Multi-stage regulation, a key to reliable adaptive biochemical pathways

Application of Systems Engineering Principles and Techniques in Biological Big Data Analytics: A Review

In the past few decades, we have witnessed tremendous advancements in biology, life sciences and healthcare. These advancements are due in no small part to the big data made available by various high-throughput technologies, the ever-advancing computing power, and the algorithmic advancements in machine learning. Specifically, big data analytics such as statistical and machine learning has become an essential tool in these rapidly developing fields. As a result, the subject has drawn increased attention and many review papers have been published in just the past few years on the subject. Different from all existing reviews, this work focuses on the application of systems, engineering principles and techniques in addressing some of the common challenges in big data analytics for biological, biomedical and healthcare applications. Specifically, this review focuses on the following three key areas in biological big data analytics where systems engineering principles and techniques have been playing important roles: the principle of parsimony in addressing overfitting, the dynamic analysis of biological data, and the role of domain knowledge in biological data analytics.

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.

Reaction-diffusion systems in intracellular molecular transport and control

Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. Most research to date has focused on active-transport mechanisms, although passive diffusion is often equally rapid and energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions-from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. These apparently diverse systems share many common features and are "wired" according to "generic" motifs such as nonlinear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times of the constituent subprocesses. Therefore, in reviewing the manifestations of cellular RD, we also describe basic theory of reaction-diffusion phenomena.

Conditional protein stabilization via the small molecules Shld-1 and rapamycin increases the signal-to-noise ratio with tet-inducible gene expression

Cellular mechanisms control one or more of the three basic levels of regulation (transcription, translation, and protein activity/locality), allowing for finely tuned spatial and temporal regulation of protein expression patterns. Gene regulation constructs in wide use today often employ a constitutively expressed transcription factor whose activity is determined by the presence or absence of a small molecule. A case in point is the tet transcription system, wherein transcription is regulated by doxycycline (Dox), allowing the researcher to turn protein expression on or off depending on the presence/absence of Dox. However in many applications of that system, there is basal transcription from the promoter element that is independent of Dox. Moreover, in vivo, heterogeneous distribution of Dox leads to concurrent differences in gene expression. We addressed these limitations by introducing conditional destabilizing elements to the system. First, we created a transactivator protein fusion regulated at the additional level of protein stability. This modification enabled a system that demonstrated an off state that is less sensitive to variations in Dox concentrations. We also regulated the stability of the protein expressed from the tet operator cassette, observing greatly improved signal-to-noise ratios. The results underscore how investigator-defined regulation at multiple levels of protein expression can attain afiner degree of control over the final expression of introduced genes.

Robust effects of Tsr–CheBp and CheA–CheYp affinity in bacterial chemotaxis

OBJECTIVE

Cell motility and chemotaxis play a role in the virulence of pathogenic bacteria, such as escape from host immune responses. Escherichia coli chemotaxis provides a well-characterized model system for the bacterial chemotaxis network. Two features of E. coli chemotaxis include signal amplification and robustly accurate adaptation. Recent simulation studies with models considering the effects of other receptors have suggested possible mechanisms for signal amplification. Although precise adaptation to aspartate has been explained by conventional kinetic models, the adaptation behavior of models incorporating the effects of other receptors remains unclear.

METHODS

We concentrated on how receptor crosstalk affects minimization of adaptation error and compared models in which the contribution of other receptors varied.

RESULTS

We demonstrated that the model is adaptable to attractant concentrations ranging from 0.1microM to 10mM with a decreased error rate (from 8% to 2%) when the kinetic constant of CheA and phosphorylated CheY dissociation is increased.

CONCLUSION

The results suggest that accurate adaptation is maintained through control of both the interaction of cytoplasmic Che proteins and the activity of the receptor complex.

Propagation of extrinsic perturbation in a negatively auto-regulated pathway

The apparent precision of the output in multi-step biochemical pathways in the face of external and intrinsic perturbations is non-obvious and conceptually difficult. Using a simple three-step negatively auto-regulated model pathway, we show that the effect of perturbation at different steps of the pathway and its transmission through the network is dependent on the context (i.e., the position) of the particular reaction step in relation to the topology of the regulatory network, stoichiometry of reactions, type of nonlinearity involved in the reactions and also on the intrinsic dynamical state of the pathway variables. We delineate the qualitative and quantitative changes in the pathway dynamics for constant ('bias') and random external perturbations acting on the pathway steps locally or globally to all steps. We show that constant perturbation induces qualitative change in dynamics, whereas random fluctuations cause significant quantitative variations in the concentrations of the different variables. Thus, the dynamic response of multi-step biochemical pathways to external perturbation depends on their biochemical, topological and dynamical features.

