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Chemical Engineering at the Cellular Scale: Cellular Signal Processing J. Krishnan*,†,‡ †
Chemical Engineering and Chemical Technology, Centre for Process Systems Engineering and ‡Institute for Systems and Synthetic Biology, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K. ABSTRACT: There has been a considerable effort in the past decade to understand different aspects of cellular processes from both a reverse engineering and, more recently, a synthetic perspective. In this article I provide a perspective on aspects of cellular signal processing which involve traditional chemical engineering elements (reactions, transport, control) and their variants, along with additional ingredients, sometimes combined in unusual ways. I also compare and contrast certain basic aspects of chemical engineering and cellular signal processing in areas of mutual overlap.
1. INTRODUCTION In the past decade there has been a huge surge of activity directed toward understanding biological processes from a quantitative perspective. This is generally described by the phrase “Systems Biology” which has as a focus the understanding of cellular (both intracellular and intercellular) processes. The application of quantitative approaches in biological systems is not new, and indeed there has been a fair amount of work in previous decades on applying quantitative and systems approaches in biological and especially physiological phenomena. A successful example of this is the work of Hodgkin and Huxley in the 1950s. However the use of quantitative approaches in understanding cellular processes through collaborative efforts has become much more widespread in the past decade. In the more recent past there has been another surge in interest in trying to engineer cells for particular purposes, under the umbrella of “Synthetic Biology”, with the promise that this might lead to the tackling of many substantial challenges ranging from bioenergy to health care and beyond. Indeed grand claims about this being the harbinger of a new “industrial revolution” are being made. Both systems and synthetic biology ultimately deal with cellular processes and the various aspects of information flow in these systems which are primarily encoded in chemical terms. This information flow which occurs in chemical networks, results in the regulation/interconversion of key molecular species, which in turn control a variety of processes. Complex chemical networks inside cells are responsible for various processes ranging from growth, division, movement, metabolism, communication, etc. In both systems and synthetic biology, the role of engineering approaches to understand and exploit these processes are recognized, and indeed a range of engineering communities are involved in these areas. Chemical engineering has a long tradition of work in the biological area ranging from basic cellular to biomedical to industrial aspects. Indeed many subjects which form the foundation of chemical engineering including reaction engineering, transport phenomena, thermodynamics, systems engineering along with modeling, computation, and the general engineering training find natural use in understanding or exploting biological processes. r 2011 American Chemical Society
In this paper I will discuss certain aspects of cellular processes —primarily cellular signal processing—which have been to a fair extent outside the focus of chemical engineering efforts. As mentioned, many aspects of cellular processes include the flow of information which occurs through chemical reactions and transformations, and it may be expected that these problems may be dealt with in chemical engineering terms. However there are also a number of characteristic ingredients/aspects which are fundamentally new, and additionally even traditional ingredients are combined in different ways. I will briefly discuss a number of these cases to demonstrate this and focus exclusively on intracellular processes. Overall, the goal of this paper is to provide a focused perspective on some relevant issues.
2. THEMES AND EXAMPLES In this section, I will discuss a number of themes and examples and discuss their connection with and differences from standard chemical engineering examples and features. To do this, I will present examples from three perspectives: reactions and reaction engineering, transport processes, and control. All three topics deal with the dynamic aspects of chemical intracellular communication. Certain issues related to modeling are discussed subsequently. The examples will all focus on cellular processes with a strong chemical character, and thus we will not examine cases, interesting though they are, such as cell mechanics. Additionally we will not examine methodological and algorithmic issues as well as data processing. It is worth emphasizing that the focus will be on fundamental aspects and basic themes. These aspects repeatedly occur in different cellular processes and apart for illustration purposes we will not discuss any specific processes in detail. 2.1. Reactions. One of the key points of focus in cellular processes is how cells orchestrate various processes in the cell and also how they respond to various kinds of cues (chemical, mechanical, electrical) in their environment. Ultimately in order Special Issue: Ananth Issue Received: February 15, 2011 Accepted: June 2, 2011 Revised: May 27, 2011 Published: June 02, 2011 13236
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Industrial & Engineering Chemistry Research to understand both these issues, one has to understand the ways in which cells receive and process signals to make decisions, and this is done via complex networks of proteins and genes, which are intricately organized. Such networks typically get much more complex as one progresses from prokaryotes (such as bacteria) to eukaryotes. Ultimately most of these processes are chemical reactions/transformations. There is of course a considerable amount of work in analyzing complex metabolic networks, etc., but our focus will be on cellular signal processing and its dynamic aspects. The focus in understanding the chemical signal processing is not primarily in terms of the kinetics of an individual reaction or the enzymatic mechanism per se (important though they are), but more on how they act to process and convert chemical information. Thus a focal point has been on trying to understand how small (and not so small) networks of reactions may act as characteristic information processors, both static and dynamic. Accordingly the focus has been to understand some ubiquitously occurring signal processing behavior. This understanding has been used to elucidate how such signaling behavior occurs in concrete cellular signaling pathways/contexts/applications though we will not discuss that here. One of the most basic descriptions of chemical reactions is the conversion of a protein from an inactive form to an active