seconds of transition regime, the activity is given by a function of the form y(t) = A(t)y1(t)+B(t)y2(t), where y1(t) is the activity corresponding to the prolongation in time of the previous harmonic activity in the k-th stage, and y2(t) is the back-propagation in time of the subsequent harmonic activity in the (k+1)-th stage. The numbers A(t) and B(t) depend on time and indicate the weights with which the activities of the subsystem in the previous and posterior stage are present during the transition time. At the beginning of the transition, say at t = t0, A(t0) is 1 and B(t0) is 0, and at the end of the transition, say at t = t1, A(t1) is 0 and B(t1) is 1. At the rest of the transition times A(t) and B(t) vary affinely. Thus, Now we will describe the way we pass from a sequence of terns A(t) and B(t) depending on time. Thus, the introduction of these transition regimes provokes the emergence of nonlinear oscillatory behaviors, both simple and complex (see for example The transition regimes are combinations of two harmonic oscillations with nonconstant coefficients k-th stage and of the previous state); when β′ belonging to  whose value is 1 when In an attempt to take into account a influence of the past in some of the DMNs, taking into account that each activity of the subsystem  depends also on some activities developed in the past, we have considered the following aspects: the state β′ belonging to  whose value is 1 when In the second case, the difference Thus k = 1, we have obtained the state x2 from x1 without taking into account the dependence of the past, which is equivalent to define x0 = x1.To overcome the need to know two initial states in the first stage, that is, when In some of our studies we have considered β as one of the control parameters.p2,1 = 0.78, p2,2 = 0.83, p2,3 = 0.94. The catalytic dissipative element MSb1 is activated by the second MSb, with q1,1 = 0.18, q1,2 = 0.02, q1,3 = 0.15 and the MSb2 is totally inhibited by MSb1, with a threshold δ = 0.1. We have fixed the value β = 0.7, where β is the past influence coefficient.We will consider the simple DMN formed by two subsystems arranged in series with two feedback loops of regulatory signals. The MSb1 is activated by the second subsystem and the MSb2 is totally inhibited by the first subsystem when this one reaches a determinate threshold value . The MSbThe initial state isAs we said before, we will not consider the influence of the past for the calculation of the next state, and we will use only the flux integration and the regulatory integration. The details of these integrations will be omitted for brevity in this first stage, but the calculations will be completely developed in the next stage. The second state that we obtain isAfter the flux integration stage we reach an intermediary stateAfter the signal regulatory integration stage we obtain the following state0A = 0.225, A = 0.125, ω = 0.35, and the second MSb is locked into an inactive state.Finally, in the DMN the first MSb will fall into a single active state, corresponding to a periodic oscillation with Next, we have considered a DMN formed by two subsystems arranged in series, which represent in a very simplified way the main interconnections between the pyruvate dehydrogenase complex (PDH) and Krebs cycle, so-called tricarboxylic acid cycle (TCA) .+ and NADH by a process called pyruvate decarboxylation which is mainly inhibited by the ratio ATP/ADP Pyruvate dehydrogenase is a large multienzymatic subsystem containing many copies of three enzymes: pyruvate dehydrogenase, dihydrolipoyl transacetylase and dihydrolipoyl dehydrogenase. This metabolic subsystem (MSb1) receives an input flux of pyruvate yielding acetyl-CoA, HAcetyl CoA, a product of the pyruvate dehydrogenase reactions is a central compound in metabolism with several functions: as input to the Krebs cycle, where the acetate moiety is further degraded to CO2, and as donor of acetate for synthesis of fatty acids, ketone bodies, and cholesterol.One of the factors controlling the MSb2 is the NADH. The citrate synthase enzyme is the primary control point in the Krebs cycle and is negatively regulated by NADH. Isocitrate dehydrogenase and α-ketoglutarate dehidrogenase are also strongly inhibited by the negative