Optimal entrainment of circadian clocks in the presence of noise

Localization of signaling receptors maximizes cellular information acquisition in spatially structured natural environments

Cells in natural environments, such as tissue or soil, sense and respond to extracellular ligands with intricately structured and non-monotonic spatial distributions, sculpted by processes such as fluid flow and substrate adhesion. In this work, we show that spatial sensing and navigation can be optimized by adapting the spatial organization of signaling pathways to the spatial structure of the environment. We develop an information-theoretic framework for computing the optimal spatial organization of a sensing system for a given signaling environment. We find that receptor localization previously observed in cells maximizes information acquisition in simulated natural contexts, including tissue and soil. Specifically, information acquisition is maximized when receptors form localized patches at regions of maximal ligand concentration. Receptor localization extends naturally to produce a dynamic protocol for continuously redistributing signaling receptors, which when implemented using simple feedback, boosts cell navigation efficiency by 30-fold.

Prediction of Time Series Gene Expression and Structural Analysis of Gene Regulatory Networks Using Recurrent Neural Networks

Methods for time series prediction and classification of gene regulatory networks (GRNs) from gene expression data have been treated separately so far. The recent emergence of attention-based recurrent neural network (RNN) models boosted the interpretability of RNN parameters, making them appealing for the understanding of gene interactions. In this work, we generated synthetic time series gene expression data from a range of archetypal GRNs and we relied on a dual attention RNN to predict the gene temporal dynamics. We show that the prediction is extremely accurate for GRNs with different architectures. Next, we focused on the attention mechanism of the RNN and, using tools from graph theory, we found that its graph properties allow one to hierarchically distinguish different architectures of the GRN. We show that the GRN responded differently to the addition of noise in the prediction by the RNN and we related the noise response to the analysis of the attention mechanism. In conclusion, this work provides a way to understand and exploit the attention mechanism of RNNs and it paves the way to RNN-based methods for time series prediction and inference of GRNs from gene expression data.

An effective model of endogenous clocks and external stimuli determining circadian rhythms

Circadian endogenous clocks of eukaryotic organisms are an established and rapidly developing research field. To investigate and simulate in an effective model the effect of external stimuli on such clocks and their components we developed a software framework for download and simulation. The application is useful to understand the different involved effects in a mathematical simple and effective model. This concerns the effects of Zeitgebers, feedback loops and further modifying components. We start from a known mathematical oscillator model, which is based on experimental molecular findings. This is extended with an effective framework that includes the impact of external stimuli on the circadian oscillations including high dose pharmacological treatment. In particular, the external stimuli framework defines a systematic procedure by input-output-interfaces to couple different oscillators. The framework is validated by providing phase response curves and ranges of entrainment. Furthermore, Aschoffs rule is computationally investigated. It is shown how the external stimuli framework can be used to study biological effects like points of singularity or oscillators integrating different signals at once. The mathematical framework and formalism is generic and allows to study in general the effect of external stimuli on oscillators and other biological processes. For an easy replication of each numerical experiment presented in this work and an easy implementation of the framework the corresponding Mathematica files are fully made available. They can be downloaded at the following link: https://www.biozentrum.uni-wuerzburg.de/bioinfo/computing/circadian/ .

Theory for the optimal detection of time-varying signals in cellular sensing systems

Living cells often need to measure chemical concentrations that vary in time, yet how accurately they can do so is poorly understood. Here, we present a theory that fully specifies, without any adjustable parameters, the optimal design of a canonical sensing system in terms of two elementary design principles: (1) there exists an optimal integration time, which is determined by the input statistics and the number of receptors; and (2) in the optimally designed system, the number of independent concentration measurements as set by the number of receptors and the optimal integration time equals the number of readout molecules that store these measurements and equals the work to store these measurements reliably; no resource is then in excess and hence wasted. Applying our theory to the Escherichia coli chemotaxis system indicates that its integration time is not only optimal for sensing shallow gradients but also necessary to enable navigation in these gradients.

