| Publications about 'biological adaptation' |
| Articles in journal or book chapters |
| The phenomenon of fold-change detection, or scale-invariance, is exhibited by a variety of sensory systems, in both bacterial and eukaryotic signaling pathways. This encyclopedia-style article gives a brief introduction to the subject. |
| Aerotaxis, the directed migration along oxygen gradients, allows many microorganisms to locate favorable oxygen concentrations. Despite oxygen's fundamental role for life, even key aspects of aerotaxis remain poorly understood. In Bacillus subtilis, for example, there is conflicting evidence of whether migration occurs to the maximal oxygen concentration available or to an optimal intermediate one, and how aerotaxis can be maintained over a broad range of conditions. Using precisely controlled oxygen gradients in a microfluidic device, spanning the full spectrum of conditions from quasi-anoxic to oxic (60nM-1mM), we resolved B. subtilis' ``oxygen preference conundrum'' by demonstrating consistent migration towards maximum oxygen concentrations. Surprisingly, the strength of aerotaxis was largely unchanged over three decades in oxygen concentration (131nM-196mM). We discovered that in this range B. subtilis responds to the logarithm of the oxygen concentration gradient, a log-sensing strategy that affords organisms high sensitivity over a wide range of conditions. |
| The phenomenon of fold-change detection, or scale invariance, is exhibited by a variety of sensory systems, in both bacterial and eukaryotic signaling pathways. It has been often remarked in the systems biology literature that certain systems whose output variables respond at a faster time scale than internal components give rise to an approximate scale-invariant behavior, allowing approximate fold-change detection in stimuli. This paper establishes a fundamental limitation of such a mechanism, showing that there is a minimal fold-change detection error that cannot be overcome, no matter how large the separation of time scales is. To illustrate this theoretically predicted limitation, we discuss two common biomolecular network motifs, an incoherent feedforward loop and a feedback system, as well as a published model of the chemotaxis signaling pathway of Dictyostelium discoideum. |
| The chemotaxis pathway of the bacterium Rhodobacter sphaeroides has many similarities to 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, in response to a scaling of its ligand input signal, Escherichia coli exhibits the same output behavior, a property known as fold-change detection (FCD). In 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 behavior. 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 behavior 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. |
| This paper studies a recently discovered remarkable feature that was shown in many adapting systems: scale invariance, which means that the initial, transient behavior stays approximately the same when the background signal level is scaled. Not every adapting system is scale-invariant: we investigate under which conditions a broadly used model of biochemical enzymatic networks will show scale invariant behavior. For all 3-node enzymatic networks, we performed a wide computational study to find candidates for scale invariance, among 16,038 possible topologies. This effort led us to discover a new necessary and sufficient mechanism that explains the behavior of all 3-node enzyme networks that have this property, which we call``uniform linearizations with fast output''. We also apply our theoretical results to a concrete biological example of order six, a model of the response of the chemotaxis signaling pathway of Dictyostelium discoideum to changes in chemoeffector cyclic adenosine monophosphate (cAMP). |
| Often, the ultimate goal of regulation is to maintain a narrow range of concentration levels of vital quantities (homeostasis, adaptation) while at the same time appropriately reacting to changes in the environment (signal detection or sensitivity). Much theoretical, modeling, and analysis effort has been devoted to the understanding of these questions, traditionally in the context of steady-state responses to constant or step-changing stimuli. In this paper, we present a new theorem that provides a necessary and sufficient characterization of invariance of transient responses to symmetries in inputs. A particular example of this property, scale invariance (a.k.a. "fold change detection"), appears to be exhibited by biological sensory systems ranging from bacterial chemotaxis pathways to signal transduction mechanisms in eukaryotes. The new characterization amounts to the solvability of an associated partial differential equation. It is framed in terms of a notion which considerably extends equivariant actions of compact Lie groups. For several simple system motifs that are recurrent in biology, the solvability criterion may be checked explicitly. |
| Certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold-changes in input, and not on absolute changes. Thus, a step change in input from, say, level 1 to 2, gives precisely the same dynamical output as a step from level 2 to 4, since the steps have the same fold-change. We ask what is the benefit of FCD, and show that FCD is necessary and sufficient for sensory search to be independent of multiplying the input-field by a scalar. Thus the FCD search pattern depends only on the spatial profile of the input, and not on its amplitude. Such scalar symmetry occurs in a wide range of sensory inputs, such as source strength multiplying diffusing/convecting chemical fields sensed in chemotaxis, ambient light multiplying the contrast field in vision, and protein concentrations multiplying the output in cellular signaling-systems.Furthermore, we demonstrate that FCD entails two features found across sensory systems, exact adaptation and Weber's law, but that these two features are not sufficient for FCD. Finally, we present a wide class of mechanisms that have FCD, including certain non-linear feedback and feedforward loops.. We find that bacterial chemotaxis displays feedback within the present class, and hence is expected to show FCD. This can explain experiments in which chemotaxis searches are insensitive to attractant source levels. This study thus suggests a connection between properties of biological sensory systems and scalar symmetry stemming from physical properties of their input-fields. |