allosteric modulator NADH Therefore, the catalytic dissipative element MSb1 is inhibited by the ATP from the second subsystem and the MSb2 receives an inhibitory signal of NADH from the MSb1.1,1 = 0.54, p1,2 = 0.60, p1,3 = 0.78) and β = 0.2. The initial states are the same that the ones belonging to the DMN shown in the example 1.The parameters considered in this DMN are the following ones: the first subsystem MSb1 receives an input flux of pyruvate with 2,1 = 0.398, p2,2 = 0.516, p2,3 = 0.5).The MSb2 receives an input flux of acetyl-CoA from MSb1, being the values of the parameters of the integration functions of .In order to simplify we have equalized the three influence coefficients of A1q, the ATP influence coefficient, and we have fixed 2q = 0.01 which represents the influence coefficient value of NADH .First, we have considered as control parameter 1q≤0.9 both subsystems are active and the two subsystems exhibit one periodical activity. Some of the values of the amplitude and oscillatory frequencies are shown below:After the numeric integration of the DMN it can be observed that for 0.1≤1q = 0.1 (MSb1) A0 = 0.3085, A = 0.3614 and ω = 0.3457.0 = 0.3477, A = 0.3290 and ω = 0.3429.   (MSb2) A1q = 0.5 (MSb1) A0 = 0.3779, A = 0.4366 and ω = 0.4187.0 = 0.3168, A = 0.2994 and ω = 0.3252.   (MSb2) A1q = 0.9 (MSb1) A0 = 0.4360, A = 0.4994 and ω = 0.4847.0 = 0.2904, A = 0.2729 and ω = 0.3049.   (MSb2) AWhen the inhibition provoked by the ATP descends  the activity of the MSb1 increases as well as the contribution of NADH and as a consequence of it the activity of the MSb2 descends.2p as control parameter, the NADH influence coefficient, and we have fixed the ATP influence coefficient value (1q = 0.01). This 1q value represents a strong inhibition of the pyruvate dehydrogenase complex due to high levels of the energy-rich end product of the tricarboxylic acid cycle and oxidative phosphorylation. Under these parametric conditions the metabolic network can present different dynamic behaviors for 2q values.We have considered now 2q ranges from 0.1 to 0.87, both subsystems are active and exhibit a single periodical activity. For example:When 2q = 0.1 (MSb1) A0 = 0.2918, A = 0.3331 and ω = 0.3205.0 = 0.3536, A = 0.3547 and ω = 0.3626.   (MSb2) A2q = 0.5 (MSb1) A0 = 0.2783, A = 0.2987 and ω = 0.2946.0 = 0.3838, A = 0.4225 and ω = 0.4119.   (MSb2) A2q = 0.87 (MSb1) A0 = 0.2684, A = 0.2859 and ω = 0.2825.0 = 0.4063, A = 0.4476 and ω = 0.4394.    (MSb2) A2q = 0.1 the two subsystems are strongly inhibited and both show a low activity. When increasing 2p values (0.1<δ≤0.87) the inhibition provoked by the NADH decreases and as a consequence of it the activity of the MSb2 is increased and the MSb1 activity diminishes due to the increment in the production of ATP.As it can be observed, for 2q≤1 the two subsystems undergoes a variation of the oscillatory evolution, emerging very complex transitions and the output activity of the both subsystems make uninterrupted transitions between more of 200 different kinds of periodic oscillations.For 0.87<Under experimental conditions, the complex temporal structure in Krebs cycle has been observed In the network the two metabolic subsystems remain always active for all the parametric conditions studied.on-off changeable regime we carried out experimental observations of intracellular calcium oscillations in Xenopus laevis oocyte.In order to study chaotic oscillations in a subsystem with an Xenopus laevis frogs were obtained from Blades Biological . Oocytes at stageV were plucked from the ovaries and defolliculated by treatment with collagenase  at 80–630 units/ml in frog Ringer's solution  for 20 min to remove the surrounding follicular and epithelial cell layers. Oocytes were maintained at 18°C in Barth's solution 2, 0.41 mM CaCl2, 0.82 mM MgSO4, 5 mM HEPES at pH 7.4+gentamicin 70 µg/ml).Laboratory-reared Membrane currents were recorded with a standard two-electrode voltage clamp  and digitized in a PC computer . Oocytes were continually superfused with Ringer's solution at room temperature (∼22°C).The membrane was usually voltage clamped at −60 mV. Fetal Bovine Serum (FBS) (Sigma-Aldrich) diluted 1∶1000 in Ringer solution were perfused to achieve the generation of voltage oscillations.


