Selective regulation of cellular processes via protein cascades acting as band-pass filters for time-limited oscillations

Transient frequency preference responses in cell signaling systems

Ligand-receptor systems, covalent modification cycles, and transcriptional networks are the fundamental components of cell signaling and gene expression systems. While their behavior in reaching a steady-state regime under step-like stimulation is well understood, their response under repetitive stimulation, particularly at early time stages is poorly characterized. Yet, early-stage responses to external inputs are arguably as informative as late-stage ones. In simple systems, a periodic stimulation elicits an initial transient response, followed by periodic behavior. Transient responses are relevant when the stimulation has a limited time span, or when the stimulated component's timescale is slow as compared to the timescales of the downstream processes, in which case the latter processes may be capturing only those transients. In this study, we analyze the frequency response of simple motifs at different time stages. We use dose-conserved pulsatile input signals and consider different metrics versus frequency curves. We show that in ligand-receptor systems, there is a frequency preference response in some specific metrics during the transient stages, which is not present in the periodic regime. We suggest this is a general system-level mechanism that cells may use to filter input signals that have consequences for higher order circuits. In addition, we evaluate how the described behavior in isolated motifs is reflected in similar types of responses in cascades and pathways of which they are a part. Our studies suggest that transient frequency preferences are important dynamic features of cell signaling and gene expression systems, which have been overlooked.

A local circadian clock for memory?

The master clock, suprachiasmatic nucleus, is believed to control peripheral circadian oscillators throughout the brain and body. However, recent data suggest there is a circadian clock involved in learning and memory, potentially housed in the hippocampus, which is capable of acting independently of the master clock. Curiously, the hippocampal clock appears to be influenced by the master clock and by hippocampal dependent learning, while under certain conditions it may also revert to its endogenous circadian rhythm. Here we propose a mechanism by which the hippocampal clock could locally determine the nature of its entrainment. We introduce a novel theoretical framework, inspired by but extending beyond the hippocampal memory clock, which provides a new perspective on how circadian clocks throughout the brain coordinate their rhythms. Importantly, a local clock for memory would suggest that hippocampal-dependent learning at the same time every day should improve memory, opening up a range of possibilities for non-invasive therapies to alleviate the detrimental effects of circadian rhythm disruption on human health.

Dose-response aligned circuits in signaling systems

Cells use biological signal transduction pathways to respond to environmental stimuli and the behavior of many cell types depends on precise sensing and transmission of external information. A notable property of signal transduction that was characterized in the Saccharomyces cerevisiae yeast cell and many mammalian cells is the alignment of dose-response curves. It was found that the dose response of the receptor matches closely the dose responses of the downstream. This dose-response alignment (DoRA) renders equal sensitivities and concordant responses in different parts of signaling system and guarantees a faithful information transmission. The experimental observations raise interesting questions about the nature of the information transmission through DoRA signaling networks and design principles of signaling systems with this function. Here, we performed an exhaustive computational analysis on network architectures that underlie the DoRA function in simple regulatory networks composed of two and three enzymes. The minimal circuits capable of DoRA were examined with Michaelis-Menten kinetics. Several motifs that are essential for the dynamical function of DoRA were identified. Systematic analysis of the topology space of robust DoRA circuits revealed that, rather than fine-tuning the network's parameters, the function is primarily realized by enzymatic regulations on the controlled node that are constrained in limiting regions of saturation or linearity.

Dynamics and feedback loops in the transforming growth factor β signaling pathway

Transforming growth factor β (TGF-β) ligands activate a signaling cascade with multiple cell context dependent outcomes. Disruption or disturbance leads to variant clinical disorders. To develop strategies for disease intervention, delineation of the pathway in further detail is required. Current theoretical models of this pathway describe production and degradation of signal mediating proteins and signal transduction from the cell surface into the nucleus, whereas feedback loops have not exhaustively been included. In this study we present a mathematical model to determine the relevance of feedback regulators (Arkadia, Smad7, Smurf1, Smurf2, SnoN and Ski) on TGF-β target gene expression and the potential to initiate stable oscillations within a realistic parameter space. We employed massive sampling of the parameters space to pinpoint crucial players for potential oscillations as well as transcriptional product levels. We identified Smad7 and Smurf2 with the highest impact on the dynamics. Based on these findings, we conducted preliminary time course experiments.

