Exponential Signaling Gain at the Receptor Level Enhances Signal-to-Noise Ratio in Bacterial Chemotaxis

Cellular signaling systems show astonishing precision in their response to external stimuli despite strong fluctuations in the molecular components that determine pathway activity. To control the effects of noise on signaling most efficiently, living cells employ compensatory mechanisms that reach from simple negative feedback loops to robustly designed signaling architectures. Here, we report on a novel control mechanism that allows living cells to keep precision in their signaling characteristics – stationary pathway output, response amplitude, and relaxation time – in the presence of strong intracellular perturbations. The concept relies on the surprising fact that for systems showing perfect adaptation an exponential signal amplification at the receptor level suffices to eliminate slowly varying multiplicative noise. To show this mechanism at work in living systems, we quantified the response dynamics of the E. coli chemotaxis network after genetically perturbing the information flux between upstream and downstream signaling components. We give strong evidence that this signaling system results in dynamic invariance of the activated response regulator against multiplicative intracellular noise. We further demonstrate that for environmental conditions, for which precision in chemosensing is crucial, the invariant response behavior results in highest chemotactic efficiency. Our results resolve several puzzling features of the chemotaxis pathway that are widely conserved across prokaryotes but so far could not be attributed any functional role.     

A computational study of feedback effects on signal dynamics in a mitogen-activated protein kinase (MAPK) pathway model

Exploiting signaling pathways for the purpose of controlling cell function entails identifying and manipulating the information content of intracellular signals. As in the case of the ubiquitously expressed, eukaryotic mitogen-activated protein kinase (MAPK) signaling pathway, this information content partly resides in the signals' dynamical properties. Here, we utilize a mathematical model to examine mechanisms that govern MAPK pathway dynamics, particularly the role of putative negative feedback mechanisms in generating complete signal adaptation, a term referring to the reset of a signal to prestimulation levels. In addition to yielding adaptation of its direct target, feedback mechanisms implemented in our model also indirectly assist in the adaptation of signaling components downstream of the target under certain conditions. In fact, model predictions identify conditions yielding ultra-desensitization of signals in which complete adaptation of target and downstream signals culminates even while stimulus recognition (i.e., receptor-ligand binding) continues to increase. Moreover, the rate at which signal decays can follow first-order kinetics with respect to signal intensity, so that signal adaptation is achieved in the same amount of time regardless of signal intensity or ligand dose. All of these features are consistent with experimental findings recently obtained for the Chinese hamster ovary (CHO) cell lines (Asthagiri et al., J. Biol. Chem. 1999, 274, 27119-27127). Our model further predicts that although downstream effects are independent of whether an enzyme or adaptor protein is targeted by negative feedback, adaptor-targeted feedback can "back-propagate" effects upstream of the target, specifically resulting in increased steady-state upstream signal. Consequently, where these upstream components serve as nodes within a signaling network, feedback can transfer signaling through these nodes into alternate pathways, thereby promoting the sort of signaling cross-talk that is becoming more widely appreciated.     

Mathematical models of protein kinase signal transduction

We have developed a mathematical theory that describes the regulation of signaling pathways as a function of a limited number of key parameters. Our analysis includes linear kinase-phosphatase cascades, as well as systems containing feedback interactions, crosstalk with other signaling pathways, and/or scaffolding and G proteins. We find that phosphatases have a more pronounced effect than kinases on the rate and duration of signaling, whereas signal amplitude is controlled primarily by kinases. The simplest model pathways allow amplified signaling only at the expense of slow signal propagation. More complex and realistic pathways can combine high amplification and signaling rates with maintenance of a stable off-state. Our models also explain how different agonists can evoke transient or sustained signaling of the same pathway and provide a rationale for signaling pathway design.     

Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways

Cellular circuits have positive and negative feedback loops that allow them to respond properly to noisy external stimuli. It is intriguing that such feedback loops exist in many cases in a particular form of coupled positive and negative feedback loops with different time delays. As a result of our mathematical simulations and investigations into various experimental evidences, we found that such coupled feedback circuits can rapidly turn on a reaction to a proper stimulus, robustly maintain its status, and immediately turn off the reaction when the stimulus disappears. In other words, coupled feedback loops enable cellular systems to produce perfect responses to noisy stimuli with respect to signal duration and amplitude. This suggests that coupled positive and negative feedback loops form essential signal transduction motifs in cellular signaling systems.     

