Chemotactic response and adaptation dynamics in Escherichia coli

Homeostasis in networks with multiple inputs

Homeostasis, also known as adaptation, refers to the ability of a system to counteract persistent external disturbances and tightly control the output of a key observable. Existing studies on homeostasis in network dynamics have mainly focused on 'perfect adaptation' in deterministic single-input single-output networks where the disturbances are scalar and affect the network dynamics via a pre-specified input node. In this paper we provide a full classification of all possible network topologies capable of generating infinitesimal homeostasis in arbitrarily large and complex multiple inputs networks. Working in the framework of 'infinitesimal homeostasis' allows us to make no assumption about how the components are interconnected and the functional form of the associated differential equations, apart from being compatible with the network architecture. Remarkably, we show that there are just three distinct 'mechanisms' that generate infinitesimal homeostasis. Each of these three mechanisms generates a rich class of well-defined network topologies-called homeostasis subnetworks. More importantly, we show that these classes of homeostasis subnetworks provides a topological basis for the classification of 'homeostasis types': the full set of all possible multiple inputs networks can be uniquely decomposed into these special homeostasis subnetworks. We illustrate our results with some simple abstract examples and a biologically realistic model for the co-regulation of calcium ( Ca ) and phosphate ( PO 4 ) in the rat. Furthermore, we identify a new phenomenon that occurs in the multiple input setting, that we call homeostasis mode interaction, in analogy with the well-known characteristic of multiparameter bifurcation theory.

Flagellar dynamics reveal fluctuations and kinetic limit in the Escherichia coli chemotaxis network

The Escherichia coli chemotaxis network, by which bacteria modulate their random run/tumble swimming pattern to navigate their environment, must cope with unavoidable number fluctuations ("noise") in its molecular constituents like other signaling networks. The probability of clockwise (CW) flagellar rotation, or CW bias, is a measure of the chemotaxis network's output, and its temporal fluctuations provide a proxy for network noise. Here we quantify fluctuations in the chemotaxis signaling network from the switching statistics of flagella, observed using time-resolved fluorescence microscopy of individual optically trapped E. coli cells. This approach allows noise to be quantified across the dynamic range of the network. Large CW bias fluctuations are revealed at steady state, which may play a critical role in driving flagellar switching and cell tumbling. When the network is stimulated chemically to higher activity, fluctuations dramatically decrease. A stochastic theoretical model, inspired by work on gene expression noise, points to CheY activation occurring in bursts, driving CW bias fluctuations. This model also shows that an intrinsic kinetic ceiling on network activity places an upper limit on activated CheY and CW bias, which when encountered suppresses network fluctuations. This limit may also prevent cells from tumbling unproductively in steep gradients.

Tethered particle motion of the adaptation enzyme CheR in bacterial chemotaxis

Bacteria perform chemotactic adaptation by sequential modification of multiple modifiable sites on chemoreceptors through stochastic action of tethered adaptation enzymes (CheR and CheB). To study the molecular kinetics of this process, we measured the response to different concentrations of MeAsp for the Tar-only Escherichia coli strain. We found a strong dependence of the methylation rate on the methylation level and established a new mechanism of adaptation kinetics due to tethered particle motion of the methylation enzyme CheR. Experiments with various lengths of the C-terminal flexible chain in the Tar receptor further validated this mechanism. The tethered particle motion resulted in a CheR concentration gradient that ensures encounter-rate matching of the sequential modifiable sites. An analytical model of multisite catalytic reaction showed that this enables robustness of methylation to fluctuations in receptor activity or cell-to-cell variations in the expression of adaptation enzymes and reduces the variation in methylation level among individual receptors.

A Mathematical Description of Bacterial Chemotaxis in Response to Two Stimuli

Bacteria are often exposed to multiple stimuli in complex environments, and their efficient chemotactic decisions are critical to survive and grow in their native environments. Bacterial responses to the environmental stimuli depend on the ratio of their corresponding chemoreceptors. By incorporating the signaling machinery of individual cells, we analyze the collective motion of a population of Escherichia coli bacteria in response to two stimuli, mainly serine and methyl-aspartate (MeAsp), in a one-dimensional and a two-dimensional environment, which is inspired by experimental results in Y. Kalinin et al., J. Bacteriol. 192(7):1796-1800, 2010. Under suitable conditions, we show that if the ratio of the main chemoreceptors of individual cells, namely Tar/Tsr, is less than a specific threshold, the bacteria move to the gradient of serine, and if the ratio is greater than the threshold, the group of bacteria moves toward the gradient of MeAsp. Finally, we examine the theory with Monte Carlo agent-based simulations and verify that our results qualitatively agree well with the experimental results in Y. Kalinin et al. (2010).

Ras inhibitor CAPRI enables neutrophil-like cells to chemotax through a higher-concentration range of gradients

Neutrophils sense and migrate through an enormous range of chemoattractant gradients through adaptation. Here, we reveal that in human neutrophils, calcium-promoted Ras inactivator (CAPRI) locally controls the GPCR-stimulated Ras adaptation. Human neutrophils lacking CAPRI (capri^kd ) exhibit chemoattractant-induced, nonadaptive Ras activation; significantly increased phosphorylation of AKT, GSK-3α/3β, and cofilin; and excessive actin polymerization. capri^kd cells display defective chemotaxis in response to high-concentration gradients but exhibit improved chemotaxis in low- or subsensitive-concentration gradients of various chemoattractants, as a result of their enhanced sensitivity. Taken together, our data reveal that CAPRI controls GPCR activation-mediated Ras adaptation and lowers the sensitivity of human neutrophils so that they are able to chemotax through a higher-concentration range of chemoattractant gradients.

How an unusual chemosensory system forms arrays on the bacterial nucleoid

Chemosensory systems are signaling pathways elegantly organized in hexagonal arrays that confer unique functional features to these systems such as signal amplification. Chemosensory arrays adopt different subcellular localizations from one bacterial species to another, yet keeping their supramolecular organization unmodified. In the gliding bacterium Myxococcus xanthus, a cytoplasmic chemosensory system, Frz, forms multiple clusters on the nucleoid through the direct binding of the FrzCD receptor to DNA. A small CheW-like protein, FrzB, might be responsible for the formation of multiple (instead of just one) Frz arrays. In this review, we summarize what is known on Frz array formation on the bacterial chromosome and discuss hypotheses on how FrzB might contribute to the nucleation of multiple clusters. Finally, we will propose some possible biological explanations for this type of localization pattern.