There is therefore a need to develop a method which is capable of automatically transforming ARL kinetic information into more detailed MRL rate constants.As computational performance steadily increases, so does interest in extending one-particle-per-molecule models to larger physiological problems. Such models however require elementary rate constants to calculate time-dependent rate coefficients under physiological conditions. Unfortunately, even when E. coli glycolytic pathways. The simulation and statistical results show that our innovative method performs well in dealing with the issues of high computation cost, stiffness, local minima and uncertainty inherent with large-scale non-convex nonlinear MRL models.By incorporating proteomic data related to enzyme abundance into an MRL modelling framework, here we present an efficient method operating at a global network level for extracting elementary rate constants from experiment-based aggregated rate law (ARL) models. The method combines two techniques that can be used to overcome the difficult properties in parameterization. The first, a hybrid MRL/ARL modelling technique, is used to divide the parameter estimation problem into sub-problems, so that the parameters of the mass action rate laws for each enzyme are estimated in separate steps. This reduces the number of parameters that have to be optimized simultaneously. The second, a hybrid algebraic-numerical simulation and optimization approach, is used to render some rate constants identifiable, as well as to greatly narrow the bounds of the other rate constants that remain unidentifiable. This is done by incorporating equality constraints derived from the King-Altman and Cleland method into the simulated annealing algorithm. We apply these two techniques to estimate the rate constants of a model of In short, this new hybrid method can ensure the proper solution of a challenging parameter estimation problem of nonlinear dynamic MRL systems, while keeping the computational effort reasonable. Moreover, the work provides us with some optimism that physiological models at the particle scale can be rooted on a firm foundation of parameters generated in the macroscopic regime on an experimental basis. Thus, the proposed method should have applications to multi-scale modelling of the real biological systems allowing for enzyme intermediates, stochastic and spatial effects inside a cell. As systems biology matures, it is moving away from static representations of network interactions based on nodes and edges to dynamic representations that describe cellular processes in space and time. Dynamic metabolic processes are quantitatively modelled with ordinary differential equations (ODEs) in two principle ways: the aggregated rate law  and massDynamic metabolic networks are predominately modelled using aggregated rate laws (ARL). An ARL simplifies the description of a single enzymatic step by aggregating the elementary steps associated with a specific mechanism into a single reaction, where the rate becomes a non-linear function of substrate, product and regulator concentrations and a typically linear function of enzyme concentration. The classical example of an ARL treatment is the Michaelis-Menten equation for the simplest irreversible reaction, the Uni-Uni mechanism. ARL models are not always derived from an underlying mechanism, and in some cases, more phenomenological formulas are adopted to empirically fit experimental data. While the simplified treatment of enzyme kinetics using an ARL-based approach has obvious appeal when attempting to model large metabolic networks, such a reduction of the underlying mechanism inevitably leads to a loss of some useful information about the reaction mechanism, e.g. the sequence of elementary reactions, dynamics of all enzyme intermediates, and so on. ARL models are therefore equipped to capture biological processes on long time scales wherein dynamics of enzyme intermediates can be ignored. To date most experimentally determined kinetic parameters are at this level.An alternative to the ARL approach is the direct use of mass action rate laws (MRL), each of which states that the rate of an elementary reaction is directly proportional to the product of the effective concentrations of each participating molecule. By definition, MRL models involve the sequence of elementary reactions as well as track dynamics of all of the elements by describing the formation and degradation of all species in an enzymatic reaction. It is particularly suitable for modeling molecular events that happen on the microsecond to millisecond time-scale ,4.Regardless of the approach taken, good models of cellular systems are often guided by a pragmatic principle: a model should be as simple as possible, but as complex as necessary. The growing necessity of dealing with complexity is however highlighted by the apparent behavioural differences exhibited by biomolecules within an intracellular environment versus the test tube . These dAs a consequence of its higher level of detail, the MRL approach is starting to receive special attention for the elucidation of complex biological systems -14. To din vitro over a range of conditions. This lack of biological context calls into question the relevance of network models based on these parameters in describing complex cellular behaviour under physiological conditions. One other limitation is that it is not always possible to uniquely determine the rate constants from existing ARL rate constants, when: 1) the number of MRL parameters is large, 2) there is a redundancy of values among ARL