Differential activation of Escherichia coli chemoreceptors by blue-light stimuli

Enteric bacteria tumble, swim slowly, and are then paralyzed upon exposure to 390- to 530-nm light. Here, we analyze this complex response in Escherichia coli using standard fluorescence microscope optics for excitation at 440 +/- 5 nm. The slow swimming and paralysis occurred only in dye-containing growth media or buffers. Excitation elicited complete paralysis within a second in 1 muM proflavine dye, implying specific motor damage, but prolonged tumbling in buffer alone. The tumbling half-response times were subsecond for onset but more than a minute for recovery. The response required the chemotaxis signal protein CheY and receptor-dependent activation of its kinase CheA. The study of deletion mutants revealed a specific requirement for either the aerotaxis receptor Aer or the chemoreceptor Tar but not the Tar homolog Tsr. The action spectrum of the wild-type response was consistent with a flavin, but the chromophores remain to be identified. The motile response processed via Aer was sustained, with recovery to either step-up or -down taking more than a minute. The response processed via Tar was transient, recovering on second time scales comparable to chemotactic responses. The response duration and amplitude were dependent on relative expression of Aer, Tar, and Tsr. The main response features were reproduced when each receptor was expressed singly from a plasmid in a receptorless host strain. However, time-resolved motion analysis revealed subtle kinetic differences that reflect the role of receptor cluster interactions in kinase activation-deactivation dynamics.

Changing cellular location of CheZ predicted by molecular simulations

In the chemotaxis pathway of the bacterium Escherichia coli, signals are carried from a cluster of receptors to the flagellar motors by the diffusion of the protein CheY-phosphate (CheYp) through the cytoplasm. A second protein, CheZ, which promotes dephosphorylation of CheYp, partially colocalizes with receptors in the plasma membrane. CheZ is normally dimeric in solution but has been suggested to associate into highly active oligomers in the presence of CheYp. A model is presented here and supported by Brownian dynamics simulations, which accounts for these and other experimental data: A minority component of the receptor cluster (dimers of CheA_short) nucleates CheZ oligomerization and CheZ molecules move from the cytoplasm to a bound state at the receptor cluster depending on the current level of cellular stimulation. The corresponding simulations suggest that dynamic CheZ localization will sharpen cellular responses to chemoeffectors, increase the range of detectable ligand concentrations, and make adaptation more precise and robust. The localization and activation of CheZ constitute a negative feedback loop that provides a second tier of adaptation to the system. Subtle adjustments of this kind are likely to be found in many other signaling pathways.

In order to function effectively, a living cell must not only synthesize the correct molecules but also put them in the correct place. Understanding how this positioning occurs, and what its consequences are, is a matter of great interest and concern to contemporary biologists. The author here proposes a novel mechanism that will enhance the ability of a bacterial cell to perform chemotaxis—the ability to swim toward sources of food or away from noxious substances. In this hypothesis, a key protein in the chemotaxis pathway moves dynamically between the membrane and the cytoplasm depending on the presence of attractants or repellents. This idea is explored and tested by means of detailed molecular simulations in which all of the relevant molecules are shown in their correct location in the cell. The simulations show that the proposed shift in location of the key molecule will improve the speed, range, and robustness of the cell's response. It seems likely that similar movements of proteins will occur in many other signaling pathways.

Design principles of a bacterial signalling network

Cellular biochemical networks have to function in a noisy environment using imperfect components. In particular, networks involved in gene regulation or signal transduction allow only for small output tolerances, and the underlying network structures can be expected to have undergone evolution for inherent robustness against perturbations. Here we combine theoretical and experimental analyses to investigate an optimal design for the signalling network of bacterial chemotaxis, one of the most thoroughly studied signalling networks in biology. We experimentally determine the extent of intercellular variations in the expression levels of chemotaxis proteins and use computer simulations to quantify the robustness of several hypothetical chemotaxis pathway topologies to such gene expression noise. We demonstrate that among these topologies the experimentally established chemotaxis network of Escherichia coli has the smallest sufficiently robust network structure, allowing accurate chemotactic response for almost all individuals within a population. Our results suggest that this pathway has evolved to show an optimal chemotactic performance while minimizing the cost of resources associated with high levels of protein expression. Moreover, the underlying topological design principles compensating for intercellular variations seem to be highly conserved among bacterial chemosensory systems.