Control of MAPK specificity by feedback phosphorylation of shared adaptor protein Ste50

Many different signaling pathways share common components but nevertheless invoke distinct physiological responses. In yeast, the adaptor protein Ste50 functions in multiple mitogen-activated protein (MAP) kinase pathways, each with unique dynamical and developmental properties. Although Kss1 activity is sustained and promotes invasive growth, Hog1 activity is transient and promotes cell adaptation to osmotic stress. Here we show that osmotic stress activates Kss1 as well as Hog1. We show further that Hog1 phosphorylates Ste50 and that phosphorylation of Ste50 limits the duration of Kss1 activation and prevents invasive growth under high osmolarity growth conditions. Thus feedback regulation of a shared component can restrict the activity of a competing MAP kinase to ensure signal fidelity.     

Natural selection governs local, but not global, evolutionary gene coexpression networks in Caenorhabditis elegans

Background

Signal duration (e.g. the time over which an active signaling intermediate persists) is a key regulator of biological decisions in myriad contexts such as cell growth, proliferation, and developmental lineage commitments. Accompanying differences in signal duration are numerous downstream biological processes that require multiple steps of biochemical regulation.

Results

Here we present an analysis that investigates how simple biochemical motifs that involve multiple stages of regulation can be constructed to differentially process signals that persist at different time scales. We compute the dynamic, frequency dependent gain within these networks and resulting power spectra to better understand how biochemical networks can integrate signals at different time scales. We identify topological features of these networks that allow for different frequency dependent signal processing properties.

Conclusion

We show that multi-staged cascades are effective in integrating signals of long duration whereas multi-staged cascades that operate in the presence of negative feedback are effective in integrating signals of short duration. Our studies suggest principles for why signal duration in connection with multiple steps of downstream regulation is a ubiquitous motif in biochemical systems.     

Dose-to-duration encoding and signaling beyond saturation in intracellular signaling networks

The cellular response elicited by an environmental cue typically varies with the strength of the stimulus. For example, in the yeast Saccharomyces cerevisiae, the concentration of mating pheromone determines whether cells undergo vegetative growth, chemotropic growth, or mating. This implies that the signaling pathways responsible for detecting the stimulus and initiating a response must transmit quantitative information about the intensity of the signal. Our previous experimental results suggest that yeast encode pheromone concentration as the duration of the transmitted signal. Here we use mathematical modeling to analyze possible biochemical mechanisms for performing this “dose-to-duration” conversion. We demonstrate that modulation of signal duration increases the range of stimulus concentrations for which dose-dependent responses are possible; this increased dynamic range produces the counterintuitive result of “signaling beyond saturation” in which dose-dependent responses are still possible after apparent saturation of the receptors. We propose a mechanism for dose-to-duration encoding in the yeast pheromone pathway that is consistent with current experimental observations. Most previous investigations of information processing by signaling pathways have focused on amplitude encoding without considering temporal aspects of signal transduction. Here we demonstrate that dose-to-duration encoding provides cells with an alternative mechanism for processing and transmitting quantitative information about their surrounding environment. The ability of signaling pathways to convert stimulus strength into signal duration results directly from the nonlinear nature of these systems and emphasizes the importance of considering the dynamic properties of signaling pathways when characterizing their behavior. Understanding how signaling pathways encode and transmit quantitative information about the external environment will not only deepen our understanding of these systems but also provide insight into how to reestablish proper function of pathways that have become dysregulated by disease.     

Induction Kinetics of a Conditional pH Stress Response System in Escherichia coli

The analysis of stress response systems in microorganisms can reveal molecular strategies for regulatory control and adaptation. In this study, we focused on the Cad module, a subsystem of Escherichia coli’s response to acidic stress that is conditionally activated at low pH only when lysine is available. When expressed, the Cad system counteracts the elevated H⁺ concentration by converting lysine to cadaverine under the consumption of H⁺ and exporting cadaverine in exchange for external lysine. Surprisingly, the cad operon displays a transient response, even when the conditions for its induction persist. To quantitatively characterize the regulation of the Cad module, we experimentally recorded and theoretically modeled the dynamics of important system variables. We established a quantitative model that adequately describes and predicts the transient expression behavior for various initial conditions. Our quantitative analysis of the Cad system supports negative feedback by external cadaverine as the origin of the transient response. Furthermore, the analysis puts causal constraints on the precise mechanism of signal transduction via the regulatory protein CadC.     

Multistable Decision Switches for Flexible Control of Epigenetic Differentiation

It is now recognized that molecular circuits with positive feedback can induce two different gene expression states (bistability) under the very same cellular conditions. Whether, and how, cells make use of the coexistence of a larger number of stable states (multistability) is however largely unknown. Here, we first examine how autoregulation, a common attribute of genetic master regulators, facilitates multistability in two-component circuits. A systematic exploration of these modules'' parameter space reveals two classes of molecular switches, involving transitions in bistable (progression switches) or multistable (decision switches) regimes. We demonstrate the potential of decision switches for multifaceted stimulus processing, including strength, duration, and flexible discrimination. These tasks enhance response specificity, help to store short-term memories of recent signaling events, stabilize transient gene expression, and enable stochastic fate commitment. The relevance of these circuits is further supported by biological data, because we find them in numerous developmental scenarios. Indeed, many of the presented information-processing features of decision switches could ultimately demonstrate a more flexible control of epigenetic differentiation.     