kinetic constants or 3) there are technical difficulties in solving nonlinear equations. Moreover, use of SMKA/GRC method alone is not able to deal with empirical ARL equations where some kinetic constants are missing or reduced to empirical constants.The classic approach combines the Schematic Method of King and Altman  with thein vitro kinetic data  involves a rapid equilibrium approximation that assumes that reactants, free enzymes and enzyme-bound intermediates reach equilibrium quickly relative to the rate of catalysis. The approach to steady-state can be controlled in the model by using large, time-invariant constant numbers (Λ and Ω) that are associated with enzyme-substrate and enzyme-inhibitor binding reactions, respectively. When compared with SMKA/GRC, this approximation method is based on fewer kinetic constants and simpler algebraic relations, leading to easier mathematical manipulations. It does however suffer from limitations such as the existence of trimolecular association reactions that are physiologically improbable (e.g. the enzyme can interact simultaneously with two substrates in a Bi Bi mechanism) and the inherent ambiguity imposed by the dependence of the rate constants on arbitrary values of Λ and Ω.Recently, Yang et al.  have proin vivo rate constants means that the optimization algorithm is easily trapped by local minima  and The validity of the MRL assembly was tested by comparing transient dynamic responses after a glucose impulse with those of the original ARL network. The stability of the model was evaluated by the eigenvalues of the Jacobian matrix (A). While A is a complete 18 × 18 matrix for the ARL network of 18 species, a reduced 36 × 36 Jacobian matrix can be implemented for the MRL network of 45 species, due to the removal of 9 dependent species as a result of the conservation relations for enzyme forms. The Jacobian matrix (A) at the steady state can be calculated for an n-dimensional dynamical system, where u satisfy the characteristic equation of the matrix AThe eigenvalues u of degree n, and I is the identity matrix. By the Fundamental Theorem of Algebra, this equation has n solutions. If all the eigenvalues of A have negative real part then the steady states of all species are stable. The time constant, which indicates how fast a deviation from a given steady state will decline, is defined as the reciprocal absolute values of the real parts of the eigenvalues [Eqn. (5) is a polynomial equation in envalues . In addipfkA) via non-integral reaction orders, thereby breaking from the pure elementary reaction schema, but maintaining the type of bimolecular reactions  are confined within a relatively small parameter space, which is based on mechanistic analysis and time-consuming trial-and-error testing. Bacterial pfkA enzyme has been found to be inhibited by PEP as a result of interaction at an allosteric site [-1 s-1, 5000 mM-1 s-1, 1000 s-1 and 1000000 s-1 for k1, k2, k3 and k4, respectively, and the backward rate constants are confined within 100 s-1 and 2000 s-1 for k-1 and k-2, respectively. The upper boundaries were further verified by random testing, where parameters out of the preset ranges appeared unable to reach a satisfactory cost function value.Parameters for phosphofructokinase  toolboxes  were usearoH – DAHP synthase (EC 2.5.1.54), eno – Enolase (EC 4.2.1.11), fba – Fructose-bisphosphate aldolase (EC 4.1.2.13), gapA – Glyceraldehyde 3-phosphate dehydrogenase (EC 1.2.1.12), glgC – Glucose-1-phosphate adenylyltransferase (EC 2.7.7.27), gnd - 6-phosphogluconate dehydrogenase (EC 1.1.1.44), gpsA – Glycerol 3-phosphate dehydrogenase (EC 1.1.1.94), pdhA – Pyruvate dehydrogenase (EC 1.2.4.1), pfkA – Phosphofructokinase (EC 2.7.1.11), pgi – Phosphoglucoisomerase (EC 5.3.1.9), pgk – Phosphoglycerate kinase (EC 2.7.2.3), pgm – Phosphoglycerate mutase (EC 5.4.2.1), pgm1 – Phosphoglucomutase (EC 5.4.2.2), ppc – Phosphoenolpyruvate carboxylase (EC 4.1.1.31), prs – Ribose phosphate pyrophosphokinase (EC 2.7.6.1), pykF – Pyruvate kinase (EC 2.7.1.40), rpe – Ribulose phosphate epimerase (EC 5.1.3.22), rpi – Ribose phosphate isomerase (EC 5.3.1.6), talA – Transaldolose (EC 2.2.1.2), tktA – Transketolase a (EC 2.2.1.1), tktB – Transketolose b (EC 2.2.1.1), tpiA – Triosephosphate isomerase (EC 5.3.3.1), zwf – Glucose-6-phosphate dehydrogenase (EC 1.1.1.49). The following abbreviations are used for metabolites: DHAP – Dihydroxyacetonephosphate, E4P – Erythrose-4-phosphate, F6P – Fructose-6-phosphate, FDP – Fructose-1,6-bisphosphate, G1P – Glucose-1-phosphate, G6P – Glucos-6-phosphate, GAP – Glyceraldehyde-3-phosphate, GLC – Glucose, PEP – Phosphoenolpyruvate, PG – 6-phosphogluconate, PG2 – 2-phosphoglycerate, PG3 – 3-phosphoglycerate, PGP – 1,3-diphosphoglycerate, PYR – Pyruvate, Rib5P – Ribose-5-phosphate, Ribu5P – Ribulose-5-phosphate, Sed7P – Sedoheptulose-7-phosphate, Xyl5P – Xylulose-5-phosphate. Other abbreviations are: ARL – Aggregated Rate Law, CI – Confidence Interval, CV – Coefficient of Variation, fval – Cost Function Value, GRC – General Rules of Cleland, MEX – MATLAB Executable Files, MRL – Mass Action Rate Law, NSO – Numerical Simulation and Optimization, ODE – Ordinary Differential Equation, PBS – Particle Based Simulation, QSSA – Quasi Stationary State Assumption, RE – Relative Errors compared to 0% noise case, SD – Standard Deviation, SMKA – Schematic Method of King and Altman.The following abbreviations are used for individual enzymes: JZ and ME conceived and designed experiments. JZ developed computer programs and performed the numerical experiments. JZ and DR analyzed the data. JZ, DR, GB, AK and ME wrote the paper.gapA. A.2. Allosteric regulation for pykF. A.3. Allosteric regulation for pfkA. A.4. Ordered Uni-Bi mechanism for fbaA.5. Reversible Uni-Uni mechanism for pgiAdditional file 1 . A.1. Ordered Bi-Bi mechanism for Click here for file