Biochemical frequency control by synchronisation of coupled repressilators: an in silico study of modules for circadian clock systems

Exploration of chronobiological systems emerges as a growing research field within bioinformatics focusing on various applications in medicine, agriculture, and material sciences. From a systems biological perspective, the question arises whether biological control systems for regulation of oscillatory signals and their technical counterparts utilise similar mechanisms. If so, modelling approaches and parameterisation adopted from building blocks can help to identify general components for frequency control in circadian clocks along with gaining insight into mechanisms of clock synchronisation to external stimuli like the daily rhythm of sunlight and darkness. Phase-locked loops could be an interesting candidate in this context. Both, biology and engineering, can benefit from a unified view resulting from systems modularisation. In a first experimental study, we analyse a model of coupled repressilators. We demonstrate its ability to synchronise clock signals in a monofrequential manner. Several oscillators initially deviate in phase difference and frequency with respect to explicit reaction and diffusion rates. Accordingly, the duration of the synchronisation process depends on dedicated reaction and diffusion parameters whose settings still lack to be sufficiently captured analytically.

Using Jensen's inequality to explain the role of regular calcium oscillations in protein activation

Oscillations of cytosolic Ca(2 +) are very important for cellular signalling in excitable and non-excitable cells. The information of various extracellular stimuli is encoded into oscillating patterns of Ca(2 +) that subsequently lead to the activation of different Ca(2 +)-sensitive target proteins in the cell. The question remains, however, why this information is transmitted by means of an oscillating rather than a constant signal. Here we show that, in fact, Ca(2 +) oscillations can achieve a better activation of target proteins than a comparable constant signal with the same amount of Ca(2 +) used. For this we use Jensen's inequality that describes the relation between the function value of the average of a set of argument values and the average of the function values of the arguments from that set. We analyse the role of the cooperativity of the binding of Ca(2 +) and of zero-order ultrasensitivity, which are two properties that are often observed in experiments on the activation of Ca(2 +)-sensitive target proteins. Our results apply to arbitrary oscillation shapes and a very general decoding model, thus generalizing the observations of several previous studies. We compare our results with data from experimental studies investigating the activation of nuclear factor of activated T cells (NFAT) and Ras by oscillatory and constant signals. Although we are restricted to specific approximations due to the lack of detailed kinetic data, we find good qualitative agreement with our theoretical predictions.

Signal amplification in biological and electrical engineering systems: universal role of cascades

In this paper we compare the cascade mechanisms of signal amplification in biological and electrical engineering systems, and show that they share the capacity to considerably amplify signals, and respond to signal changes both quickly and completely, which effectively preserves the form of the input signal. For biological systems, these characteristics are crucial for efficient and reliable cellular signaling. We show that this highly-efficient biological mechanism of signal amplification that has naturally evolved is mathematically fully equivalent with some man-developed amplifiers, which indicates parallels between biological evolution and successful technology development.

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 Ca(2+)-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.

Spatio-temporal modelling explains the effect of reduced plasma membrane Ca2+ efflux on intracellular Ca2+ oscillations in hepatocytes

In many non-excitable eukaryotic cells, including hepatocytes, Ca(2+) oscillations play a key role in intra- and intercellular signalling, thus regulating many cellular processes from fertilisation to death. Therefore, understanding the mechanisms underlying these oscillations, and consequently understanding how they may be regulated, is of great interest. In this paper, we study the influence of reduced Ca(2+) plasma membrane efflux on Ca(2+) oscillations in hepatocytes. Our previous experiments with carboxyeosin show that a reduced plasma membrane Ca(2+) efflux increases the frequency of Ca(2+) oscillations, but does not affect the duration of individual transients. This phenomenon can be best explained by taking into account not only the temporal, but also the spatial dynamics underlying the generation of Ca(2+) oscillations in the cell. Here we divide the cell into a grid of elements and treat the Ca(2+) dynamics as a spatio-temporal phenomenon. By converting an existing temporal model into a spatio-temporal one, we obtain theoretical predictions that are in much better agreement with the experimental observations.

