arXiv subjects

Andrew Mugler

Publications and source records attributed to Andrew Mugler.

59 records · Page 4Linked to original sources

arXiv2009

Spectral solutions to stochastic models of gene expression with bursts and regulation

Signal-processing molecules inside cells are often present at low copy number, which necessitates probabilistic models to account for intrinsic noise. Probability distributions have traditionally been found using simulation-based approaches which then require estimating the distributions from many samples. Here we present in detail an alternative method for directly calculating a probability distribution by expanding in the natural eigenfunctions of the governing equation, which is linear. We apply the resulting spectral method to three general models of stochastic gene expression: a single gene with multiple expression states (often used as a model of bursting in the limit of two states), a gene regulatory cascade, and a combined model of bursting and regulation. In all cases we find either analytic results or numerical prescriptions that greatly outperform simulations in efficiency and accuracy. In the last case, we show that bimodal response in the limit of slow switching is not only possible but optimal in terms of information transmission.

q-bio.MN↗

arXiv2008

A stochastic spectral analysis of transcriptional regulatory cascades

The past decade has seen great advances in our understanding of the role of noise in gene regulation and the physical limits to signaling in biological networks. Here we introduce the spectral method for computation of the joint probability distribution over all species in a biological network. The spectral method exploits the natural eigenfunctions of the master equation of birth-death processes to solve for the joint distribution of modules within the network, which then inform each other and facilitate calculation of the entire joint distribution. We illustrate the method on a ubiquitous case in nature: linear regulatory cascades. The efficiency of the method makes possible numerical optimization of the input and regulatory parameters, revealing design properties of, e.g., the most informative cascades. We find, for threshold regulation, that a cascade of strong regulations converts a unimodal input to a bimodal output, that multimodal inputs are no more informative than bimodal inputs, and that a chain of up-regulations outperforms a chain of down-regulations. We anticipate that this numerical approach may be useful for modeling noise in a variety of small network topologies in biology.

q-bio.MN↗

arXiv2008

Statistical properties of multistep enzyme-mediated reactions

Enzyme-mediated reactions may proceed through multiple intermediate conformational states before creating a final product molecule, and one often wishes to identify such intermediate structures from observations of the product creation. In this paper, we address this problem by solving the chemical master equations for various enzymatic reactions. We devise a perturbation theory analogous to that used in quantum mechanics that allows us to determine the first ( ) and the second (variance) cumulants of the distribution of created product molecules as a function of the substrate concentration and the kinetic rates of the intermediate processes. The mean product flux V=d /dt (or "dose-response" curve) and the Fano factor F=variance/ are both realistically measurable quantities, and while the mean flux can often appear the same for different reaction types, the Fano factor can be quite different. This suggests both qualitative and quantitative ways to discriminate between different reaction schemes, and we explore this possibility in the context of four sample multistep enzymatic reactions. We argue that measuring both the mean flux and the Fano factor can not only discriminate between reaction types, but can also provide some detailed information about the internal, unobserved kinetic rates, and this can be done without measuring single-molecule transition events.

q-bio.QM↗

arXiv2008

Quantifying evolvability in small biological networks

We introduce a quantitative measure of the capacity of a small biological network to evolve. We apply our measure to a stochastic description of the experimental setup of Guet et al. (Science 296:1466, 2002), treating chemical inducers as functional inputs to biochemical networks and the expression of a reporter gene as the functional output. We take an information-theoretic approach, allowing the system to set parameters that optimize signal processing ability, thus enumerating each network's highest-fidelity functions. We find that all networks studied are highly evolvable by our measure, meaning that change in function has little dependence on change in parameters. Moreover, we find that each network's functions are connected by paths in the parameter space along which information is not significantly lowered, meaning a network may continuously change its functionality without losing it along the way. This property further underscores the evolvability of the networks.

q-bio.MN↗

arXiv2008

Serially-regulated biological networks fully realize a constrained set of functions

We show that biological networks with serial regulation (each node regulated by at most one other node) are constrained to {\it direct functionality}, in which the sign of the effect of an environmental input on a target species depends only on the direct path from the input to the target, even when there is a feedback loop allowing for multiple interaction pathways. Using a stochastic model for a set of small transcriptional regulatory networks that have been studied experimentally, we further find that all networks can achieve all functions permitted by this constraint under reasonable settings of biochemical parameters. This underscores the functional versatility of the networks.

q-bio.MN↗