Adaptive tuning of cell sensory diversity without changes in gene expression

In the face of uncertainty, cell populations tend to diversify to enhance survival and growth. Previous studies established that cells can optimize such bet hedging upon environmental change by modulating gene expression to adapt both the average and diversity of phenotypes. Here, we demonstrate that cells can tune phenotypic diversity also using posttranslational modifications. In the chemotaxis network of Escherichia coli, we find, for both major chemoreceptors Tar and Tsr, that cell-to-cell variation in response sensitivity is dynamically modulated depending on the presence or absence of their cognate chemoeffector ligands in the environment. Combining experiments with mathematical modeling, we show that this diversity tuning requires only the environment-dependent covalent modification of chemoreceptors and a standing cell-to-cell variation in their allosteric coupling. Thus, when environmental cues are unavailable, phenotypic diversity enhances the population's readiness for many signals. However, once a signal is perceived, the population focuses on tracking that signal.

Molecules involved in motility regulation in Escherichia coli cells: a review

The initial colonization of the host organism by commensal, probiotic, and pathogenic Escherichia coli strains is an important step in the development of infections and biofilms. Sensing and colonization of host cell surfaces are governed by flagellar and fimbriae/pili appendages, respectively. Biofilm formation confers great advantages on pathogenic E. coli cells such as protection against the host immune system, antimicrobial agents, and several environmental stress factors. The transition from planktonic to sessile physiological states involves several signaling cascades and factors responsible for the regulation of flagellar motility in E. coli cells. These regulatory factors have thus become important targets to control pathogenicity. Hence, attenuation of flagellar motility is considered a potential therapy against pathogenic E. coli. The present review describes signaling pathways and proteins involved in direct or indirect regulation of flagellar motility. Furthermore, application strategies for antimotility natural or synthetic compounds are discussed also.

Multi-omics response of Pannonibacter phragmitetus BB to hexavalent chromium

The release of hexavalent chromium [Cr(VI)] into water bodies poses a major threat to the environment and human health. However, studies of the biological response to Cr(VI) are limited. In this study, a toxic bacterial mechanism of Cr(VI) was investigated using Pannonibacter phragmitetus BB (hereafter BB), which was isolated from chromate slag. The maximum Cr(VI) concentrations with respect to the resistance and reduction by BB are 4000 mg L^-1 and 2500 mg L^-1, respectively. In the BB genome, more genes responsible for Cr(VI) resistance and reduction are observed compared with other P. phragmitetus strains. A total of 361 proteins were upregulated to respond to Cr(VI) exposure, including enzymes for Cr(VI) uptake, intracellular reduction, ROS detoxification, DNA repair, and Cr(VI) efflux and proteins associated with novel mechanisms involving extracellular reduction mediated by electron transfer, quorum sensing, and chemotaxis. Based on metabolomic analysis, 174 metabolites were identified. Most of the upregulated metabolites are involved in amino acid, glucose, lipid, and energy metabolisms. The results show that Cr(VI) induces metabolite production, while metabolites promote Cr(VI) reduction. Overall, multi-enzyme expression and metabolite production by BB contribute to its high ability to resist/reduce Cr(VI). This study provides details supporting the theory of Cr(VI) reduction and a theoretical basis for the efficient bioremoval of Cr(VI) from the environment.

Modular DNA strand-displacement controllers for directing material expansion

Soft materials that swell or change shape in response to external stimuli show extensive promise in regenerative medicine, targeted therapeutics, and soft robotics. Generally, a stimulus for shape change must interact directly with the material, limiting the types of stimuli that may be used and necessitating high stimulus concentrations. Here, we show how DNA strand-displacement controllers within hydrogels can mediate size change by interpreting, amplifying, and integrating stimuli and releasing signals that direct the response. These controllers tune the time scale and degree of DNA-crosslinked hydrogel swelling and can actuate dramatic material size change in response to <100 nM of a specific biomolecular input. Controllers can also direct swelling in response to small molecules or perform logic. The integration of these stimuli-responsive materials with biomolecular circuits is a major step towards autonomous soft robotic systems in which sensing and actuation are implemented by biomolecular reaction networks.

Materials which change shape in response to a trigger are of interest for soft robotics and targeted therapeutic delivery. Here, the authors report on the development of DNA-crosslinked hydrogels which can expand upon the detection of different biomolecular inputs mediated by DNA strand-displacement.

Modeling Procedures

Being concerned by the understanding of the mechanism underlying chronic degenerative diseases , we presented in the previous chapter the medical systems biology conceptual framework that we present for that purpose in this volume. More specifically, we argued there the clear advantages offered by a state-space perspective when applied to the systems-level description of the biomolecular machinery that regulates complex degenerative diseases. We also discussed the importance of the dynamical interplay between the risk factors and the network of interdependencies that characterizes the biochemical, cellular, and tissue-level biomolecular reactions that underlie the physiological processes in health and disease. As we pointed out in the previous chapter, the understanding of this interplay (articulated around cellular phenotypic plasticity properties, regulated by specific kinds of gene regulatory networks) is necessary if prevention is chosen as the human-health improvement strategy (potentially involving the modulation of the patient's lifestyle). In this chapter we provide the medical systems biology mathematical and computational modeling tools required for this task.

Behavioral Variability and Phenotypic Diversity in Bacterial Chemotaxis

Living cells detect and process external signals using signaling pathways that are affected by random fluctuations. These variations cause the behavior of individual cells to fluctuate over time (behavioral variability) and generate phenotypic differences between genetically identical individuals (phenotypic diversity). These two noise sources reduce our ability to predict biological behavior because they diversify cellular responses to identical signals. Here, we review recent experimental and theoretical advances in understanding the mechanistic origin and functional consequences of such variation in Escherichia coli chemotaxis-a well-understood model of signal transduction and behavior. After briefly summarizing the architecture and logic of the chemotaxis system, we discuss determinants of behavior and chemotactic performance of individual cells. Then, we review how cell-to-cell differences in protein abundance map onto differences in individual chemotactic abilities and how phenotypic variability affects the performance of the population. We conclude with open questions to be addressed by future research.