Perceptual judgments via sensory-motor interaction assisted by cortical GABA

Recurrent input to sensory cortex, via long-range reciprocal projections between motor and sensory cortices, is essential for accurate perceptual judgments. GABA levels in sensory cortices correlate with perceptual performance. We simulated a neuron-astrocyte network model to investigate how top-down, feedback signaling from a motor network (Nmot) to a sensory network (Nsen) affects perceptual judgments in association with ambient (extracellular) GABA levels. In the Nsen, astrocytic transporters modulated ambient GABA levels around pyramidal cells. A simple perceptual task was implemented: detection of a feature stimulus presented to the Nsen. The Nmot showed distinct perceptual behaviors: hit, fault, and miss. A hit is a correct response to the stimulus, a fault is a wrong response to the stimulus, and a miss is no response to the stimulus. In hits, the feedback signaling increased the gain of Nsen pyramidal cells and accelerated the reaction speed of Nmot pyramidal cells to the stimulus. Without feedback signaling, the Nsen but not Nmot responded to the stimulus, resulting in a miss. With too strong feedback signaling, the Nmot resulted in a fault, namely, stimulus-insensitive but not stimulus-sensitive pyramidal cells wrongly responded. Balancing the feedforward and feedback signaling formed a coherent, ongoing-spontaneous neuronal state, by which the highest hit rate was achieved. A transient reduction in local ambient GABA levels, triggered by the stimulus, contributed to accelerating the reaction speed under noisy environmental conditions. Adjusting the basal ambient GABA level ensured high hit rates. We suggest that motor cortex feedback may accelerate reaction speed to sensory stimulation by promoting coherency in ongoing-spontaneous neuronal activity between sensory and motor cortices, thereby achieving prompt perceptual judgments. Spatiotemporal modulation of ambient GABA levels, possibly by astrocytic transporters, assists in making reliable perceptual judgments.     

Effect of the MAPK cascade structure, nuclear translocation and regulation of transcription factors on gene expression

The mitogen activated protein kinase (MAP kinase) cascade system represents a highly conserved prototype of signal transduction by enzyme cascades. One of the best-studied properties of the MAPK system is its ability to convert graded input stimulus to switch-like all-or-none responses. Previous theoretical studies have centered on quantifying dual phosphorylated MAPK as a final output response and have not incorporated its influence on the regulation of gene expression. The main objective of the current work is to understand the regulatory effect of positive feedback loop embedded in the MAPK cascade, nuclear translocation of active MAPK, phosphorylation and activation of nuclear target proteins on the regulation of specific gene expression. To achieve this objective, we have simulated the MAPK cascade system, which resembles Hog1p activation pathway in yeast, at steady state. Thus, the input signal to the MAPK system is correlated with gene expression as a final system-level output response. The steady state simulation results suggest that other than regulating the signal propagation through cascades, the nuclear translocation of activated MAPK and subsequent regulation of gene expression represent one of the key modes to control the threshold level of response. This work proposes that, it is essential to consider the compartmental distributions of signaling species and the corresponding regulatory mechanisms of gene expression to study the system-level performance of signaling modules such as the MAPK cascade. Such an analysis will relate the extracellular cues to the final phenotypic response by capturing the mechanistic details of the signaling pathway.     

A network model of the barrel cortex combined with a differentiator detector reproduces features of the behavioral response to single-neuron stimulation

The stimulation of a single neuron in the rat somatosensory cortex can elicit a behavioral response. The probability of a behavioral response does not depend appreciably on the duration or intensity of a constant stimulation, whereas the response probability increases significantly upon injection of an irregular current. Biological mechanisms that can potentially suppress a constant input signal are present in the dynamics of both neurons and synapses and seem ideal candidates to explain these experimental findings. Here, we study a large network of integrate-and-fire neurons with several salient features of neuronal populations in the rat barrel cortex. The model includes cellular spike-frequency adaptation, experimentally constrained numbers and types of chemical synapses endowed with short-term plasticity, and gap junctions. Numerical simulations of this model indicate that cellular and synaptic adaptation mechanisms alone may not suffice to account for the experimental results if the local network activity is read out by an integrator. However, a circuit that approximates a differentiator can detect the single-cell stimulation with a reliability that barely depends on the length or intensity of the stimulus, but that increases when an irregular signal is used. This finding is in accordance with the experimental results obtained for the stimulation of a regularly-spiking excitatory cell.     