form. The reaction is typically reversible and the forward (or reverse) reaction is mediated by an enzyme which controls this reaction. Since the enzyme may be controlled by upstream or external signals, this is a very basic example of chemical information transfer. While this is a simple example, some additional variations can be added to this structure to give rise to nontrivial signal processing. Monostable Switches. If one examines a simple reversible reaction, mediated by two enzymes, with for instance the enzyme regulated by the forward reaction being regulated by some upstream signal, then some nontrivial signaling behavior can emerge with just minimal additional features. Thus if both the forward and reverse enzymatic reactions are described by Michaelis Menten kinetics, and further both act close to saturation, we see that both forward and backward reactions are essentially zero order reactions for a wide range of substrate concentrations. This being the case, we see that the net reaction will progress essentially (though not exactly) to conclusion in the forward or backward reaction depending on the relative concentrations of the two enzymes. Thus we immediately see that if for example the enzyme catalyzing the forward reaction is positively regulated by an upstream signal, a sharp transition is seen in the output, as the upstream signal crosses a threshold. Thus this simple chemical reaction functions in what is referred to as an ultrasensitive way and is an example of a simple chemical reaction whose steady state output is essentially binary. It should also be mentioned that such a switch is completely reversible, and when the upstream signal declines below a threshold, the switch is turned off. This is an example studied by Goldbeter and Koshland.1 Another way in which sharp switch-like behavior may be realized in simple chemical networks is embodied in the socalled MAP kinase pathway. This is an example of a cascade of three reversible reactions, where the output of the reaction at each stage acts to catalyze the reaction at the next stage. The upstream signal catalyzes the first reaction, and the output of this system is the product in the final reaction stage. All reactions are described by Michaelis Menten kinetics. An analysis of this system also shows that this system of cascaded reactions acts as a
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sharp switch, which is again completely reversible. Importantly the sharp switching behavior arises from the cascading effect with no individual reaction by itself acting as a sharp switch.2 The effect of having multiple reactions in the cascade, is to sharpen the steady state input output curve, but this happens along with the slowing down of the signal propagation. This has particular implications for how time varying signals are processed in this network. There are other examples of such switches, but we now examine a different class of switching mechanisms. Bistable Switches. Bistable switches in biological networks are examples of irreversible (or partially irreversible) switches and hence have been used to model irreversible or partially irreversible behavior. These switches again have the switch-like feature of possessing a threshold, but instead possess the important additional feature of being irreversible. These switches arise typically in biological networks through positive feedback with the product of a reaction directly or indirectly aiding its own production.3 The positive feedback could also arise through a double negative feedback, wherein the product inhibits its inhibitor. While positive feedback by itself can result in different kinds of switches, it is an essential ingredient in bistable switches. Bistable switches of course possess a region of parameter space where multiple steady states may occur, and this switch exhibits the expected hysteresis (see Figure 1). Multiphosphorylation Switches. We briefly discuss these switches separately as they been the focus of much attention in the recent literature motivated by evidence of their natural occurrence in different contexts, including notably in cell cycle regulation. Here the switch-type response in the concentration of the active form of species arises directly from the fact that an enzyme can phosphorylate this species at multiple locations, either distributively or processively. Multiphosphorylation switches naturally embody a highly nonlinear form of signal processing and an analytical study of the effect of the number of phosphorylation sites in signal transduction reveals that this creates a good threshold, and a switch like effect, though not necessarily a sharp switch.4 Under certain conditions multiphosphorylation switches can themselves exhibit bistability. Thus they represent a class of systems which can exhibit both monostable and bistable switch-like behavior. An elegant theoretical study of multisite phosphorylation is performed in ref 5. Oscillations. All the above examples were those of switch-like behaviors. There are also other characteristic kinds of signal processing which are encountered. One is that of oscillators. The role of oscillations in various contexts in cell biology is well established. Oscillatory behaviors from reaction networks is responsible for maintaining parts of the cell cycle, migration, and is also involved in various kinds of rhythms like circadian and ultradian rhythms. From the perspective of reactions it is important to note that these oscillations are primarily maintained by chemical reactions and may be controlled temporally and spatially. Further, in some cases, certain aspects of the oscillatory behavior are quite robust to disturbances. From the point of view of modeling, such oscillators are examples of fully nonlinear dynamic phenomena which are naturally employed by the cell. In the modeling of such reactions, typically (though not always) the oscillations appear as Hopf bifurcations destabilizing the steady state as parameters are varied.6 In many cases oscillatory behavior arises as the result of delayed negative feedback effects, with the delay being due to a number of intermediate reactions, transport, or a combination of factors. Ultimately the capability of sustained oscillatory behavior 13237
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Figure 1. Schematic of modules and characteristics. (a) A typical input output curve for bistable switches is shown, revealing a broad region of multiple steady states. (b) Oscillatory behavior is ubiquitous and very often due to negative feedback. A schematic of a circuit studied in ref 6 is shown. (c) A typical minimal feedforward adaptive module: here the signal S coregulates two opposing pathways marked A and I, each regulating the response R. (d) A minimal negative feedback module, resulting in adaptive behavior. The output P acts to inhibit its own production. This results in an adaptive response which in some cases is very close to adaptive.