Mathematical Analysis of the Escherichia coli Chemotaxis Signalling Pathway

We undertake a detailed mathematical analysis of a recent nonlinear ordinary differential equation (ODE) model describing the chemotactic signalling cascade within an Escherichia coli cell. The model includes a detailed description of the cell signalling cascade and an average approximation of the receptor activity. A steady-state stability analysis reveals the system exhibits one positive real steady state which is shown to be asymptotically stable. Given the occurrence of a negative feedback between phosphorylated CheB (CheB-P) and the receptor state, we ask under what conditions the system may exhibit oscillatory-type behaviour. A detailed analysis of parameter space reveals that whilst variation in kinetic rate parameters within known biological limits is unlikely to lead to such behaviour, changes in the total concentration of the signalling proteins do. We postulate that experimentally observed overshoot behaviour can actually be described by damped oscillatory dynamics and consider the relationship between overshoot amplitude, total cell protein concentration and the magnitude of the external ligand stimulus. Model reductions in the full ODE model allow us to understand the link between phosphorylation events and the negative feedback between CheB-P and receptor methylation, as well as elucidate why some mathematical models exhibit overshoot and others do not. Our paper closes by discussing intercell variability of total protein concentration as a means of ensuring the overall survival of a population as cells are subjected to different environments.

Multiple sources of slow activity fluctuations in a bacterial chemosensory network

Cellular networks are intrinsically subject to stochastic fluctuations, but analysis of the resulting noise remained largely limited to gene expression. The pathway controlling chemotaxis of Escherichia coli provides one example where posttranslational signaling noise has been deduced from cellular behavior. This noise was proposed to result from stochasticity in chemoreceptor methylation, and it is believed to enhance environment exploration by bacteria. Here we combined single-cell FRET measurements with analysis based on the fluctuation-dissipation theorem (FDT) to characterize origins of activity fluctuations within the chemotaxis pathway. We observed surprisingly large methylation-independent thermal fluctuations of receptor activity, which contribute to noise comparably to the energy-consuming methylation dynamics. Interactions between clustered receptors involved in amplification of chemotactic signals are also necessary to produce the observed large activity fluctuations. Our work thus shows that the high response sensitivity of this cellular pathway also increases its susceptibility to noise, from thermal and out-of-equilibrium processes.

Phenotypic diversity and temporal variability in a bacterial signaling network revealed by single-cell FRET

We present in vivo single-cell FRET measurements in the Escherichia coli chemotaxis system that reveal pervasive signaling variability, both across cells in isogenic populations and within individual cells over time. We quantify cell-to-cell variability of adaptation, ligand response, as well as steady-state output level, and analyze the role of network design in shaping this diversity from gene expression noise. In the absence of changes in gene expression, we find that single cells demonstrate strong temporal fluctuations. We provide evidence that such signaling noise can arise from at least two sources: (i) stochastic activities of adaptation enzymes, and (ii) receptor-kinase dynamics in the absence of adaptation. We demonstrate that under certain conditions, (ii) can generate giant fluctuations that drive signaling activity of the entire cell into a stochastic two-state switching regime. Our findings underscore the importance of molecular noise, arising not only in gene expression but also in protein networks.

Many sophisticated computer programs use random number generators to help solve challenging problems. These problems range from achieving secure communication across the Internet to deciding how best to invest in the stock market. Much research in recent years has found that randomness is also widespread in living cells, where it is often called “noise”. For example, the activity of some genes is so unpredictable to the extent that it appears random. Yet, relatively little is known about how such gene-expression noise propagates up to change how the cell behaves. Many open questions also remain about how cells might exploit these or other fluctuations to achieve complex tasks, like people use random number generators.

Bacteria perform a number of complex tasks. Some bacteria will swim toward chemicals that suggest a potential reward, such as food. Yet they swim away from chemicals that could lead them to harm. This ability is called chemotaxis and it relies on a network of interacting enzymes and other proteins that coordinates a bacterium’s movements with the input from its senses.

Keegstra et al. set out to find sources of noise that might act as random number generators and help the bacterium E. coli to best perform chemotaxis. An improved version of a technique called in vivo Förster resonance energy transfer (or in vivo FRET for short) was used to give a detectable signal when two proteins involved in the chemotaxis network interacted inside a single bacterium. The experiments showed that this protein network amplifies gene-expression noise for some genes while lessening it for others. In addition, the interactions between proteins encoded by genes acted as an extra source of noise, even when gene-expression noise was eliminated.

Keegstra et al. found that the amount of signaling within the chemotaxis network, as measured by in vivo FRET, varied wildly over time. This revealed two sources of noise at the level of protein signaling. One was due to randomness in the activity of the enzymes involved in tuning the cell’s sensitivity to changes in its environment. The other was due to protein interactions within a large complex that acts as the cell’s sensor. Unexpectedly, this second source of noise under some conditions could be so strong that it flipped the output of the cell’s signaling network back and forth between just two states: “on” and “off”.

Together these findings uncover how signaling networks can not only amplify or lessen gene-expression noise, but can themselves become a source of random events. The new knowledge of how such random events interact with a complex trait in a living cell – namely chemotaxis – could aid future antimicrobial strategies, because many bacteria use chemotaxis to help them establish infections. More generally, the new insights about noise in protein networks could help engineers seeking to build synthetic biochemical networks or produce useful compounds in living cells.

Drift and Behavior of E. coli Cells

Chemotaxis of the bacterium Escherichia coli is well understood in shallow chemical gradients, but its swimming behavior remains difficult to interpret in steep gradients. By focusing on single-cell trajectories from simulations, we investigated the dependence of the chemotactic drift velocity on attractant concentration in an exponential gradient. Whereas maxima of the average drift velocity can be interpreted within analytical linear-response theory of chemotaxis in shallow gradients, limits in drift due to steep gradients and finite number of receptor-methylation sites for adaptation go beyond perturbation theory. For instance, we found a surprising pinning of the cells to the concentration in the gradient at which cells run out of methylation sites. To validate the positions of maximal drift, we recorded single-cell trajectories in carefully designed chemical gradients using microfluidics.