Induction and expression of long- and short-term neurosecretory potentiation in a neural cell line

In a neural cell line, the secretion of excitatory amino acids in response to a depolarizing stimulus is potentiated by the addition of serotonin. The duration of this potentiation is dependent on the strength of the stimulus. Persistent secretory potentiation induced by a strong stimulus requires the activation of both serotonin and NMDA receptors. Inhibiting the NMDA receptor during serotonin presentation prevented the induction of potentiation. The temporal characteristic of the potentiation is correlated with the elevation of cAMP levels. Serotonin exposure while inhibiting NMDA receptors results in a transient elevation of cAMP levels, whereas coactivation with NMDA and serotonin results in a persistent elevation of cAMP. Thus, it is possible to obtain potentiation of secretion in a single cell either transiently or persistently. The timing of potentiated responses in this system is of the same magnitude as that in similar systems used as models for short-term and long-term memory.     

Cyclic 3'', 5''-AMP relay in dictyostelium discoideum. IV. Recovery of the cAMP signaling response after adaptation to cAMP

In dictyoselium discoideum, an increase in extracellular cAMP activates adenylate cyclase, leading to an increase in intracellular cAMP and the rate of cAMP secretion. Cells adapt to any constant cAMP stimulus after several minutes, but still respond to an increase in the concentration of the stimulus. We have now characterized the decay of adaptation (deadaptation) after the removal of cAMP stimuli. Levels of adaptation were established by the perfusion of [(3)H]adenosine-labeled amoebae with a defined cAMP stimulus. After a variable recovery period, the magnitude of the signaling response to a second stimulus was measured; its attenuation was taken as a measure of residual adaption to the first stimulus. The level of adaptation established by the first stimulus depended on both its magnitude and duration. Deadaptation began as soon as the first stimulus was removed. The magnitude of the response to the second stimulus increased with the recovery time in a first-order fashion, with a t(1/2)=3-4 min for stimuli of 10(-8) M to 10(-5) M cAMP. Responses to test stimuli, although reduced in magnitude, had an accelerated time-course when they closely followed a prior response that had not completely subsided. This effect is called priming; we believe it reveals a reversible, rate-limiting step that modulates the onset and termination of the signaling responses of amoebae that have not recently responded to a cAMP stimulus. We have suggested that the cAMP signaling response is controlled by two antagonistic cellular processes, excitation and adaptation. The data reported here imply that both the rate of rise in the adaptation process and the final level reached depend on the occupancy of cAMP surface receptors and that the decay of adaptation when external cAMP is removed proceeds with first-order kinetics.     

Adaptive Responses Limited by Intrinsic Noise

Sensory systems have mechanisms to respond to the external environment and adapt to them. Such adaptive responses are effective for a wide dynamic range of sensing and perception of temporal change in stimulus. However, noise generated by the adaptation system itself as well as extrinsic noise in sensory inputs may impose a limit on the ability of adaptation systems. The relation between response and noise is well understood for equilibrium systems in the form of fluctuation response relation. However, the relation for nonequilibrium systems, including adaptive systems, are poorly understood. Here, we systematically explore such a relation between response and fluctuation in adaptation systems. We study the two network motifs, incoherent feedforward loops (iFFL) and negative feedback loops (nFBL), that can achieve perfect adaptation. We find that the response magnitude in adaption systems is limited by its intrinsic noise, implying that higher response would have higher noise component as well. Comparing the relation of response and noise in iFFL and nFBL, we show that whereas iFFL exhibits adaptation over a wider parameter range, nFBL offers higher response to noise ratio than iFFL. We also identify the condition that yields the upper limit of response for both network motifs. These results may explain the reason of why nFBL seems to be more abundant in nature for the implementation of adaption systems.     

Spatial frequency and visual persistence: cortical reset

Psychophysical studies show that the duration of visual persistence increases with spatial frequency of gratings. Previous theories ascribe this finding to differences between the spatial and temporal properties of sustained and transient pathways. This paper proposes an alternative account that explains persistence as a side-effect of excitatory feedback in neural circuits for contour extraction. Mechanisms to break excitatory feedback include inhibitory reset signals at stimulus offset. Simulations demonstrate how gratings with lower spatial frequency generate stronger inhibitory reset signals, thereby resulting in shorter persistence for lower spatial frequencies. Additional simulations account for interactions of spatial frequency with stimulus duration, effects of adaptation, and properties of residual traces, as opposed to visual persistence.