is contained in the dynamics/dynamical capability of the network in suitable parameter regimes. Pulse Generation. In many contexts in signal transduction, a steady stimulus is either partially or completely filtered out through a reaction network. This characteristic feature is called adaptation, and allows for the signaling pathway/target to reset its value independent of the level of the (steady) stimulus. Thus in effect a step input is converted into a pulse output, again through a chemical reaction network. There are typically two ways in which this adaptive signal processing is achieved through reaction networks. One is through a feedforward pathway (eg., ref 7), wherein the activation of the pathway by the external signal, also involves a parallel (typically slower) inhibitor effect. This allows for the inhibitory pathway to counteract the activatory pathway to offset the effect of the upstream signal. The second way is through negative feedback regulation. Here the activation of a pathway results in the activation of some negative feedback effect which helps to shut the pathway off.9 This is an example of negative feedback control acting at the level of reactions to result in pulse generation (see Figure 1). The adaptive response may be exact, in which case a step change in input is converted into a pulse, with the final steady state of the output matches the initial steady state, or inexact, where a pulse-like output is observed, but the final steady state is not the same as the initial steady state: in this case, a permanent trace of the level of the input is contained in the output. An analysis of inexact adaptation as a perturbation of adaptive modules is contained in ref 8.
It should be mentioned that while the different kinds of chemical signal processing mentioned above are seen naturally in cell signaling, they have also been realized artificially in synthetic biological circuits. Thus for instance, in genetic circuits, a bistable switch has been artificially created with the positive feedback being created through two elements which mutually repress each others transcription (and hence protein synthesis). This is an example of a synthetic switch which is bistable. Likewise, synthetic genetic oscillators have also been engineered using negative feedback and delay, by having three elements repressing the next in a circular fashion. Pulse-generators have also been synthetically constructed using feedforward regulation. It is interesting to compare and contrast chemical reactions from an industrial/engineering chemistry and a cellular signal processing perspective. While chemical kinetics may be nonlinear in both cases, it is striking to see the nonlinear dynamic feature coming to the fore in cellular signal processing. The fact that multiple steady states (typically more encountered in nonisothermal reactions in chemical engineering) is seen in multiple cellular contexts (under isothermal conditions) is one example; the example of self-sustained oscillations is another. The other aspect is that of feedback control regulation built in at the level of reactions, to generate highly nonlinear behavior (discussed later). Another striking aspect unique to cellular signal processing is that of intrinsic stochasticity in the reactions owing to the small number of molecules. This stochasticity, whose presence is clearly detected in experiments, plays highly nontrivial roles 13238
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Industrial & Engineering Chemistry Research when one examines individual as well as population level outcomes of reactions in cellular populations. From a modeling perspective, understanding the stochastic aspects of these reactions implies that one has to change the model formalism from kinetics-based ordinary differntial equations to formalisms which account for the stochasticity and describe the system in terms of number of molecules as a function of time and aims to obtain probability distributions for the state of the system. Examining the stochastic dynamics of the reacting system is much more complex as it involves studying the chemical master equation. Here an approach which is essentially a stochastic population balance is used. The study is facillated by the use of stochastic simulation algorithms (SSA) such as Gillespie’s algorithm. In some cases, stochasticity results in steady-state chemical concentration distributions, which are simple distributions centered around the deterministic steady state values. The presence of multiple steady states in the deterministic kinetics is in many cases mirrored as multimodality in the stochastic description. However the connection is in general not so simple, and it is possible to have for example bimodal distributions stochastically without bistable kinetics.10,11 In general the stochastic element can introduce very nontrivial aspects to the behavior of the reaction network. Thus the stochasticity along with the nonlinearity brings in another dimension to chemical reactions at the cellular scale. 