Emergent properties of bacterial chemotaxis pathway

The chemotaxis pathway of Escherichia coli is the most studied sensory system in prokaryotes. The highly conserved general architecture of this pathway consists of two modules which mediate signal transduction and adaptation. The signal transduction module detects and amplifies changes in environmental conditions and rapidly transmits these signals to control bacterial swimming behavior. The adaptation module gradually resets the activity and sensitivity of the first module after initial stimulation and thereby enables the temporal comparisons necessary for bacterial chemotaxis. Recent experimental and theoretical work has unraveled multiple quantitative features emerging from the interplay between these two modules. This has laid the groundwork for rationalization of these emerging properties in the context of the evolutionary optimization of the chemotactic behavior.

Reconstructing the genotype-to-fitness map for the bacterial chemotaxis network and its emergent behavioural phenotypes

The signal-transduction network responsible for chemotaxis in Escherichia coli has been characterised in extraordinary detail. Yet, relatively little is known about eco-evolutionary aspects of chemotaxis, such as how the network has been shaped by selection and to what extent natural populations may fine-tune their chemotactic behaviour to the ecological conditions. To address these questions, we here develop an evolutionary-systems-biology model of the chemotaxis network of E. coli, which we apply to estimate the resource accumulation rate (here used as a proxy for fitness) of wildtype and a large number of potential mutant genotypes. Mutant genotypes differ from the wildtype in the concentrations of one or more constituent proteins of the chemotaxis signalling network or in one or more of its kinetic parameters. To guarantee model consistency across the genotype space, we explicitly incorporated biochemical constraints that underly observed phenotypic trade-offs. The model was validated by reconstructing the phenotypic properties of several known mutant genotypes. We also characterised differences in the fitness distribution between genotypes, and reconstructed adaptive walks in genotype space for populations exposed to different environmental conditions. We found that the local fitness landscape is rugged, due to non-additive interactions between mutations. When selection has a consistent direction, just a few adaptive mutations are required to reach a local peak, and different local peaks can be reached by adaptive walks starting from the same initial genotype. However, when the direction of selection is fluctuating, evolutionary paths are much longer and genotype space is explored further. Longer adaptive walks were also observed when evolution was started from a low-fitness genotype such as a CheZ knockout mutant. In line with empirical observations, the initial ΔcheZ mutant did not respond to a step-down stimulus, but a dynamic response similar to the wildtype was recovered following the fixation of compensatory mutations.

Feedback between motion and sensation provides nonlinear boost in run-and-tumble navigation

Many organisms navigate gradients by alternating straight motions (runs) with random reorientations (tumbles), transiently suppressing tumbles whenever attractant signal increases. This induces a functional coupling between movement and sensation, since tumbling probability is controlled by the internal state of the organism which, in turn, depends on previous signal levels. Although a negative feedback tends to maintain this internal state close to adapted levels, positive feedback can arise when motion up the gradient reduces tumbling probability, further boosting drift up the gradient. Importantly, such positive feedback can drive large fluctuations in the internal state, complicating analytical approaches. Previous studies focused on what happens when the negative feedback dominates the dynamics. By contrast, we show here that there is a large portion of physiologically-relevant parameter space where the positive feedback can dominate, even when gradients are relatively shallow. We demonstrate how large transients emerge because of non-normal dynamics (non-orthogonal eigenvectors near a stable fixed point) inherent in the positive feedback, and further identify a fundamental nonlinearity that strongly amplifies their effect. Most importantly, this amplification is asymmetric, elongating runs in favorable directions and abbreviating others. The result is a “ratchet-like” gradient climbing behavior with drift speeds that can approach half the maximum run speed of the organism. Our results thus show that the classical drawback of run-and-tumble navigation—wasteful runs in the wrong direction—can be mitigated by exploiting the non-normal dynamics implicit in the run-and-tumble strategy.

Countless bacteria, larvae and even larger organisms (and robots) navigate gradients by alternating periods of straight motion (runs) with random reorientation events (tumbles). Control of the tumble probability is based on previously-encountered signals. A drawback of this run-and-tumble strategy is that occasional runs in the wrong direction are wasteful. Here we show that there is an operating regime within the organism’s internal parameter space where run-and-tumble navigation can be extremely efficient. We characterize how the positive feedback between behavior and sensed signal results in a type of non-equilibrium dynamics, with the organism rapidly tumbling after moving in the wrong direction and extending motion in the right ones. For a distant source, then, the organism can find it fast.

Barrier Crossing in Escherichia coli Chemotaxis

We study cell navigation in spatiotemporally complex environments by developing a microfluidic racetrack device that creates a traveling wave with multiple peaks and a tunable wave speed. We find that while the population-averaged chemotaxis drift speed increases with wave speed for low wave speed, it decreases sharply for high wave speed. This reversed dependence of population-averaged chemotaxis drift speed on wave speed is caused by a "barrier-crossing" phenomenon, where a cell hops backwards from one peak attractant location to the peak behind by crossing an unfavorable (barrier) region with low attractant concentrations. By using a coarse-grained model of chemotaxis, we map bacterial motility in an attractant field to the random motion of an overdamped particle in an effective potential. The observed barrier-crossing phenomenon of living cells and its dependence on the spatiotemporal profile of attractant concentration are explained quantitatively by Kramers reaction rate theory.

Networked Chemoreceptors Benefit Bacterial Chemotaxis Performance

Motile bacteria use large receptor arrays to detect and follow chemical gradients in their environment. Extended receptor arrays, composed of networked signaling complexes, promote cooperative stimulus control of their associated signaling kinases. Here, we used structural lesions at the communication interface between core complexes to create an Escherichia coli strain with functional but dispersed signaling complexes. This strain allowed us to directly study how networking of signaling complexes affects chemotactic signaling and gradient-tracking performance. We demonstrate that networking of receptor complexes provides bacterial cells with about 10-fold-heightened detection sensitivity to attractants while maintaining a wide dynamic range over which receptor adaptational modifications can tune response sensitivity. These advantages proved especially critical for chemotaxis toward an attractant source under conditions in which bacteria are unable to alter the attractant gradient.

Chemoreceptor arrays are found in many motile bacteria. However, although our understanding of bacterial chemotaxis is quite detailed, the signaling and behavioral advantages of networked receptor arrays had not been directly studied in cells. We have recently shown that lesions in a key interface of the E. coli receptor array diminish physical connections and functional coupling between core signaling complexes while maintaining their basic signaling capacity. In this study, we exploited an interface 2 mutant to show, for the first time, that coupling between core complexes substantially enhances stimulus detection and chemotaxis performance.