Single-cell FRET imaging of phosphatase activity in the Escherichia coli chemotaxis system

Two-component signaling systems, in which a receptor-coupled kinase is used to control the phosphorylation level of a response regulator, are commonly used in bacteria to sense their environment. In the chemotaxis system of Escherichia coli, the receptors, and thus the kinase, are clustered on the inner cell membrane. The phosphatase of this system also is recruited to receptor clusters, but the reason for this association is not clear. By using FRET imaging of single cells, we show that in vivo the phosphatase activity is substantially larger at the cluster, indicating that the signaling source (the kinase) and the signaling sink (the phosphatase) tend to be located at the same place in the cell. When this association is disrupted, a gradient in the concentration of the phosphorylated response regulator appears, and the chemotactic response is degraded. Such colocalization is inevitable in systems in which the activity of the kinase and the phosphatase are produced by the same enzyme. Evidently, this design enables a more rapid and spatially uniform response.

Robustness of cellular functions

Robustness, the ability to maintain performance in the face of perturbations and uncertainty, is a long-recognized key property of living systems. Owing to intimate links to cellular complexity, however, its molecular and cellular basis has only recently begun to be understood. Theoretical approaches to complex engineered systems can provide guidelines for investigating cellular robustness because biology and engineering employ a common set of basic mechanisms in different combinations. Robustness may be a key to understanding cellular complexity, elucidating design principles, and fostering closer interactions between experimentation and theory.

Model of bacterial band formation in aerotaxis

Aerotaxis is a particular form of "energy taxis". It is based on a largely elusive signal transduction machinery. In aerotaxis, oxygen dissolved in water plays the role of both attractant (at moderate concentrations) and repellent (at high and low concentrations). Cells swimming from favorable oxygen concentrations into regions with unfavorable concentrations increase the frequency of reversals, turn back into the favorable domain, and become effectively trapped there. At the same time, bacteria consume oxygen, creating an oxygen gradient. This behavior leads to a pattern formation phenomenon: bacteria self-organize into a dense band at a certain distance from the air-water interface. We incorporate experimental observations of the aerotactic bacterium, Azospirillum brasilense, into a mathematical model. The model consists of a system of differential equations describing swimming bacterial cells and diffusing oxygen. The cells' frequency of reversals depends on the concentration of oxygen and its time derivative while oxygen is depleted by the bacteria. We suggest a hypothetical model of energy sensing mediated by aerotactic receptors Aer and Tsr. Computer simulations and analysis of the model equations allow comparisons of theoretical and experimental results and provide insight into the mechanisms of bacterial pattern formation and underlying signal transduction machinery. We make testable predictions about position and density of the bacterial band.

Necessary conditions for a minimal model of receptor to show adaptive response over a wide range of levels of stimulus

Sensory systems respond to temporal changes in the stimulus and adapt to the new level when it persists, this pattern of response being maintained in a wide range of levels of stimulus. Here we use a simple model of adaptation developed by Segel et al. (J. Theor. Biol. 120 (1986) 151-179) and extended by Hauri and Ross (Biophys. J. 68 (1995) 708-722) to study the conditions in which it shows wide range of response. The model consists of a receptor that switches between a variable number of states, either by mass action law or by covalent modification. Using a global optimization procedure, we have optimized the adaptive response of the alternatives of the model with different number of states. We find that it is impossible to obtain a wide range of response if the receptor switches between states following mass-action laws, irrespective of the number of states. Instead, a wide range (of five orders of magnitude of ligand concentration) can be obtained if the receptor switches between several states by irreversible covalent modification, in agreement with previous models. Therefore, in this model, expenditure of energy to maintain a large number of covalent modification cycles operating outside equilibrium is necessary to achieve a wide range of response. The optimal values of the parameters present similar patterns to those reported for specific receptors, but there is no quantitative agreement. For instance, ligand affinity varies several orders of magnitude between the different states of the receptor, what is unlikely to be fulfilled by real systems. To see if the minimal model can show adaptive response and range with quantitatively plausible parameter values a sub-optimal receptor was studied, finding that adaptive response of high intensity can still be obtained in at least three orders of magnitude.

Modeling the cell's guidance system

Cell locomotion can be directed by external gradients of diffusible substances leading to chemotaxis. Recently, the mechanisms of gradient sensing, the cell guidance system, came under scrutiny both in experimental analysis and computational modeling. Here, we review several recent computational models of gradient sensing in eukaryotic cells, demonstrating why some of them predict little sensitivity to changes in the gradient and response "locking," whereas others predict high gradient sensitivity at the expense of signal gain. We also propose a way to view chemotaxis regulation as a highly coupled combination of semi-independent control modules, leading to simplifying modeling of this complex cellular behavior.