Dehalococcoides strains respire a wide variety of chloro-organic compounds and are important for the bioremediation of toxic, persistent, carcinogenic, and ubiquitous ground water pollutants. In order to better understand metabolism and optimize their application, we have developed a pan-genome-scale metabolic network and constraint-based metabolic model of Dehalococcoides. The pan-genome was constructed from publicly available complete genome sequences of Dehalococcoides sp. strain CBDB1, strain 195, strain BAV1, and strain VS. We found that Dehalococcoides pan-genome consisted of 1118 core genes , 457 dispensable genes (shared by some), and 486 unique genes (found in only one genome). The model included 549 metabolic genes that encoded 356 proteins catalyzing 497 gene-associated model reactions. Of these 497 reactions, 477 were associated with core metabolic genes, 18 with dispensable genes, and 2 with unique genes. This study, in addition to analyzing the metabolism of an environmentally important phylogenetic group on a pan-genome scale, provides valuable insights into Dehalococcoides metabolic limitations, low growth yields, and energy conservation. The model also provides a framework to anchor and compare disparate experimental data, as well as to give insights on the physiological impact of “incomplete” pathways, such as the TCA-cycle, CO2 fixation, and cobalamin biosynthesis pathways. The model, referred to as iAI549, highlights the specialized and highly conserved nature of Dehalococcoides metabolism, and suggests that evolution of Dehalococcoides species is driven by the electron acceptor availability. Dehalococcoides are strictly anaerobic bacteria capable of detoxifying widespread and harmful ground water pollutants — chlorinated ethenes, chlorinated benzenes, polychlorinated biphenyls and dioxins — largely originated from industry and agriculture sectors. However, how this unique niche has been acquired by these microbes is not well understood, specifically at the level of metabolism. In addition, these bacteria harness energy from the pollutant detoxification process — reductive dechlorination — for their growth; but they grow very slowly. Their slow growth rate, as well as their low growth yield, can hamper bioremediation processes. Thus, in order to obtain an improved understanding of Dehalococcoides' metabolism and the factors limiting their growth, we developed a constraint-based metabolic model of Dehalococcoides from publicly accessible genome sequences of 4 strains. This model, in addition to creating a valuable knowledgebase on Dehalococcoides, offers researchers in the bioremediation community a valuable tool for generating experimentally testable hypothesis for improving the efficacy of bioremediation by Dehalococcoides. Dehalococcoides, or any other known dechlorinating bacterium.Genome sequencing has enabled the characterization of biological systems in a more comprehensive manner. Recent research in bioinformatics and systems biology has resulted in the development of numerous systematic approaches for the analysis of cellular physiology that have been reviewed elsewhere Dehalococcoides are capable of dehalogenating a variety of halogenated organic compounds as electron acceptors, of which many are problematic ground water pollutants Dehalococcoides ethenogenes strain 195 (strain 195) is the first member of this phylogenetic branch that was grown as an isolate Dehalococcoides strains were isolated: strain CBDB1 rdh) genes, are pivotal membrane-associated enzymes of the ETC rdh genes in each strain rdh genes determine a significant part of Dehalococcoides' phenotypes. Functional characterization of only 5 of the over 190 rdh genes reveals that cobalamin — a corrinoid compound — is an essential cofactor for the corresponding RDases 2ase) is another key enzyme of Dehalococcoides ETC Dehalococcoides strains encode 5 different types of H2ases: membrane-bound hup, ech, hyc, hym, and cytoplasmic vhu2ases clearly emphasizes the importance of H2 in their energy metabolism 2ases and RDases further highlights redundancy in the organisms' energy conservation process that may ensure a rapid and efficient response of their energy metabolism towards changing growth conditions Using acetate as a carbon source and hydrogen as an electron donor, small, disc-shaped anaerobic bacteria 2ase, the ETC likely requires an in vivo electron carrier to mediate electron transport between these enzymes. Previous studies have shown that the reductive dechlorination reaction requires an in vivo electron donor of redox potential (E0′) ≤−360 mV 0′) of Co(II)/Co(I) couple is between −500 and −600 mV Dehalococcoides0′ = −70 mV, Ubiquinone ox/red E0′ = +113 mV; DehalococcoidesIn addition to RDase and HDehalococcoides are capable of harnessing free energy from the RDase catalyzed exergonic reductive dechlorination reactions by coupling to ATP generation for growth Dehalococcoides genomes are more than 85% identical at the amino acid level in silico metabolic model of Dehalococcoides. The model was constructed from the complete genome sequences of 4 geographically distinct strains: strain CBDB1 from the Saale river near Jena, Germany Dehalococcoides regulatory networks. Nonetheless, the model was primarily used to investigate the intrinsic metabolic limitations, in addition to addressing