Information processing in bacteria: memory, computation, and statistical physics: a key issues review

Living systems have to constantly sense their external environment and adjust their internal state in order to survive and reproduce. Biological systems, from as complex as the brain to a single E. coli cell, have to process these data in order to make appropriate decisions. How do biological systems sense external signals? How do they process the information? How do they respond to signals? Through years of intense study by biologists, many key molecular players and their interactions have been identified in different biological machineries that carry out these signaling functions. However, an integrated, quantitative understanding of the whole system is still lacking for most cellular signaling pathways, not to say the more complicated neural circuits. To study signaling processes in biology, the key thing to measure is the input-output relationship. The input is the signal itself, such as chemical concentration, external temperature, light (intensity and frequency), and more complex signals such as the face of a cat. The output can be protein conformational changes and covalent modifications (phosphorylation, methylation, etc), gene expression, cell growth and motility, as well as more complex output such as neuron firing patterns and behaviors of higher animals. Due to the inherent noise in biological systems, the measured input-output dependence is often noisy. These noisy data can be analysed by using powerful tools and concepts from information theory such as mutual information, channel capacity, and the maximum entropy hypothesis. This information theory approach has been successfully used to reveal the underlying correlations between key components of biological networks, to set bounds for network performance, and to understand possible network architecture in generating observed correlations. Although the information theory approach provides a general tool in analysing noisy biological data and may be used to suggest possible network architectures in preserving information, it does not reveal the underlying mechanism that leads to the observed input-output relationship, nor does it tell us much about which information is important for the organism and how biological systems use information to carry out specific functions. To do that, we need to develop models of the biological machineries, e.g. biochemical networks and neural networks, to understand the dynamics of biological information processes. This is a much more difficult task. It requires deep knowledge of the underlying biological network-the main players (nodes) and their interactions (links)-in sufficient detail to build a model with predictive power, as well as quantitative input-output measurements of the system under different perturbations (both genetic variations and different external conditions) to test the model predictions to guide further development of the model. Due to the recent growth of biological knowledge thanks in part to high throughput methods (sequencing, gene expression microarray, etc) and development of quantitative in vivo techniques such as various florescence technology, these requirements are starting to be realized in different biological systems. The possible close interaction between quantitative experimentation and theoretical modeling has made systems biology an attractive field for physicists interested in quantitative biology. In this review, we describe some of the recent work in developing a quantitative predictive model of bacterial chemotaxis, which can be considered as the hydrogen atom of systems biology. Using statistical physics approaches, such as the Ising model and Langevin equation, we study how bacteria, such as E. coli, sense and amplify external signals, how they keep a working memory of the stimuli, and how they use these data to compute the chemical gradient. In particular, we will describe how E. coli cells avoid cross-talk in a heterogeneous receptor cluster to keep a ligand-specific memory. We will also study the thermodynamic costs of adaptation for cells to maintain an accurate memory. The statistical physics based approach described here should be useful in understanding design principles for cellular biochemical circuits in general.

Understanding the link between single cell and population scale responses of Escherichia coli in differing ligand gradients

We formulate an agent-based population model of Escherichia coli cells which incorporates a description of the chemotaxis signalling cascade at the single cell scale. The model is used to gain insight into the link between the signalling cascade dynamics and the overall population response to differing chemoattractant gradients. Firstly, we consider how the observed variation in total (phosphorylated and unphosphorylated) signalling protein concentration affects the ability of cells to accumulate in differing chemoattractant gradients. Results reveal that a variation in total cell protein concentration between cells may be a mechanism for the survival of cell colonies across a wide range of differing environments. We then study the response of cells in the presence of two different chemoattractants. In doing so we demonstrate that the population scale response depends not on the absolute concentration of each chemoattractant but on the sensitivity of the chemoreceptors to their respective concentrations. Our results show the clear link between single cell features and the overall environment in which cells reside.

A minimal model for metabolism-dependent chemotaxis in Rhodobacter sphaeroides (†)

Chemotaxis is vital cellular movement in response to environmental chemicals. Unlike the canonical chemotactic pathway in Escherichia coli, Rhodobacter sphaeroides has both transmembrane and cytoplasmic sensory clusters, with the latter possibly interacting with essential components in the electron transport system. However, the effect of the cytoplasmic sensor and the mechanism of signal integration from both sensory clusters remain unclear. Based on a minimal model of the chemotaxis pathway in this species, we show that signal integration at the motor level produces realistic chemotactic behaviour in line with experimental observations. Our model also suggests that the core pathway of R. sphaeroides, at least its ancestor, may represent a metabolism-dependent selective stopping strategy, which alone can steer cells to favourable environments. Our results not only clarify the potential roles of the two sensory clusters but also put in question the current definitions of attractants and repellents.

Predicting chemical environments of bacteria from receptor signaling

Sensory systems have evolved to respond to input stimuli of certain statistical properties, and to reliably transmit this information through biochemical pathways. Hence, for an experimentally well-characterized sensory system, one ought to be able to extract valuable information about the statistics of the stimuli. Based on dose-response curves from in vivo fluorescence resonance energy transfer (FRET) experiments of the bacterial chemotaxis sensory system, we predict the chemical gradients chemotactic Escherichia coli cells typically encounter in their natural environment. To predict average gradients cells experience, we revaluate the phenomenological Weber's law and its generalizations to the Weber-Fechner law and fold-change detection. To obtain full distributions of gradients we use information theory and simulations, considering limitations of information transmission from both cell-external and internal noise. We identify broad distributions of exponential gradients, which lead to log-normal stimuli and maximal drift velocity. Our results thus provide a first step towards deciphering the chemical nature of complex, experimentally inaccessible cellular microenvironments, such as the human intestine.