2.2. Transport. Since cellular signal processing is ultimately concerned with the receiving, processing, and transmission of chemical signals, transport plays an important role in this regard. Transport in cellular systems is of two types: passive (diffusive) and active. We examine the roles of these transport mechanisms and more complex variants. Diffusion is a well-understood transport mechanism, which plays a vital role in components moving from one location to another and hence in the transmission of information. While pure diffusion by itself is well understood, its interaction with reactions is not necessarily very simple. For instance while it is expected that diffusion of components acts to smooth out gradient information received from upstream enzyme signals, we demonstrated a case where diffusion could have a very counterintuitive effect,12 which depended on its interaction with the network. Viewed from the perspective of signal processing again, diffusion could have unexpected effects. For example in considering an analogue of a feedforward adaptive circuit mentioned above with diffusible elements, it was found that having one component diffusible allowed the dynamic concentration range of the output to exceed the bounds in purely temporal signaling.13 In addition having one element highly diffusible allowed the same circuit to exhibit perfect adaptation to spatially homogeneous signals (filtering out the effect of the stimulus) but still register a persistent response to spatial gradient signals. These examples begin to illustrate how the effects of diffusion when considered in conjunction with the chemical reaction become interesting. Another example of this kind has to do the effects of diffusion in driving a spatial pattern. The classical work of Turing demonstrates how the difference in diffusivities in species can destabilize an otherwise stable chemical reaction network, leading to a spatial pattern. This idea has been expanded upon to demonstrate how localized patterns in cellular systems may be created and maintained.14 While the Turing mechanisms has not been clearly demonstrated experimentally in an intracellular system, it has been demonstrated in liquid-phase chemical
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reaction systems. Again this is an example of how diffusion effects prove to be highly nontrivial when considered in conjunction with reactions. Another mode of transport which is routinely encountered in cellular systems is active transport. One example of this is how ions are pumped in actively from the external environment, with the expenditure of energy. We examine another case which is in some respects similar to a convective transport, namely active directed transport of material along microtubule and actin filaments. Cellular systems routinely exploit the driven transport of “cargo” along filaments, with the expenditure of energy. Noting that the material being transported may then be involved in some reaction and hence signal transmission, we see that active transport is an important mode of transmission of chemical information. The transport of elements by motor proteins along filaments is often described at the macroscopic level, by equations which are combinations of diffusion, advection, and reaction (conversion).15 These descriptions incorporate the movement of motor proteins along a track at the density level, including (where relevant) population densities of motor proteins moving in each direction, their binding and unbinding from filaments and regulation. In many cases it is of interest to develop stochastic descriptions of such active transport processes. Thus the interest is for example to examine the effects of multiple particles being transported unidirectionally along a filament, with an aim to incorporate realistic elements of their interaction such as mutual exclusivity. A formalism for describing such processes stochastically is based on that of driven lattice gases, studied in nonequilibrium statistical mechanics. Thus purely unidirectional motor driven transport in one dimension is described by a formalism called the Totally Asymmetric Simple Exclusion Process (TASEP)16,17 This formalism incorporates the features of multiple entities being transported in one direction on a lattice, while strictly imposing mutual exclusivity and nonpenetrability. Thus the particles on a lattice form an example of an interacting particle system, each of which may hop to the next site with some probability, as long as it is unoccupied. The characteristics of these TASEP processes have been studied in great detail, analytically and through simulations, and even the most basic TASEP processes exhibit highly nontrivial features such as phase transitions, nonuniform distributions, and jamming, etc.17 It is worth pointing out that additional elements such as variable speeds of transport (perhaps dependent on the location on the filament or on other chemical reactions) make this even more complex. In this context, it is worth mentioning another process which, while technically not regarded as transport, bears some similarities to the above process. The process of translation (a process of biopolymer synthesis/assembly) is a central genetic process, which follows transcription. Here the mRNA is “read” and used to synthesize the appropriate protein. This is accomplished by motors called ribosomes which progress along the mRNA in a unidirectional fashion, and with every step taken, adding to the protein chain being built (see Figure 2). This progression is in a strictly unidirectional manner with the ribosome progressing three codons per step using the current codon location to build an appropirate aminoacid to the chain being synthesized. There are typically many ribosomes progressing unidirectionally on the mRNA. The synthesis of proteins may be described kinetically similar to a polymerization reaction on one hand, and also stochastically using the TASEP formalism which enforces mutual 13239
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Figure 2. Active (motor) driven transport of particles. (a) A schematic of transport of particles along a one-dimensional filament is shown. The first and last particles are capable of moving forward, while the second particle is obstructed from moving by the third particle. (b) A schematic of the ribosome movement on the mRNA (only a single ribosome is shown). This in many respects resembles the situation shown in panel a. The ribosomal movement is accompanied by the gradual building of the polypeptide chain.