open questions regarding Dehalococcoides physiology, such as the incomplete nature of various metabolic pathways, and attendant implications on metabolism and growth. We also identified the environmental conditions from the model simulations that resulted in faster in silico growth of Dehalococcoides. Furthermore, the constraint-based model, along with the comparative analysis of 4 genomes, clarifies both similarities and differences among the strains in terms of their core metabolism and other biosynthetic processes leading to an improved understanding of metabolism and evolution in Dehalococcoides.Although, Streptococcus agalactiaeDehalococcoides pan-genome from the complete sequenced genomes of four Dehalococcoides strains. Method details are provided in the Dehalococcoides. Genes that are involved in DNA repair and metabolism, as well as encoding putative transposable elements and insertion elements The concept of a pan-genome was first investigated by Tettelin and colleagues for the 8 isolates of common human pathogen Dehalococcoides is very well conserved across strains since core genes are shared by all rdh genes  were found in the core genome while only a small number of those were identified in the dispensable (75) and unique (61) genomes. This abundance of core metabolic genes in the pan-genome indicate that the central metabolism of dh genes . In addirdh genes, most of these were found in the dispensable genome  were shared by all strains and found in the core genome  are provided in The reconstructed metabolic network of iAI549 includes 518 model reactions and 549 metabolites where 497 reactions are gene associated and 21 (4%) are non-gene associated  are core, which again indicates that the basic central metabolism of Dehalococcoides is strictly conserved  and the molybdate (required for synthesizing cofactor for the nitrogenase) transport reaction (TC-3.A.1.8) belonging to strain 195 only.sociated . The nonsociated  were addsociated  which poiAI549 to a number of in silico genome-scale models of other Bacteria and Archaea  are more versatile in their lifestyle and metabolism compared to obligate anaerobes . These differences are further supported by the presence of a high number of transporters in iAF1260 and iYO844 compared to the presence of only 32 transporters in iAI549 , and fumarate reductase/succinate dehydrogenase (with 31–33% amino acid sequence identity to the E. coli gene)  and yield (0.72 gDCW/eeq vs. 0.71 gDCW/eeq) was observed  — which produces oxaloacetate from pyruvate  enzyme encoded by 4 putative Dehalococcoides genes  is from extracellular acetate through acetyl-CoA synthetase  encoded by 4 putative genes of 12 is essential for RDase activity; however, the pathway for producing cobalamin is incomplete in Dehalococcoidesde novo biosynthesis (aerobic or anaerobic) of vitamin B12 requires around 30 genes Dehalococcoides. Seven (7) of these genes belong to the “anaerobic” pathway while 2 are found to be involved in the “aerobic” pathway of cobalamin biosynthesis. Several key enzyme encoding genes required for the precorrin ring formation, cobalt insertion, and methylation were not found in Dehalococcoides genomes  Dehalococcoides growth rate as a function of weight fraction of cobalamin in the biomass and cobalamin salvage rate from the medium  compared to the yield when B12 is salvaged from the medium  e medium . Predicte medium . Also, toccoides . From thdentical . Only ifDehalococcoides is more rapid in mixed microbial communities than in pure cultures Dehalococcoides growth yields under two different conditions: 1) allowing unlimited flux of amino acids in the medium at a hydrogen flux of 10 mmol.gDCW−1.h1  without allowing any amino acid flux in the medium. The first condition mimics a carbon-rich environment while the second one represents an energy-rich situation. The model predicts that adding unlimited amount of any or all of the amino acids in the growth medium (obviating the need for the cell to synthesize these amino acids) increased the growth yield by a maximum of 55% (1.13 gDCW/eeq) compared to the case with no amino acids in the medium (0.72 gDCW/eeq) (Growth of DCW/eeq) . HoweverDCW/eeq) .in silico growth yields of Dehalococcoides as a function of both acetate flux (carbon availability) and energy flux, represented by the energy transfer efficiency. This analysis  compared to 65% efficient (corresponding to the red arrow) in a mixed culture  while strain 195 and strain BAV1 genome sequences were downloaded from the IMG database (http://img.jgi.doe.gov/cgi-bin/pub/main.cgi). Strain VS genome sequence was obtained from Alfred Spormann at Stanford University, CA. The genome sequences were compared using OrthoMCL Dehalococcoides pan-genome was developed following a previously described approach In order to develop the pan-genome of Dehalococcoides pan-genome in order to capture the entire gene repertoire of Dehalococcoides species Dehalococcoides pan-genome using methods described previously First, we identified putative orthologs between a reference genome and a subject genome which were selected arbitrarily from the 4 genomes compared. The analysis was conducted by OrthoMCL keeping the parameters of the algorithm in default settings. Subsequently, those genes that were present only in subject genome 1 were identified and combined with the reference genome to create the augmented genome 1 /g DCW (dry cell weight)  of 1 gram of Dehalococcoides cell (1.8 mmol ATP.gDCW−1.h−1) was calculated from the experimental decay rate (0.09 day−1) −1; Table 26 in Maintenance energy accounts for the ATP