Outside the laboratory, bacteria live in complex microenvironments characterized by competition for space and available nutrients. Although often inaccessible by experiments, understanding the spatio-temporal dynamics of bacterial microenvironments is biomedically important. For instance, the chemical environment that symbiotic Escherichia coli encounter in the human gut relates to health of the gastrointestinal tract, gut metabolism, immune response, and tissue homeostasis. Other complex microenvironments include soil and biofilms. Assuming that bacterial sensory systems have evolved to optimally sense typical gradients, we treat signaling data, the signaling pathway with its architecture and reaction rates, and computer simulations of swimming bacteria in different gradients as “prior knowledge” to “reverse engineer” E. coli's habitat. Our identified gradients are exponentially shaped with wide-ranging rate values. These microenvironments most likely stem from local fluctuating nutrient sources and degradation by competing species, in which bacteria have evolved to swim with optimal performance.

Fold-change detection in a whole-pathway model of Escherichia coli chemotaxis

There has been recent interest in sensory systems that are able to display a response which is proportional to a fold change in stimulus concentration, a feature referred to as fold-change detection (FCD). Here, we demonstrate FCD in a recent whole-pathway mathematical model of Escherichia coli chemotaxis. FCD is shown to hold for each protein in the signalling cascade and to be robust to kinetic rate and protein concentration variation. Using a sensitivity analysis, we find that only variations in the number of receptors within a signalling team lead to the model not exhibiting FCD. We also discuss the ability of a cell with multiple receptor types to display FCD and explain how a particular receptor configuration may be used to elucidate the two experimentally determined regimes of FCD behaviour. All findings are discussed in respect of the experimental literature.

Unraveling adaptation in eukaryotic pathways: lessons from protocells

Eukaryotic adaptation pathways operate within wide-ranging environmental conditions without stimulus saturation. Despite numerous differences in the adaptation mechanisms employed by bacteria and eukaryotes, all require energy consumption. Here, we present two minimal models showing that expenditure of energy by the cell is not essential for adaptation. Both models share important features with large eukaryotic cells: they employ small diffusible molecules and involve receptor subunits resembling highly conserved G-protein cascades. Analyzing the drawbacks of these models helps us understand the benefits of energy consumption, in terms of adjustability of response and adaptation times as well as separation of cell-external sensing and cell-internal signaling. Our work thus sheds new light on the evolution of adaptation mechanisms in complex systems.

Adaptation is a common feature in sensory systems, well familiar to us from light and dark adaptation of our visual system. Biological cells, ranging from bacteria to complex eukaryotes, including single-cell organisms and human sensory receptors, adopt different strategies to fulfill this property. However, all of them require substantial amounts of energy to adapt. Here, we compare the different biological strategies and design two minimal models which allow adaptation without requiring energy consumption. Schemes similar to the ones we proposed in our minimal models could have been adopted by ancient protocells, that have evolved into the pathways we now know and study. Analyzing our models can thus help elucidate the advantages brought to the cells by consumption of energy, including the bypassing of hard-wired cell parameters such as diffusion constants with increased control over time scales.

Structure and activity of the flagellar rotor protein FliY: a member of the CheC phosphatase family

BACKGROUND

FliY is a flagellar rotor protein of the CheC phosphatase family.

RESULTS

The FliY structure resembles that of the rotor protein FliM but contains two active centers for CheY dephosphorylation.

CONCLUSION

FliY incorporates properties of the FliM/FliN rotor proteins and the CheC/CheX phosphatases to serve multiple functions in the flagellar switch.

SIGNIFICANCE

FliY distinguishes flagellar architecture and function in different types of bacteria. Rotating flagella propel bacteria toward favorable environments. Sense of rotation is determined by the intracellular response regulator CheY, which when phosphorylated (CheY-P) interacts directly with the flagellar motor. In many different types of bacteria, the CheC/CheX/FliY (CXY) family of phosphatases terminates the CheY-P signal. Unlike CheC and CheX, FliY is localized in the flagellar switch complex, which also contains the stator-coupling protein FliG and the target of CheY-P, FliM. The 2.5 Å resolution crystal structure of the FliY catalytic domain from Thermotoga maritima bears strong resemblance to the middle domain of FliM. Regions of FliM that mediate contacts within the rotor compose the phosphatase active sites in FliY. Despite the similarity between FliY and FliM, FliY does not bind FliG and thus is unlikely to be a substitute for FliM in the center of the switch complex. Solution studies indicate that FliY dimerizes through its C-terminal domains, which resemble the Escherichia coli switch complex component FliN. FliY differs topologically from the E. coli chemotaxis phosphatase CheZ but appears to utilize similar structural motifs for CheY dephosphorylation in close analogy to CheX. Recognition properties and phosphatase activities of site-directed mutants identify two pseudosymmetric active sites in FliY (Glu(35)/Asn(38) and Glu(132)/Asn(135)), with the second site (Glu(132)/Asn(135)) being more active. A putative N-terminal CheY binding domain conserved with FliM is not required for binding CheY-P or phosphatase activity.

Excitation and adaptation in bacteria-a model signal transduction system that controls taxis and spatial pattern formation

The machinery for transduction of chemotactic stimuli in the bacterium E. coli is one of the most completely characterized signal transduction systems, and because of its relative simplicity, quantitative analysis of this system is possible. Here we discuss models which reproduce many of the important behaviors of the system. The important characteristics of the signal transduction system are excitation and adaptation, and the latter implies that the transduction system can function as a "derivative sensor" with respect to the ligand concentration in that the DC component of a signal is ultimately ignored if it is not too large. This temporal sensing mechanism provides the bacterium with a memory of its passage through spatially- or temporally-varying signal fields, and adaptation is essential for successful chemotaxis. We also discuss some of the spatial patterns observed in populations and indicate how cell-level behavior can be embedded in population-level descriptions.

Statistical mechanics of Monod-Wyman-Changeux (MWC) models

The 50th anniversary of the classic Monod-Wyman-Changeux (MWC) model provides an opportunity to survey the broader conceptual and quantitative implications of this quintessential biophysical model. With the use of statistical mechanics, the mathematical implementation of the MWC concept links problems that seem otherwise to have no ostensible biological connection including ligand-receptor binding, ligand-gated ion channels, chemotaxis, chromatin structure and gene regulation. Hence, a thorough mathematical analysis of the MWC model can illuminate the performance limits of a number of unrelated biological systems in one stroke. The goal of our review is twofold. First, we describe in detail the general physical principles that are used to derive the activity of MWC molecules as a function of their regulatory ligands. Second, we illustrate the power of ideas from information theory and dynamical systems for quantifying how well the output of MWC molecules tracks their sensory input, giving a sense of the "design" constraints faced by these receptors.

