Signal duration and the time scale dependence of signal integration in biochemical pathways

Signal duration (e.g. the time scales 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. 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 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. Our studies suggest design principles for why signal duration in connection with multiple steps of downstream regulation is a ubiquitous control motif in biochemical systems.Comment: 27 pages, 4 figure

Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity

We present a novel formulation for biochemical reaction networks in the context of signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select a set of 'source' species, which receive input signals. Signals are transmitted to all other species in the system (the 'target' species) with a specific delay and transmission strength. The delay is computed as the maximal reaction time until a stable equilibrium for the target species is reached, in the context of all other reactions in the system. The transmission strength is the concentration change of the target species. The computed input-output transfer functions can be stored in a matrix, fitted with parameters, and recalled to build discrete dynamical models. By separating reaction time and concentration we can greatly simplify the model, circumventing typical problems of complex dynamical systems. The transfer function transformation can be applied to mass-action kinetic models of signal transduction. The paper shows that this approach yields significant insight, while remaining an executable dynamical model for signal transduction. In particular we can deconstruct the complex system into local transfer functions between individual species. As an example, we examine modularity and signal integration using a published model of striatal neural plasticity. The modules that emerge correspond to a known biological distinction between calcium-dependent and cAMP-dependent pathways. We also found that overall interconnectedness depends on the magnitude of input, with high connectivity at low input and less connectivity at moderate to high input. This general result, which directly follows from the properties of individual transfer functions, contradicts notions of ubiquitous complexity by showing input-dependent signal transmission inactivation.Comment: 13 pages, 5 tables, 15 figure

Gain control in molecular information processing: Lessons from neuroscience

Statistical properties of environments experienced by biological signaling systems in the real world change, which necessitate adaptive responses to achieve high fidelity information transmission. One form of such adaptive response is gain control. Here we argue that a certain simple mechanism of gain control, understood well in the context of systems neuroscience, also works for molecular signaling. The mechanism allows to transmit more than one bit (on or off) of information about the signal independently of the signal variance. It does not require additional molecular circuitry beyond that already present in many molecular systems, and, in particular, it does not depend on existence of feedback loops. The mechanism provides a potential explanation for abundance of ultrasensitive response curves in biological regulatory networks.Comment: 10 pages, 5 figure

The Evolution of Reaction-diffusion Controllers for Minimally Cognitive Agents

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Computational investigations into the orgins of 'short term' biochemical memory in T cell activation

Recent studies have reported that T cells can integrate signals between interrupted encounters with Antigen Presenting Cells (APCs) in such a way that the process of signal integration exhibits a form of memory. Here, we carry out a computational study using a simple mathematical model of T cell activation to investigate the ramifications of interrupted T cell-APC contacts on signal integration. We consider several mechanisms of how signal integration at these time scales may be achieved and conclude that feedback control of immediate early gene products (IEGs) appears to be a highly plausible mechanism that allows for effective signal integration and cytokine production from multiple exposures to APCs. Analysis of these computer simulations provides an experimental roadmap involving several testable predictions.Comment: 11 pages, published July 18th 200

Information transfer in signaling pathways : a study using coupled simulated and experimental data

Background: The topology of signaling cascades has been studied in quite some detail. However, how information is processed exactly is still relatively unknown. Since quite diverse information has to be transported by one and the same signaling cascade (e.g. in case of different agonists), it is clear that the underlying mechanism is more complex than a simple binary switch which relies on the mere presence or absence of a particular species. Therefore, finding means to analyze the information transferred will help in deciphering how information is processed exactly in the cell. Using the information-theoretic measure transfer entropy, we studied the properties of information transfer in an example case, namely calcium signaling under different cellular conditions. Transfer entropy is an asymmetric and dynamic measure of the dependence of two (nonlinear) stochastic processes. We used calcium signaling since it is a well-studied example of complex cellular signaling. It has been suggested that specific information is encoded in the amplitude, frequency and waveform of the oscillatory Ca2+-signal. Results: We set up a computational framework to study information transfer, e.g. for calcium signaling at different levels of activation and different particle numbers in the system. We stochastically coupled simulated and experimentally measured calcium signals to simulated target proteins and used kernel density methods to estimate the transfer entropy from these bivariate time series. We found that, most of the time, the transfer entropy increases with increasing particle numbers. In systems with only few particles, faithful information transfer is hampered by random fluctuations. The transfer entropy also seems to be slightly correlated to the complexity (spiking, bursting or irregular oscillations) of the signal. Finally, we discuss a number of peculiarities of our approach in detail. Conclusion: This study presents the first application of transfer entropy to biochemical signaling pathways. We could quantify the information transferred from simulated/experimentally measured calcium signals to a target enzyme under different cellular conditions. Our approach, comprising stochastic coupling and using the information-theoretic measure transfer entropy, could also be a valuable tool for the analysis of other signaling pathways

Bioengineering models of cell signaling

Strategies for rationally manipulating cell behavior in cell-based technologies and molecular therapeutics and understanding effects of environmental agents on physiological systems may be derived from a mechanistic understanding of underlying signaling mechanisms that regulate cell functions. Three crucial attributes of signal transduction necessitate modeling approaches for analyzing these systems: an ever-expanding plethora of signaling molecules and interactions, a highly interconnected biochemical scheme, and concurrent biophysical regulation. Because signal flow is tightly regulated with positive and negative feedbacks and is bidirectional with commands traveling both from outside-in and inside-out, dynamic models that couple biophysical and biochemical elements are required to consider information processing both during transient and steady-state conditions. Unique mathematical frameworks will be needed to obtain an integrated perspective on these complex systems, which operate over wide length and time scales. These may involve a two-level hierarchical approach wherein the overall signaling network is modeled in terms of effective "circuit" or "algorithm" modules, and then each module is correspondingly modeled with more detailed incorporation of its actual underlying biochemical/biophysical molecular interactions

Information transfer in signaling pathways : a study using coupled simulated and experimental data

Background: The topology of signaling cascades has been studied in quite some detail. However, how information is processed exactly is still relatively unknown. Since quite diverse information has to be transported by one and the same signaling cascade (e.g. in case of different agonists), it is clear that the underlying mechanism is more complex than a simple binary switch which relies on the mere presence or absence of a particular species. Therefore, finding means to analyze the information transferred will help in deciphering how information is processed exactly in the cell. Using the information-theoretic measure transfer entropy, we studied the properties of information transfer in an example case, namely calcium signaling under different cellular conditions. Transfer entropy is an asymmetric and dynamic measure of the dependence of two (nonlinear) stochastic processes. We used calcium signaling since it is a well-studied example of complex cellular signaling. It has been suggested that specific information is encoded in the amplitude, frequency and waveform of the oscillatory Ca2+-signal. Results: We set up a computational framework to study information transfer, e.g. for calcium signaling at different levels of activation and different particle numbers in the system. We stochastically coupled simulated and experimentally measured calcium signals to simulated target proteins and used kernel density methods to estimate the transfer entropy from these bivariate time series. We found that, most of the time, the transfer entropy increases with increasing particle numbers. In systems with only few particles, faithful information transfer is hampered by random fluctuations. The transfer entropy also seems to be slightly correlated to the complexity (spiking, bursting or irregular oscillations) of the signal. Finally, we discuss a number of peculiarities of our approach in detail. Conclusion: This study presents the first application of transfer entropy to biochemical signaling pathways. We could quantify the information transferred from simulated/experimentally measured calcium signals to a target enzyme under different cellular conditions. Our approach, comprising stochastic coupling and using the information-theoretic measure transfer entropy, could also be a valuable tool for the analysis of other signaling pathways