Decoding of calcium oscillations by phosphorylation cycles: analytic results

Experimental studies have demonstrated that Ca(2+)-regulated proteins are sensitive to the frequency of Ca(2+) oscillations, and several mathematical models for specific proteins have provided insight into the mechanisms involved. Because of the large number of Ca(2+)-regulated proteins in signal transduction, metabolism and gene expression, it is desirable to establish in general terms which molecular properties shape the response to oscillatory Ca(2+) signals. Here we address this question by analyzing in detail a model of a prototypical Ca(2+)-decoding module, consisting of a target protein whose activity is controlled by a Ca(2+)-activated kinase and the counteracting phosphatase. We show that this module can decode the frequency of Ca(2+) oscillations, at constant average Ca(2+) signal, provided that the Ca(2+) spikes are narrow and the oscillation frequency is sufficiently low--of the order of the phosphatase rate constant or below. Moreover, Ca(2+) oscillations activate the target more efficiently than a constant signal when Ca(2+) is bound cooperatively and with low affinity. Thus, the rate constants and the Ca(2+) affinities of the target-modifying enzymes can be tuned in such a way that the module responds optimally to Ca(2+) spikes of a certain amplitude and frequency. Frequency sensitivity is further enhanced when the limited duration of the external stimulus driving Ca(2+) signaling is accounted for. Thus, our study identifies molecular parameters that may be involved in establishing the specificity of cellular responses downstream of Ca(2+) oscillations.

Deviant effects in molecular reaction pathways

In biological networks, any manifestations of behaviors substantially 'deviant' from the predictions of continuous-deterministic classical chemical kinetics (CCK) are typically ascribed to systems with complex dynamics and/or a small number of molecules. Here we show that in certain cases such restrictions are not obligatory for CCK to be largely incorrect. By systematically identifying properties that may cause significant divergences between CCK and the more accurate discrete-stochastic chemical master equation (CME) system descriptions, we comprehensively characterize potential CCK failure patterns in biological settings, including consequences of the assertion that CCK is closer to the 'mode' rather than the 'average' of stochastic reaction dynamics, as generally perceived. We demonstrate that mechanisms underlying such nonclassical effects can be very simple, are common in cellular networks and result in often unintuitive system behaviors. This highlights the importance of deviant effects in biotechnologically or biomedically relevant applications, and suggests some approaches to diagnosing them in situ.

Hierarchical modularity of nested bow-ties in metabolic networks

Background

The exploration of the structural topology and the organizing principles of genome-based large-scale metabolic networks is essential for studying possible relations between structure and functionality of metabolic networks. Topological analysis of graph models has often been applied to study the structural characteristics of complex metabolic networks.

Results

In this work, metabolic networks of 75 organisms were investigated from a topological point of view. Network decomposition of three microbes (Escherichia coli, Aeropyrum pernix and Saccharomyces cerevisiae) shows that almost all of the sub-networks exhibit a highly modularized bow-tie topological pattern similar to that of the global metabolic networks. Moreover, these small bow-ties are hierarchically nested into larger ones and collectively integrated into a large metabolic network, and important features of this modularity are not observed in the random shuffled network. In addition, such a bow-tie pattern appears to be present in certain chemically isolated functional modules and spatially separated modules including carbohydrate metabolism, cytosol and mitochondrion respectively.

Conclusion

The highly modularized bow-tie pattern is present at different levels and scales, and in different chemical and spatial modules of metabolic networks, which is likely the result of the evolutionary process rather than a random accident. Identification and analysis of such a pattern is helpful for understanding the design principles and facilitate the modelling of metabolic networks.

Role of cascades in converting oscillatory signals into stationary step-like responses

In biological signal transduction pathways intermediates are often oscillatory and need to be converted into smooth output signals at the end. We show by mathematical modelling that protein kinase cascades enable converting oscillatory signals into sharp stationary step-like outputs. The importance of this result is demonstrated for the switch-like protein activation by calcium oscillations, which is of biological importance for regulating different cellular processes. In addition, we found that protein kinase cascades cause memory effects in the protein activation, which might be of a physiological advantage since a smaller amount of calcium transported in the cell is required for an effective activation of cellular processes.

A minimal model for decoding of time-limited Ca2+ oscillations

Calcium oscillations regulate several cellular processes by activating particular proteins. Most theoretical studies focused on the idealized situation of infinitely long oscillations. Here we analyze information transfer by time-limited calcium spike trains. We show that proteins can be selectively activated in a resonance-like manner by time-limited spike trains of different frequencies, while infinitely long oscillations do not show this resonance phenomenon. We found that proteins are activated more specifically by shorter oscillatory signals with narrower spikes.