Shaping Robust System through Evolution

Biological functions are generated as a result of developmental dynamics that form phenotypes governed by genotypes. The dynamical system for development is shaped through genetic evolution following natural selection based on the fitness of the phenotype. Here we study how this dynamical system is robust to noise during development and to genetic change by mutation. We adopt a simplified transcription regulation network model to govern gene expression, which gives a fitness function. Through simulations of the network that undergoes mutation and selection, we show that a certain level of noise in gene expression is required for the network to acquire both types of robustness. The results reveal how the noise that cells encounter during development shapes any network's robustness, not only to noise but also to mutations. We also establish a relationship between developmental and mutational robustness through phenotypic variances caused by genetic variation and epigenetic noise. A universal relationship between the two variances is derived, akin to the fluctuation-dissipation relationship known in physics

Stochastic timing in gene expression for simple regulatory strategies

Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to reach in a precise time a threshold level of expression that triggers a specific downstream process. However, gene expression is subject to stochastic fluctuations, naturally inducing an uncertainty in this threshold-crossing time with potential consequences on biological functions and phenotypes. Here, we consider such "timing fluctuations", and we ask how they can be controlled. Our analytical estimates and simulations show that, for an induced gene, timing variability is minimal if the threshold level of expression is approximately half of the steady-state level. Timing fuctuations can be reduced by increasing the transcription rate, while they are insensitive to the translation rate. In presence of self-regulatory strategies, we show that self-repression reduces timing noise for threshold levels that have to be reached quickly, while selfactivation is optimal at long times. These results lay a framework for understanding stochasticity of endogenous systems such as the cell cycle, as well as for the design of synthetic trigger circuits.Comment: 10 pages, 5 figure

Fan-out in Gene Regulatory Networks

In synthetic biology, gene regulatory circuits are often constructed by combining smaller circuit components. Connections between components are achieved by transcription factors acting on promoters. If the individual components behave as true modules and certain module interface conditions are satisfied, the function of the composite circuits can in principle be predicted. In this paper, we investigate one of the interface conditions: fan-out. We quantify the fan-out, a concept widely used in electric engineering, to indicate the maximum number of the downstream inputs that an upstream output transcription factor can regulate. We show that the fan-out is closely related to retroactivity studied by Del Vecchio, et al. We propose an efficient operational method for measuring the fan-out that can be applied to various types of module interfaces. We also show that the fan-out can be enhanced by self-inhibitory regulation on the output. We discuss the potential role of the inhibitory regulations found in gene regulatory networks and protein signal pathways. The proposed estimation method for fanout not only provides an experimentally efficient way for quantifying the level of modularity in gene regulatory circuits but also helps characterize and design module interfaces, enabling the modular construction of gene circuits.Comment: 28 pages, 5 figure

Stochastic noise reduction upon complexification: positively correlated birth-death type systems

Cell systems consist of a huge number of various molecules that display specific patterns of interactions, which have a determining influence on the cell's functioning. In general, such complexity is seen to increase with the complexity of the organism, with a concomitant increase of the accuracy and specificity of the cellular processes. The question thus arises how the complexification of systems - modeled here by simple interacting birth-death type processes - can lead to a reduction of the noise - described by the variance of the number of molecules. To gain understanding of this issue, we investigated the difference between a single system containing molecules that are produced and degraded, and the same system - with the same average number of molecules - connected to a buffer. We modeled these systems using Ito stochastic differential equations in discrete time, as they allow straightforward analytical developments. In general, when the molecules in the system and the buffer are positively correlated, the variance on the number of molecules in the system is found to decrease compared to the equivalent system without a buffer. Only buffers that are too noisy by themselves tend to increase the noise in the main system. We tested this result on two model cases, in which the system and the buffer contain proteins in their active and inactive state, or protein monomers and homodimers. We found that in the second test case, where the interconversion terms are non-linear in the number of molecules, the noise reduction is much more pronounced; it reaches up to 20% reduction of the Fano factor with the parameter values tested in numerical simulations on an unperturbed birth-death model. We extended our analysis to two arbitrary interconnected systems.Comment: 38 pages, 5 figures, to appear in J. Theor. Bio