Response kinetics in the complex chemotaxis signalling pathway of Rhodobacter sphaeroides

Chemotaxis is one of the best-characterized signalling systems in biology. It is the mechanism by which bacteria move towards optimal environments and is implicated in biofilm formation, pathogenesis and symbiosis. The properties of the bacterial chemosensory response have been described in detail for the single chemosensory pathway of Escherichia coli. We have characterized the properties of the chemosensory response of Rhodobacter sphaeroides, an α-proteobacterium with multiple chemotaxis pathways, under two growth conditions allowing the effects of protein expression levels and cell architecture to be investigated. Using tethered cell assays, we measured the responses of the system to step changes in concentration of the attractant propionate and show that, independently of the growth conditions, R. sphaeroides is chemotactic over at least five orders of magnitude and has a sensing profile following Weber's Law. Mathematical modelling also shows that, as E. coli, R. sphaeroides is capable of showing fold-change detection (FCD). Our results indicate that general features of bacterial chemotaxis such as the range and sensitivity of detection, adaptation times, adherence to Weber's Law and the presence of FCD may be integral features of chemotaxis systems in general, regardless of network complexity, protein expression levels and cellular architecture across different species.

Transient dynamic phenotypes as criteria for model discrimination: fold-change detection in Rhodobacter sphaeroides chemotaxis

The chemotaxis pathway of the bacterium Rhodobacter sphaeroides shares many similarities with that of Escherichia coli. It exhibits robust adaptation and has several homologues of the latter's chemotaxis proteins. Recent theoretical results have correctly predicted that the E. coli output behaviour is unchanged under scaling of its ligand input signal; this property is known as fold-change detection (FCD). In the light of recent experimental results suggesting that R. sphaeroides may also show FCD, we present theoretical assumptions on the R. sphaeroides chemosensory dynamics that can be shown to yield FCD behaviour. Furthermore, it is shown that these assumptions make FCD a property of this system that is robust to structural and parametric variations in the chemotaxis pathway, in agreement with experimental results. We construct and examine models of the full chemotaxis pathway that satisfy these assumptions and reproduce experimental time-series data from earlier studies. We then propose experiments in which models satisfying our theoretical assumptions predict robust FCD behaviour where earlier models do not. In this way, we illustrate how transient dynamic phenotypes such as FCD can be used for the purposes of discriminating between models that reproduce the same experimental time-series data.

Evaluation of design strategies for time course experiments in genetic networks: case study of the XlnR regulon in Aspergillus niger

One of the challenges in genetic network reconstruction is finding experimental designs that maximize the information content in a data set. In this paper, the information value of mRNA transcription time course experiments was used to compare experimental designs. The study concerns the dynamic response of genes in the XlnR regulon of Aspergillus niger, with the goal to find the best moment in time to administer an extra pulse of inducing D-xylose. Low and high D-xylose pulses were used to perturb the XlnR regulon. Evaluation of the experimental methods was based on simulation of the regulon. Models that govern the regulation of the target genes in this regulon were used for the simulations. Parameter sensitivity analysis, the Fisher Information Matrix (FIM) and the modified E-criterion were used to assess the design performances. The results show that the best time to give a second D-xylose pulse is when the D-xylose concentration from the first pulse has not yet completely faded away. Due to the presence of a repression effect the strength of the second pulse must be optimized, rather than maximized. The results suggest that the modified E-criterion is a better metric than the sum of integrals of absolute sensitivity for comparing alternative designs.

Theoretical insights into bacterial chemotaxis

Research into understanding bacterial chemotactic systems has become a paradigm for Systems Biology. Experimental and theoretical researchers have worked hand-in-hand for over 40 years to understand the intricate behavior driving bacterial species, in particular how such small creatures, usually not more than 5 µm in length, detect and respond to small changes in their extracellular environment. In this review we highlight the importance that theoretical modeling has played in providing new insight and understanding into bacterial chemotaxis. We begin with an overview of the bacterial chemotaxis sensory response, before reviewing the role of theoretical modeling in understanding elements of the system on the single cell scale and features underpinning multiscale extensions to population models.

Role for cheR of Vibrio fischeri in the Vibrio-squid symbiosis

Upon hatching, the Hawaiian squid Euprymna scolopes is rapidly colonized by its symbiotic partner, the bioluminescent marine bacterium Vibrio fischeri . Vibrio fischeri cells present in the seawater enter the light organ of juvenile squid in a process that requires bacterial motility. In this study, we investigated the role chemotaxis may play in establishing this symbiotic colonization. Previously, we reported that V. fischeri migrates toward numerous attractants, including N-acetylneuraminic acid (NANA), a component of squid mucus. However, whether or not migration toward an attractant such as squid-derived NANA helps the bacterium to localize toward the light organ is unknown. When tested for the ability to colonize juvenile squid, a V. fischeri chemotaxis mutant defective for the methyltransferase CheR was outcompeted by the wild-type strain in co-inoculation experiments, even when the mutant was present in fourfold excess. Our results suggest that the ability to perform chemotaxis is an advantage during colonization, but not essential.

Responding to chemical gradients: bacterial chemotaxis

Chemotaxis allows bacteria to follow gradients of nutrients and other environmental stimuli. The bacterium Escherichia coli performs chemotaxis via a run-and-tumble strategy in which sensitive temporal comparisons lead to a biased random walk, with longer runs in the preferred gradient direction. The chemotaxis network of E. coli has developed over the years into one of the most thoroughly studied model systems for signal transduction and behavior, yielding general insights into such properties of cellular networks as signal amplification, signal integration, and robustness. Despite its relative simplicity, the operation of the E. coli chemotaxis network is highly refined and evolutionarily optimized at many levels. For example, recent studies revealed that the network adjusts its signaling properties dependent on the extracellular environment, apparently to optimize chemotaxis under particular conditions. The network can even utilize potentially detrimental stochastic fluctuations in protein levels and reaction rates to maximize the chemotactic performance of the population.

