Gene expression in self-repressing system with multiple gene copies

Analytic solutions for stochastic hybrid models of gene regulatory networks

Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely large. Therefore hybrid models, in which protein counts are replaced by average protein concentrations, have become a popular alternative. The evolution of the corresponding probability density functions is given by a coupled system of hyperbolic PDEs. This system has Markovian nature but its hyperbolic structure makes it difficult to apply standard functional analytical methods. We are able to prove convergence towards the stationary solution and determine such equilibrium explicitly by combining abstract methods from the theory of positive operators and elementary ideas from potential analysis.

Informatics Inference of Exercise-Induced Modulation of Brain Pathways Based on Cerebrospinal Fluid Micro-RNAs in Myalgic Encephalomyelitis/Chronic Fatigue Syndrome

Introduction: The post-exertional malaise of myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) was modeled by comparing micro-RNA (miRNA) in cerebrospinal fluid from subjects who had no exercise versus submaximal exercise. Materials and Methods: Differentially expressed miRNAs were examined by informatics methods to predict potential targets and regulatory pathways affected by exercise. Results: miR-608, miR-328, miR-200a-5p, miR-93-3p, and miR-92a-3p had higher levels in subjects who rested overnight (nonexercise n=45) compared to subjects who had exercised before their lumbar punctures (n=15). The combination was examined in DIANA MiRpath v3.0, TarBase, Cytoscape, and Ingenuity software® to select the intersection of target mRNAs. DIANA found 33 targets that may be elevated after exercise, including TGFBR1, IGFR1, and CDC42. Adhesion and adherens junctions were the most frequent pathways. Ingenuity selected seven targets that had complementary mechanistic pathways involving GNAQ, ADCY3, RAP1B, and PIK3R3. Potential target cells expressing high levels of these genes included choroid plexus, neurons, and microglia. Conclusion: The reduction of this combination of miRNAs in cerebrospinal fluid after exercise suggested upregulation of phosphoinositol signaling pathways and altered adhesion during the post-exertional malaise of ME/CFS. Clinical Trial Registration Nos.: NCT01291758 and NCT00810225.

Dissipation in Non-Steady State Regulatory Circuits

In order to respond to environmental signals, cells often use small molecular circuits to transmit information about their surroundings. Recently, motivated by specific examples in signaling and gene regulation, a body of work has focused on the properties of circuits that function out of equilibrium and dissipate energy. We briefly review the probabilistic measures of information and dissipation and use simple models to discuss and illustrate trade-offs between information and dissipation in biological circuits. We find that circuits with non-steady state initial conditions can transmit more information at small readout delays than steady state circuits. The dissipative cost of this additional information proves marginal compared to the steady state dissipation. Feedback does not significantly increase the transmitted information for out of steady state circuits but does decrease dissipative costs. Lastly, we discuss the case of bursty gene regulatory circuits that, even in the fast switching limit, function out of equilibrium.

Influence of gene copy number on self-regulated gene expression

Using an analytically solvable stochastic model, we study the properties of a simple genetic circuit consisting of multiple copies of a self-regulating gene. We analyse how the variation in gene copy number and the mutations changing the auto-regulation strength affect the steady-state distribution of protein concentration. We predict that one-reporter assay, an experimental method where the extrinsic noise level is inferred from the comparison of expression variance of a single and duplicated reporter gene, may give an incorrect estimation of the extrinsic noise contribution when applied to self-regulating genes. We also show that an imperfect duplication of an auto-activated gene, changing the regulation strength of one of the copies, may lead to a hybrid, binary+graded response of these genes to external signal. The analysis of relative changes in mean gene expression before and after duplication suggests that evolutionary accumulation of gene duplications may, at a given mean burst size, non-trivially depend on the inherent noisiness of a given gene, quantified by the inverse of the maximal mean frequency of bursts. Moreover, we find that the dependence of gene expression noise on gene copy number and auto-regulation strength may qualitatively differ, e.g. in monotonicity, depending on whether the noise is measured by Fano factor or coefficient of variation. Thus, experimentally-based hypotheses linking gene expression noise and evolutionary optimisation in the context of gene copy number variation may be ambiguous as they are dependent on the particular function chosen to quantify noise.