| This note provides a simple result showing, under suitable technical assumptions, that if a system S adapts to a class of external signals U, then S must necessarily contain a subsystem which is capable of generating all the signals in U. It is not assumed that regulation is robust, nor is there a prior requirement for the system to be partitioned into separate plant and controller components. Instead, a "signal detection" capability is imposed. These weaker assumptions make the result better applicable to cellular phenomena such as the adaptation of E-coli chemotactic tumbling rate to constant concentrations. |
| Conference articles |
| Integral feedback can help achieve robust tracking independently of external disturbances. Motivated by this knowledge, biological engineers have proposed various designs of biomolecular integral feedback controllers to regulate biological processes. In this paper, we theoretically analyze the operation of a particular synthetic biomolecular integral controller, which we have recently proposed and implemented experimentally. Using a combination of methods, ranging from linearized analysis to sum-of-squares (SOS) Lyapunov functions, we demonstrate that, when the controller is operated in closed-loop, it is capable of providing integral corrections to the concentration of an output species in such a manner that the output tracks a reference signal linearly over a large dynamic range. We investigate the output dependency on the reaction parameters through sensitivity analysis, and quantify performance using control theory metrics to characterize response properties, thus providing clear selection guidelines for practical applications. We then demonstrate the stable operation of the closed-loop control system by constructing quartic Lyapunov functions using SOS optimization techniques, and establish global stability for a unique equilibrium. Our analysis suggests that by incorporating effective molecular sequestration, a biomolecular closed-loop integral controller that is capable of robustly regulating gene expression is feasible. |
| This conference paper (a) summarizes material from "A fundamental limitation to fold-change detection by biological systems with multiple time scales" (IET Systems Biology 2014) and presents additional remarks regarding (b) expansion techniques to compute FCD error and (c) stochastic adaptation and FCD |
| Recent experimental work has shown that transient E. coli chemotactic response is unchanged by a scaling of its ligand input signal (fold change detection, or FCD), and this is in agreement with earlier mathematical predictions. However, this prediction was based on certain particular assumptions on the structure of the chemotaxis pathway. In this work, we begin by showing that behavior similar to FCD can be obtained under weaker conditions on the system structure. Namely, we show that under relaxed conditions, a scaling of the chemotaxis system's inputs leads to a time scaling of the output response. We propose that this may be a contributing factor to the robustness of the experimentally observed FCD. We further show that FCD is a special case of this time scaling behavior for which the time scaling factor is unity. We then proceed to extend the conditions for output time scaling to more general adapting systems, and demonstrate this time scaling behavior on a published model of the chemotaxis pathway of the bacterium Rhodobacter sphaeroides. This work therefore provides examples of how robust biological behavior can arise from simple yet realistic conditions on the underlying system structure. |
| This is a conference version of ``A characterization of scale invariant responses in enzymatic networks. |
| This paper studies invariance with respect to symmetries in sensory fields, a particular case of which, scale invariance, has recently been found in certain eukaryotic as well as bacterial cell signaling systems. We describe a necessary and sufficient characterization of symmetry invariance in terms of equivariant transformations, show how this characterization helps find all possible symmetries in standard models of biological adaptation, and discuss symmetry-invariant searches. |
| The proper function of many biological systems requires that external perturbations be detected, allowing the system to adapt to these environmental changes. It is now well established that this dual detection and adaptation requires that the system have an internal model in the feedback loop. In this paper we relax the requirement that the response of the system adapt perfectly, but instead allow regulation to within a neighborhood of zero. We show, in a nonlinear setting, that systems with the ability to detect input signals and approximately adapt require an approximate model of the input. We illustrate our results by analyzing a well-studied biological system. These results generalize previous work which treats the perfectly adapting case. |
| This conference paper presented a version of an approximate internal model principle, for linear systems. A subsequent paper at the IFAC 2008 conference improved on this result by extending it to a class of nonlinear systems. |
| Internal reports |
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