Effects of receptor modification and temperature on dynamics of sensory complexes in Escherichia coli chemotaxis

BACKGROUND

Extracellular stimuli in chemotaxis of Escherichia coli and other bacteria are processed by large clusters of sensory complexes. The stable core of these clusters is formed by transmembrane receptors, a kinase CheA, and an adaptor CheW, whereas adaptation enzymes CheR and CheB dynamically associate with the clusters via interactions with receptors and/or CheA. Several biochemical studies have indicated the dependence of the sensory complex stability on the adaptive modification state of receptors and/or on temperature, which may potentially allow environment-dependent tuning of its signalling properties. However, the extent of such regulation in vivo and its significance for chemotaxis remained unclear.

RESULTS

Here we used fluorescence recovery after photobleaching (FRAP) to confirm in vivo that the exchange of CheA and CheW shows a modest dependency on the level of receptor modification/activity. An even more dramatic effect was observed for the exchange kinetics of CheR and CheB, indicating that their association with clusters may depend on the ability to bind substrate sites on receptors and on the regulatory phosphorylation of CheB. In contrast, environmental temperature did not have a discernible effect on stability of the cluster core. Strain-specific loss of E. coli chemotaxis at high temperature could instead be explained by a heat-induced reduction in the chemotaxis protein levels. Nevertheless, high basal levels of chemotaxis and flagellar proteins in common wild type strains MG1655 and W3110 enabled these strains to maintain their chemotactic ability up to 42°C.

CONCLUSIONS

Our results confirmed that clusters formed by less modified receptors are more dynamic, which can explain the previously observed adjustment of the chemotaxis response sensitivity according to the level of background stimulation. We further propose that the dependency of CheR exchange on the availability of unmethylated sites on receptors is important to improve the overall chemotaxis efficiency by suppressing molecular noise under conditions of high ligand concentrations. Moreover, the observed stability of the cluster core at high temperature is in line with the overall thermal robustness of the chemotaxis pathway and allows maintenance of chemotaxis up to 42°C in the common wild type strains of E. coli.

Noise characteristics of the Escherichia coli rotary motor

Background

The chemotaxis pathway in the bacterium Escherichia coli allows cells to detect changes in external ligand concentration (e.g. nutrients). The pathway regulates the flagellated rotary motors and hence the cells' swimming behaviour, steering them towards more favourable environments. While the molecular components are well characterised, the motor behaviour measured by tethered cell experiments has been difficult to interpret.

Results

We study the effects of sensing and signalling noise on the motor behaviour. Specifically, we consider fluctuations stemming from ligand concentration, receptor switching between their signalling states, adaptation, modification of proteins by phosphorylation, and motor switching between its two rotational states. We develop a model which includes all signalling steps in the pathway, and discuss a simplified version, which captures the essential features of the full model. We find that the noise characteristics of the motor contain signatures from all these processes, albeit with varying magnitudes.

Conclusions

Our analysis allows us to address how cell-to-cell variation affects motor behaviour and the question of optimal pathway design. A similar comprehensive analysis can be applied to other two-component signalling pathways.

Effects of saturation and enzyme limitation in feedforward adaptive signal transduction

In this study, the author examines the effects of saturation and enzyme limitation in temporal and spatial signal transduction in a generic feedforward adaptive module. The feedforward module encompasses a range of temporal and spatial signal processing, and this study systematically examines the effect of enzyme limitation/saturating effects in each of the feedforward pathways, and their interplay. It is found that this saturation makes the adaptation inexact, and this effect is more pronounced for higher levels of input signals. Further, it has a very significant role in affecting the temporal dynamics of this module. In examining the role of saturation in the module response to static gradients, the author finds that in certain cases, saturation can completely alter the gradient response. The author examines various aspects of the response systematically using analytical methods and simulations. Overall the author studies a framework and basis for examining and understanding the roles of saturating effects in multiple pathways involved in adaptive responses and sheds light on the relationship and connection between exact and inexact adaptation.

Feedback control architecture and the bacterial chemotaxis network

Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to ‘reset’ (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a ‘cascade control’ feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance.

Bacteria move towards favourable environments by changing their swimming pattern. An important feature of this response, which is called bacterial chemotaxis, is that their sensing ability remains independent of the background environment in which they find themselves. This feature has been studied extensively in the bacterium E. coli, which has a simple chemotaxis decision mechanism. However, it has been recently found that most bacteria could potentially have a much more complicated decision mechanism for this response. In this paper, we look at the chemotaxis behaviour of one such bacterium, R. sphaeroides. We develop mathematical models of possible decision mechanisms and undertake an experimental procedure to investigate their validity. We find that only one of four such models can explain the chemotaxis response in R. sphaeroides. Compared to the other models, this model corresponds to a decision mechanism that provides the bacterium with improved swimming performance over the others. Moreover, this decision mechanism has been used extensively to improve performance in several engineering systems. We suggest that this mechanism may play an important role in improving chemotactic performance in other bacteria and in other signalling pathways.

Optimal receptor-cluster size determined by intrinsic and extrinsic noise

Biological cells sense external chemical stimuli in their environment using cell-surface receptors. To increase the sensitivity of sensing, receptors often cluster. This process occurs most noticeably in bacterial chemotaxis, a paradigm for sensing and signaling in general. While amplification of weak stimuli is useful in the absence of noise, its usefulness is less clear in the presence of extrinsic input noise and intrinsic signaling noise. Here, exemplified in a bacterial chemotaxis system, we combine the allosteric Monod-Wyman-Changeux model for signal amplification by receptor complexes with calculations of noise to study their interconnectedness. Importantly, we calculate the signal-to-noise ratio, describing the balance of beneficial and detrimental effects of clustering for the cell. Interestingly, we find that there is no advantage for the cell to build receptor complexes for noisy input stimuli in the absence of intrinsic signaling noise. However, with intrinsic noise, an optimal complex size arises in line with estimates of the size of chemoreceptor complexes in bacteria and protein aggregates in lipid rafts of eukaryotic cells.

Model-based inference of biochemical parameters and dynamic properties of microbial signal transduction networks

Because of the inherent uncertainty about quantitative aspects of signalling networks it is of substantial interest to use computational methods that allow inferring non-measurable quantities such as rate constants, from measurable quantities such as changes in protein abundances. We argue that true biochemical parameters like rate constants can generally not be inferred using models due to their non-identifiability. Recent advances, however, facilitate the analysis of parameter identifiability of a given model and automated discrimination of candidate models, both being important techniques to still extract quantitative biological information from experimental data.