Molecular noise induces concentration oscillations in chemical systems with stable node steady states

Finding gene network topologies for given biological function with recurrent neural network

Searching for possible biochemical networks that perform a certain function is a challenge in systems biology. For simple functions and small networks, this can be achieved through an exhaustive search of the network topology space. However, it is difficult to scale this approach up to larger networks and more complex functions. Here we tackle this problem by training a recurrent neural network (RNN) to perform the desired function. By developing a systematic perturbative method to interrogate the successfully trained RNNs, we are able to distill the underlying regulatory network among the biological elements (genes, proteins, etc.). Furthermore, we show several cases where the regulation networks found by RNN can achieve the desired biological function when its edges are expressed by more realistic response functions, such as the Hill-function. This method can be used to link topology and function by helping uncover the regulation logic and network topology for complex tasks.

Networks are useful ways to describe interactions between molecules in a cell, but predicting the real topology of large networks can be challenging. Here, the authors use deep learning to predict the topology of networks that perform biologically-plausible functions.

Graph-facilitated resonant mode counting in stochastic interaction networks

Oscillations in dynamical systems are widely reported in multiple branches of applied mathematics. Critically, even a non-oscillatory deterministic system can produce cyclic trajectories when it is in a low copy number, stochastic regime. Common methods of finding parameter ranges for stochastically driven resonances, such as direct calculation, are cumbersome for any but the smallest networks. In this paper, we provide a systematic framework to efficiently determine the number of resonant modes and parameter ranges for stochastic oscillations relying on real root counting algorithms and graph theoretic methods. We argue that stochastic resonance is a network property by showing that resonant modes only depend on the squared Jacobian matrix J2, unlike deterministic oscillations which are determined by J By using graph theoretic tools, analysis of stochastic behaviour for larger interaction networks is simplified and stochastic dynamical systems with multiple resonant modes can be identified easily.

Promoters Architecture-Based Mechanism for Noise-Induced Oscillations in a Single-Gene Circuit

It is well known that single-gene circuits with negative feedback loop can lead to oscillatory gene expression when they operate with time delay. In order to generate these oscillations many processes can contribute to properly timing such delay. Here we show that the time delay coming from the transitions between internal states of the cis-regulatory system (CRS) can drive sustained oscillations in an auto-repressive single-gene circuit operating in a small volume like a cell. We found that the cooperative binding of repressor molecules is not mandatory for a oscillatory behavior if there are enough binding sites in the CRS. These oscillations depend on an adequate balance between the CRS kinetic, and the synthesis/degradation rates of repressor molecules. This finding suggest that the multi-site CRS architecture can play a key role for oscillatory behavior of gene expression. Finally, our results can also help to synthetic biologists on the design of the promoters architecture for new genetic oscillatory circuits.

Dynamics of Gamma Bursts in Local Field Potentials

In this letter, we provide a stochastic analysis of, and supporting simulation data for, a stochastic model of the generation of gamma bursts in local field potential (LFP) recordings by interacting populations of excitatory and inhibitory neurons. Our interest is in behavior near a fixed point of the stochastic dynamics of the model. We apply a recent limit theorem of stochastic dynamics to probe into details of this local behavior, obtaining several new results. We show that the stochastic model can be written in terms of a rotation multiplied by a two-dimensional standard Ornstein-Uhlenbeck (OU) process. Viewing the rewritten process in terms of phase and amplitude processes, we are able to proceed further in analysis. We demonstrate that gamma bursts arise in the model as excursions of the modulus of the OU process. The associated pair of stochastic phase and amplitude processes satisfies their own pair of stochastic differential equations, which indicates that large phase slips occur between gamma bursts. This behavior is mirrored in LFP data simulated from the original model. These results suggest that the rewritten model is a valid representation of the behavior near the fixed point for a wide class of models of oscillatory neural processes.

Effects of bursty protein production on the noisy oscillatory properties of downstream pathways

Experiments show that proteins are translated in sharp bursts; similar bursty phenomena have been observed for protein import into compartments. Here we investigate the effect of burstiness in protein expression and import on the stochastic properties of downstream pathways. We consider two identical pathways with equal mean input rates, except in one pathway proteins are input one at a time and in the other proteins are input in bursts. Deterministically the dynamics of these two pathways are indistinguishable. However the stochastic behavior falls in three categories: (i) both pathways display or do not display noise-induced oscillations; (ii) the non-bursty input pathway displays noise-induced oscillations whereas the bursty one does not; (iii) the reverse of (ii). We derive necessary conditions for these three cases to classify systems involving autocatalysis, trimerization and genetic feedback loops. Our results suggest that single cell rhythms can be controlled by regulation of burstiness in protein production.