requirements of cellular processes, such as turnover of the amino acid pools, polymerization of cellular macromolecules, and ion transport, which are not included in the biomass synthesis reaction −), carbondioxide (CO2), sulphate (SO4−2) etc., to represent the in silico minimal medium   is presented as Flux Balance Analysis (FBA) relies on the imposition of a series of constraints including stoichiometric mass balance constraints derived from the metabolic network, thermodynamic reversibility constraints and any available enzyme capacity constraints l medium  for DehaDataset S1Dehalococcoides Metabolic Model, iAI549.SBML File for (0.48 MB XML)Click here for additional data file.Text S1Dehalococcoides pan-metabolic-model, iAI549. Tables 3–7 are gene correspondences where a unique gene number is provided for each gene in the model (Model gene number) so that a gene or corresponding reaction can be located conveniently irrespective of the 4 genomes of interest. Strain VS gene locus names are obtained from Alfred Spormann at Stanford University, CA. A reaction can be associated with more than one gene where some genes are core, some are dispensable and others can be unique. For such instances, 2 additional gene correspondence tables (Table 5 and Table 7) are created for dispensable and unique genes respectively.This file contains the detailed list of genes, proteins, reactions and metabolites included in the (5.41 MB PDF)Click here for additional data file.Text S2Dehalococcoides cell, experimental values of various pan-model parameters and the detailed procedure to calculate those parameters, as well as supplemental text regarding energy conservation process of Dehalococcoides. In addition, all the supplemental figures are included at the end of this document.This file contains the tables of detailed macromolecular composition of a gram of (0.31 MB PDF)Click here for additional data file.


A wide range of research areas in molecular biology and medical biochemistry require a reliable enzyme classification system, e.g., drug design, metabolic network reconstruction and system biology. When research scientists in the above mentioned areas wish to unambiguously refer to an enzyme and its function, the EC number introduced by the Nomenclature Committee of the International Union of Biochemistry and Molecular Biology (IUBMB) is used. However, each and every one of these applications is critically dependent upon the consistency and reliability of the underlying data for success. We have developed tools for the validation of the EC number classification scheme. In this paper, we present validated data of 3788 enzymatic reactions including 229 sub-subclasses of the EC classification system. Over 80% agreement was found between our assignment and the EC classification. For 61  reactions we found that their assignment was inconsistent with the rules of the nomenclature committee; they have to be transferred to other sub-subclasses. We demonstrate that our validation results can be used to initiate corrections and improvements to the EC number classification scheme. The fundamental understanding of metabolism in organisms which can only be achieved by integrated studies on their biology using a systems biology approach will aid in the design of future metabolic engineering strategies. Metabolic network reconstruction provides insight into the molecular mechanisms of a particular organism. An annotated genome containing the specific metabolic genes found in a particular organism can be used to reconstruct its metabolic network. The correlation between the genome and metabolism is made by searching gene databases or by searching protein databases with a known EC number in order to find the associated gene. The success of the search process is critically dependent upon the consistency and reliability of the underlying data. Therefore we have developed tools which can be used to identify wrong or inconsistent classification of enzymes and help to remove them from the relevant search databases. With the several thousand proteins found in each organism a highly developed hierarchical and consistent classification scheme is absolutely essential for a comparison of metabolic capacities of the organisms. Unfortunately such a system exists only for the enzymes and not for the other protein classes but for the enzymes the classification scheme allows an immediate access or the enzyme functional properties including catalysed reaction, substrate specificity, etc. In this respect a quick comparative assessment of enzymatic pathways between organisms is possible even when the enzymes in the different organisms have totally different sequences as long as they belong to the same EC-class. A well reconstructed metabolic network provides a unified platform to integrate all the biological and medical information on genes, enzymes, metabolites, drugs and drug targets for a system level study of the relationship between metabolism and disease. Therefore an accurate representation of biochemical and metabolic networks by mathematical models is one of the major goals of integrative systems biology. Metabolic networks have been constructed for a number of genomes The objective of the study was the automatic assignment of reactions to the EC number classification system. The approach is designed to adapt the EC number classification system as closely as possible. Therefore in most cases the results corresponds to the given sub-subclass by the IUBMB, but it some cases it differs from the established classification. We decided to subdivide the results into nine different subsets.As