Synchronization of circadian locomotor activity behavior in Caernorhabditis elegans: Interactions between light and temperature

Circadian rhythms are driven by an endogenous clock which is synchronized by daily environmental cycles (known as zeitgebers). Although the circadian responses of C. elegans to light have been recently reported, the mechanisms and pathways involved in their synchronization are still unknown. Here we present, by means of a novel behavioral approach, a complete characterization of C. elegans circadian synchronization to light and temperature cycles. Moreover, we screened mutant strains in search of defects of photic and thermal responses in order to study their putative pathways. We show that the wild-type strain is able to synchronize to combined cycles of light and temperature, with the best performance achieved under an optimal combination and phase-relationship of zeitgebers (high temperature in the dark phase and low temperature in the light phase). A lower responsiveness for the mutant strains MT21793 (lite-1/gur3 ko) and IK597 (gcy 8, 18 and 23 ko) was found in response to light and temperature, respectively. However, both mutants were still able to synchronize to a combined cycle of both stimuli. Our results shed light on the response of C. elegans to different zeitgebers as well as their possible synchronization pathways, the molecular components involved in these pathways, and their relative strength.

Robustness against additional noise in cellular information transmission

Fluctuations in intracellular reactions (intrinsic noise) reduce the information transmitted from an extracellular input to a cellular response. However, recent studies have demonstrated that the decrease in the transmitted information with respect to extracellular input fluctuations (extrinsic noise) is smaller when the intrinsic noise is larger. Therefore, it has been suggested that robustness against extrinsic noise increases with the level of the intrinsic noise. We call this phenomenon intrinsic noise-induced robustness (INIR). As previous studies on this phenomenon have focused on complex biochemical reactions, the relation between INIR and the input-output of a system is unclear. Moreover, the mechanism of INIR remains elusive. In this paper, we address these questions by analyzing simple models. We first analyze a model in which the input-output relation is linear. We show that the robustness against extrinsic noise increases with the intrinsic noise, confirming the INIR phenomenon. Moreover, the robustness against the extrinsic noise is more strongly dependent on the intrinsic noise when the variance of the intrinsic noise is larger than that of the input distribution. Next, we analyze a threshold model in which the output depends on whether the input exceeds the threshold. When the threshold is equal to the mean of the input, INIR is realized, but when the threshold is much larger than the mean, the threshold model exhibits stochastic resonance, and INIR is not always apparent. The robustness against extrinsic noise and the transmitted information can be traded off against one another in the linear model and the threshold model without stochastic resonance, whereas they can be simultaneously increased in the threshold model with stochastic resonance.

Quantifying the degree of locking in weakly forced stochastic systems

Controlling an stochastic nonlinear system with a small amplitude signal is a fundamental problem with many practical applications. Quantifying locking is challenging, and current methods, such as spectral or correlation analysis, do not provide a precise measure of the degree of locking. Here we study locking in an experimental system, consisting of a semiconductor laser with optical feedback operated in the regime where it randomly emits abrupt spikes. To quantify the locking of the optical spikes to small electric perturbations, we use two measures, the success rate (SR) and the false positive rate (FPR). The SR counts the spikes that are emitted shortly after each perturbation, while the FPR counts the additional extra spikes. We show that the receiver operating characteristic (ROC) curve (SR versus FPR plot) uncovers parameter regions where the electric perturbations fully control the laser spikes, such that the laser emits, shortly after each perturbation, one and only one spike. To demonstrate the general applicability of the ROC analysis we also study a stochastic bistable system under square-wave forcing and show that the ROC curve allows identifying the parameters that produce best locking.

Robustness of Clocks to Input Noise

To estimate the time, many organisms, ranging from cyanobacteria to animals, employ a circadian clock which is based on a limit-cycle oscillator that can tick autonomously with a nearly 24 h period. Yet, a limit-cycle oscillator is not essential for knowing the time, as exemplified by bacteria that possess an "hourglass": a system that when forced by an oscillatory light input exhibits robust oscillations from which the organism can infer the time, but that in the absence of driving relaxes to a stable fixed point. Here, using models of the Kai system of cyanobacteria, we compare a limit-cycle oscillator with two hourglass models, one that without driving relaxes exponentially and one that does so in an oscillatory fashion. In the limit of low input noise, all three systems are equally informative on time, yet in the regime of high input-noise the limit-cycle oscillator is far superior. The same behavior is found in the Stuart-Landau model, indicating that our result is universal.