exclusivity of ribosomes and other features. The TASEP formalism may be further extended to include variable progression rates and other features. This is another example of the driven “transport” of particles in one direction, and specific nontrivial interactions between the particles playing a crucial role in determining the rate of chemical signal processing (in this protein synthesis rates). A different case of “transport” of chemical signals which builds on the above features, and is still distinct, must be mentioned. This is the feature of chemical waves. Chemical waves of different kinds are observed in different cellular contexts. A specific example is that of calcium intracellular signals,18 which propagate as waves in different systems, with different kinds of traveling waves, including pulses and fronts which are observed often excited by different classes of signals. These are purely chemical waves and are fully fledged nonlinear dynamic phenomena arising from the interplay of nonlinear kinetics and diffusion. The waves can result in the propagation of either a transient signal (pulse) which in turn relies on the interplay of excitable/ oscillatory kinetics and diffusion or a permanent signal (front) which relies of the interplay of bistable kinetics and diffusion. This wave propagation has very different characteristics from pure diffusion and active transport, and it has been suggested that this might be an effective way of propagation of chemical signals over long distances, quickly enough. Looking at these examples, we see that from the point of view of transport, there are familiar ingredients such as diffusion, but even these can contribute in a highly nontrivial manner to cellular signal processing. The active motor transport is something which to some extent resembles convective transport, but with its own special features. The role of stochasticity here involves the consideration of driven interacting particles, and is being actively studied using tools from nonequilibrium statistical mechanics. Finally wave propagation, while of course not exclusive to intracellular systems, is more frequently encountered here, and may be a very desirable mode of chemical signal transmission. 2.3. Control Regulation. In this subsection, we shift focus from topics which lie at the foundation of chemical engineering science to a topic which lies at the systems end of chemical engineering, namely control regulation. Control systems of course lie at the heart of proper design of processes in engineering. Likewise control regulation is repeatedly encountered in cellular signal processing. This is not surprising when one notes
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that cells receive a variety of signals which need to be interpreted to make decisions or be resisted. The term control is used quite literally in the biological literature to simply imply some form of causal link, but here we discuss cases which can be reasonably interpreted as control in the engineering sense. The first point to note is that these cellular signaling networks involve control regulation naturally. Some of this control regulation may have been incorporated through the process of evolution. This makes it difficult to infer the purpose of control regulation in some cases. The second point to note that a considerable amount of control regulation occurs at the level of “reactions”. This includes regulation of the genetic processes which result in protein synthesis, as well as regulation of protein networks “downstream”. It should also be noted that other kinds of feedback involving mechanical elements occur in cellular processes. Finally, in some cases, the purpose of control regulation in certain cases is to filter out external disturbances either to maintain homeostasis or reject disturbances for other reasons (see later). The control regulation which is encountered may broadly be of a feedforward or a feedback type. Feedforward regulation is found either directly or indirectly when a stimulus activates a pathways but also activates some antagonist of the pathway. In this case the feedforward regulation acts to partially or completely offset the original activation, resulting in a partially or completely adaptive response. Thus a step input in stimulus is converted into a pulse, or a partially reset response. Depending on the players involved in each of these pathways, a significant period of transient response may be observed. Feedback regulation is ubiquitously observed in signaling. Negative feedback generally acts to attenuate the effects of stimuli and give rise to some degree of rejection of the input stimulus. The difference between engineering and cellular systems is that the feedback does not act on an error which measures the deviation from a prescribed set point. The presence of negative feedback is repeatedly encountered in cellular pathways. Additionally it is believed the delay in negative feedback regulation is a key element underlying oscillatory behavior in signaling circuits. In addition to negative feedback, positive feedback is also repeatedly encountered. While positive feedback does not damp out resistance, it creates threshold and switch-like behavior with bistability in some cases. The positive feedback may play a critical role in shaping the nature of the response. In addition to the above, different cases of more complex feedback regulation are observed. This includes multiple negative feedback regulation as well as negative feedback regulation combined with positive feedback regulation. In these cases, it appears that each of the individual regulatory effects has a specific role to play, and their roles may best be understood when one considers the variety of stimuli and stimuli ranges which activates given pathways. We now briefly examine cases of control regulation intended to reject disturbances. One example of such a control response is when the cell is subject to a heat shock. One such example studied involves the heat shock control system in yeast.19 Here the control system appears to be built on a combination of feedforward and feedback regulation. Another kind of control regulation occurs when the cell is subject to other kinds of stress such as osmotic stress.20 Here the stress signals enter the cell from the outside, and it appears that one of the predominant modes of control regulation is to lead to an upregulation of 13240