shown in + or NADP+ as acceptor’, but it can also be assigned the sub-subclass 1.2.1 which covers enzymes ‘Acting on the aldehyde or oxo-group of donors, with NAD+ or NADP+ as acceptor’.A reaction catalysed by pyridoxal 4-dehydrogenase represents an example of subset 3 . This en+ or NADP+ as acceptor which corresponds to sub-subclass 1.3.1 as it is defined by the NC-IUBMB. The transfer of the EC Number of 1.1.1.158 into sub-subclass 1.3.1 issued on our initiative is already accepted by the IUBMB. The other 60 errors have also been reported to the IUBMB and are currently under examination.Subset 4 contains enzymes where the assignment is definitely inconsistent assigned with the NC-IUBMB rules . For exaCholine oxidase (EC 1.1.3.17) an example of subset 5 of our results is a bifunctional enzyme which catalyses two different kinds of reactions. The overall reaction shown is The subset 6 involves all enzymes catalysing reactions which are identified as unclear assignement. The reaction shown in An example for subset 7 is shown in Subset 8 is composed of enzymes which could not be clearly assigned to any defined sub-subclass. For example the trimethylamine dehydrogenase is assigned to sub-subclass 1.5.8 which contains enzymes ‘Acting on the CH-NH group of donors,with a flavin as acceptor’, but as shown in In subset 9 we have summarized enzymes where the assignment to a subclass is not unequivocally determined by the chemical reaction given. The reaction ATP + H2O = ADP + phosphate as shown in Our approach has been used for the classification of 3788 enzymatic reactions including 229 sub-subclasses of the EC classification system. We demonstrated that enzyme-catalysed reactions can be classified efficiently and reliably by our approach. Furthermore, reactions can be assigned even if full characteristics of enzymes are not known. Moreover we have shown that this method can be used to identify wrong or inconsistent classification of enzymes and help to remove them.With one of the authors being the present chairman of the NC-IUBMB it is planned to use this and related tools to identify and remove errors and inconsistencies in the current EC-system and to optimise the system in a transparent and stable way. We plan to develop a tool that assign EC sub-subclasses to new reactions, access to which will be provided to the scientific community in the Internet’.We used 3,788 different enzyme-catalysed reactions from an in-house-developed Database named BiReDa . The database held exclusively error-free MDL/MOL files as well as stoichiometrically and stereochemically correct reaction data from the BRENDA Database The key idea of this approach is to reproduce the classification system given by the IUBMB as closely as possible and not to create new classification rules. The underlying procedure is divided into two steps:The chemical similarity calculationIn order to identify the corresponding partners within a biochemical reaction every atom of each compound is coded as follows:sCCCOOOHNNNSSSPPPRRRAsAsAsMMMXXXcwhere ‘s’ is the symbol of the corresponding element of the given atom and each other letter represents the symbols of the connected atoms except for a few exceptions: ‘R’ stands for any rest, ‘M’ represents any metal ion, ‘X’ is any halogen and ‘c’ is the charge of the considered atom. In most cases there are three entries for each symbol: e.g. ‘CCC’, the first position represents the number of carbon atoms connected via a single bond, the second the number of atoms connected via a double bond and the third the number of atoms connected via a triple bond with the given atom. In the case of ‘H’ only one placeholder is needed because hydrogen forms only single bonds. A few examples of complete atom coding operators are shown in In addition to the atoms which are affected in the enzyme-catalyzed reactions, the bonds cleaved have to be identified. This in particular is necessary for the lyases which catalyzes the breakage of a carbon-oxygen, carbon-carbon or carbon-nitrogen bond in non-oxidative manner .Therefore each bond is coded as follows:For the scoring scheme describing the similarity between each substrate and product molecule the Tanimoto Coefficient was used ‘a’ is the sum of the number of atom-types and bond-types which have the same frequency of occurrence in both the given substrate and the given product.‘b’ is the number of atom-types and bond-types which have a higher frequency of occurrence in the given substrate than in the corresponding product molecule.‘c’ is the number of atom-types and bond-types which have a lower frequency of occurrence in the given substrate than in the corresponding product molecule.‘T’ is the Tanimoto coefficient which lies between 0 for unequal and 1 for identical molecules.As a result we obtain a list of substrate/product pairs sorted according to their similarity.The characterization of the individual reactionAt the beginning compounds of known substrate/product pairs see , which aIn this step the atom coding operators generated during chemical similarity calculation (Step 1) are used to identify the important molecular functional groups responsible for the characteristics of each biochemical reaction.As an example a carboxilic acid is shown in 2+ and Fe3+ the charge of the iron atom has to be taken into account too  is shown in on steps . As a reon steps , countedon steps  and elemon steps  and finaon steps . The aboTable S1Wrong assigned EC Numbers and new suggested Sub-Sub-Classes. Contains enzymes which were definitely wrong assigned by the NC-IUBMB.(0.02 MB DOC)Click here for additional data file.