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Industrial & Engineering Chemistry Research production of transporters which pump the signal out. This is another example of a negative feedback which in this case reduces the signal effect by removing it from the cell. A very similar effect is observed in certain cases when one considers the effect of drugs (e.g., anticancer drugs) on cells. It has long been known that a sublethal dose of drug can lead to the cell being resistant to more rounds of drugs. While this is quite a complex process, it is known that one way in which drug resistance occurs is through cells upregulating p-glycoproteins which play a role in transporting drug out of cells. Another related context in which control regulation plays a role is in certain kinds of sensory transduction. Here the apparent purpose of the regulation is not homeostatic in essence, but rather to help filter out certain kinds of signals to aid the sensing process and enable a dynamic response which is maintained across a range of stimuli. Examples of this arise in both visual signal transduction21 as well as in the movement of cells in response to gradients of chemical concentration (chemotaxis). For instance in bacteria such as E. coli the temporal gradient of the external chemical concentration is sensed, and in order for this mechanism to work over a wide range of chemical concentrations, the cellular circuitry naturally includes a mechanism which resets the signal processing pathway which controls the motility apparatus. This is achieved through a negative feedback mechanism which involves reactions acting close to saturation. This ensures that a step input of stimulus is rejected completely (at steady state) over a very wide range of stimuli concentrations (though recent work shows certain small deviations from this in part of the signaling range). It is known in control engineering that for robust rejection of step inputs, a control mechanism must incorporate some form of an integral control regulation and in fact this is what is observed. Thus this is an example of a naturally realized control mechanism occurring at the level of reaction networks and embodying an integral control.22 When one examines control regulation in these cellular systems when compared with chemical engineering control regulation, we note clear distinctions—the control is most often at the level of reaction networks, the control may involve combinations of feedforward and feedback regulation, or complex combinations of feedback regulation. Further they occur in different contexts, and it is not always easy to discern the purpose of particular control structures. Another feature which is peculiar to cellular signal processing is the effect of noise and the role of control to affect this. As mentioned noise in chemical reaction networks arises naturally from the small number of molecules and in many cases (but not all) negative feedback acts to suppress the noise. The role of feedback regulation in affecting noise is the focus of a number of studies, include recent theoretical studies.23 Finally it should be mentioned that control regulation may be overlaid upon very complex processes. One example is the process of translation mentioned in the last section is subject to different kinds of feedback control at multiple locations. 2.4. Modeling and Analysis. In previous subsections, aspects of reaction engineering, transport and control engineering which naturally arise in cellular signal processing were discussed. We now discuss some approaches and challenges involved in trying to understand cellular signal processing from a modeling perspective. The first and most obvious thing about cellular signal processing is that modeling is really needed to understand different aspects, given the natural complexity of the elements involved, and the generic nonlinearity which arises from such interactions. While much of the related modeling in chemical engineering is
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differential equation based (ODEs, PDEs, DAEs), the situation is a little different in cellular signal processing. ODEs are widely used to model interactions and decision making, even if spatial effects may be involved. Typically a general approach will be to adopt a formalism which will focus on the relevant issues of the given system, without unnecessarily increasing the model or computational complexity. Thus even though spatial transport effects may be involved, a simpler compartmental ODE model may be used. For the same reason, in some cases to obtain key insights into the nature of interactions of a reaction network, a simpler Boolean network may be employed, using discrete time simulations. In certain gene-regulatory networks, a modeling approach of a hybrid system, combining both continuous and discrete elements may be used. When spatial effects play important roles, typically PDE-based modeling is employed. On the other hand when the small number of molecules may play an important role, stochastic simulations of the reaction network may be employed. This involves studying the chemical master equation, which may be facillitated by the use of Gillespie algorithms. The use of a stochastic formalism, while relevant, is also more time-consuming, and thus a hybrid approach which combines deterministic and stochastic approaches may be used, to focus on the stochastic approach, where needed, but couple it with deterministic approaches for greater tractability. We see immediately that a rather wide range of approaches and formalisms are used in modeling. It is worth pointing out that even for a particular process the kind of model, formalism used, and emphasis strongly depend on the question being addressed by the model. This implies that even for fixed processes, there may be different models which are very different in focus, which are reasonable, and may be essentially correct. On the other hand, the complexity of processes also has implications for validation of such models (see later). The size of models can vary considerably from a small number of equations to tens of thousands of equations. We find that a comprehensive model of even a few pathways in a cell can easily result in hundreds of components, when contrasted with standard reaction engineering models, and this would exceed the number of components in chemical reaction engineering modeling. Likewise, different signaling processes can occur over a range of time scales from seconds to hours and even longer. When one considers the nonlinear dynamic behavior and other complexities, we can see that quantitatively even modeling some selected processes in a cell can lead to quite a large system. It is also very clear that if one considers the entire cell as a system, this exhibits considerably more complexity than any industrial plant which has been built in a modular way, from well-characterized elements. General tools for the analysis of models such as sensitivity analysis and its refinements and bifurcation analysis, where appropriate, prove useful in understanding the model behavior. A particular focus of interest in modeling is how robust certain behavior is to changes in parameters, and such parametric analysis is useful in checking for behavior which is quite sensitive for parameters. While such tools are very useful in small models, the situation in larger models is not quite so clear. In general, in such applications, the understanding of a model behavior is not often easily reduced to a problem of checking the effects of parameters, for various reasons. First, even estimates of “known” parameters may vary considerably. Second, certain steps in a model may actually not be correct for the system at hand (either because they have been incorrectly extrapolated from different systems, or incorrectly interpreted from other experiments, or 13241
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Industrial & Engineering Chemistry Research simply based on incorrect information in the biological literature). There may be important features which are missing in the model. Finally with a large number of parameters, and perhaps unmodelled dynamics which are relevant, the results of such analysis must be interpreted with caution. In some cases a clear understanding and appreciation of the structure of the model, provides important insights, which give a clearer picture of the model behavior and which can be complemented by sensitivity analysis, and this could be more useful than just generic sensitivity analysis. Additional tools which allow for making clear-cut statements about qualitative features of a model, such as the Chemical Reaction Network Theory,24 can prove very useful as well. In many cases a proper appreciation of particular signaling pathways can be obtained by using detailed and simplified models in conjunction. The simplified model could be obtain as a formal reduction of the main model, or be constructed separately. Simplified models could provide transparent explicit insight into the behavior of key elements and also provide a basis for understanding the extra details. Thus finding suitable simplified models as well as abstractions can prove to be extremely useful. It can compactly encapsulate certain signal behavior and both allow for its better understanding and be used in more detailed models. In chemical reaction engineering two basic abstractions, the perfect CSTR and the ideal PFR, have formed a basis for understanding many aspects of reaction engineering. Furthermore such simplified models are much more than simplifications for better understanding. From a pragmatic viewpoint, these models are actually used in process simulators used in simulating reactors in entire plants. To be sure certain detailed aspects of flow and transport in reactors have also been investigated in much more detail using modeling and computation, and specific software has also been developed for this. These are sometimes used side-by-side with simplified descriptions in actual full plant/process simulations. Finally, in modeling cellular signaling, the typical goal as in other modeling is to compare model predictions with data for validation. Even this step is not that straightforward. In a given signaling model, if very limited experimental monitoring is performed, then a match between experiments and modeling cannot always reasonably claim to validate a model: indeed there may be different models, which could be very different qualitatively, which could give rise to the same behavior of monitored elements. Thus a combination of more thorough experimental interrogation and analysis of model structure may be needed. Overall we see that the sheer complexity of cell signaling provides many challenges for modeling and analysis, and involves a broader range of modeling approaches.
3. CONCLUSION In this article, I have highlighted certain aspects of cellular systems from a chemical engineering perspective which are different from the usual focus of chemical engineers, and in so doing highlighted some of the parallels as well as essential differences which arise when examining cellular signal processing. It is evident that the principles which form the basis of chemical engineering science (and associated systems thinking) play roles in understanding cellular processes, and indeed chemical engineers have a long history of being involved in biological processes in a number of areas including metabolic engineering, biomedical processes, and exploiting cellular processes in a wide
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variety of applications, etc. The aspects I have tried to highlight in this article relate to how basic themes of chemical engineering are present and combined in new ways along with important new ingredients repeatedly in cellular signal processing. The themes focused on were naturally primarily dynamicscentric and included reactions and kinetics, transport, and control regulation, though it is clear that other elements are also present. From the reaction engineering perspective, cellular signal processing involves biological information being transmitted in chemical terms, and hence reactions form a basic element. Here, the focus is more on small sets of reactions which have characteristic signal transduction and input output characteristics: indeed various kinds of reaction network modules are found which exhibit characteristic signal processing behavior such as switches (both monostable and bistable), oscillators, and pulse generators, etc. The clear aspect which emerges from this is that not only nonlinearity but the nonlinear dynamic aspects of chemical reactions and their role in generating characteristic temporal behavior. This nonlinearity often arises through built-in feedback regulatory effects. Another element which emerges is the fact that owing to small number of molecules, the intrinsic stochasticity plays a very nontrivial role, and formalisms similar to stochastic population balances are used to understand these features. At the level of transport, diffusion is routinely encountered. The diffusion can play a very nontrivial and sometimes counterintuitive role when examined in context of the signal transduction and interplay with reaction networks: it can completely alter the signal transduction and also possibly be a driver for creation of self-organized chemical patterns. Active directed transport, for example through motor proteins moving on cytoskeletal filaments is also encountered. The macroscopic descriptions of these processes may be cast in terms of diffusion-advectionreaction type equations, while stochastic descriptions of collective transport of interacting particles employs formalisms from nonequilibrium statistical mechanics. These nonequilibrium statistical mechanics formalisms also apply to related processes such as the polymer assembly process which constitutes the key genetic process of translation, and is driven by a unidirectionally moving ribosome motor. Diffusion can again combine with the nonlinearity of kinetics to give rise to wave propagation, which may be viewed as another form of transport. Control regulation is built in at various levels and various stages at the level of reactions. Analogues of both feedforward and feedback control (both positive and negative feedback) are observed, and here too nonlinearity and stochasticity become very important. Feedback regulation is very important in attenuating the effects of disturbances to ensure homeostatic regulation and also facillitates different aspects of sensory transduction. It is interesting to note that feedback effects can be encountered even in other active transport processes as well. Overall from the control engineering point of view, we find a broad prevalence of control regulation in various signaling pathways. If one compares the control regulation in cell signaling pathways to that in an entire plant, we see that while one might expect on the order of 10 control loops in a plant, the control regulation in signaling pathways is much more widespread and broadly distributed. There is a fair amount of interconnection between these topics as presented. Thus control regulation plays an important role in producing particular kinds of chemical signal transduction, while transport may nontrivially affect both the reaction and its location. Likewise, in considering transport (especially active 13242
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Industrial & Engineering Chemistry Research transport), various kinetic aspects become important, as also their control regulation. Finally in considering control regulation in cellular processes, both the nonlinearity as the signal processing nature of reactions involved in the control regulation as well as transport play important roles. Taken together, by examining cellular signal processing from an engineering perspective a number of points emerge. First, it is clear that the roles of strong nonlinearity, stochasticity, and the nonequilibrium nature of many processes involved come to the fore in cellular signal processing, and these aspects are not easily bypassed, if at all. Thus engineering science and systems approaches need to deal with these aspects effectively. Second, what the core basic elements in cellular signal processing are is somewhat different from that in chemical engineering, despite sharing common underlying structures. Third, the elements which are familiar in chemical engineering are combined in very different ways, as they have fundamentally different roles to play in the cellular setting. Fourth, while the discussion here has been in terms of intracellular signal processing, many of these aspects apply equally to cellular communication. Finally, in order to model and elucidate these various complexities, a broader range of model approaches and formalisms as well as the use of both detailed and simplified models is needed. In addition a series of theoretical and computational methodologies and approaches to both understand different aspects of the complexity and appropriately encapsulate their behavior is also required. Overall one of the main challenges to be confronted (especially as more data are becoming available) is to tackle effectively the highly nonlinear, often stochastic, and nonequilibrium nature of various subprocesses in the cell and understand how these aspects are effectively harnessed, suppressed, or controlled in individual contexts. The roles of these features need to be carefully understood in the context of a range of specific processes with their attendant complexity in conjunction with experiment. This brings with it a number of difficulties including conceptual, modeling, experimental, and computational. These present some of the main new challenges to expanding the chemical engineering perspective to understand and effectively exploit cellular signal processing in natural and synthetic settings and make cells the engineering playground of tomorrow.
’ AUTHOR INFORMATION Corresponding Author
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[email protected]. Tel.: 44-20-7594-6633. Fax: 44-20-7594-6606.
’ DEDICATION This paper is dedicated to Professor M. S. Ananth, with best wishes for his 65th birthday. The author acknowledges many interesting discussions with Professor Ananth during his undergraduate days and beyond.
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