Matthew Scott

Emergence of robust growth laws from optimal regulation of ribosome synthesis

Bacteria must constantly adapt their growth to changes in nutrient availability; yet despite large‐scale changes in protein expression associated with sensing, adaptation, and processing different environmental nutrients, simple growth laws connect the ribosome abundance and the growth rate. Here, we investigate the origin of these growth laws by analyzing the features of ribosomal regulation that coordinate proteome‐wide expression changes with cell growth in a variety of nutrient conditions in the model organism Escherichia coli. We identify supply‐driven feedforward activation of ribosomal protein synthesis as the key regulatory motif maximizing amino acid flux, and autonomously guiding a cell to achieve optimal growth in different environments. The growth laws emerge naturally from the robust regulatory strategy underlying growth rate control, irrespective of the details of the molecular implementation. The study highlights the interplay between phenomenological modeling and molecular mechanisms in uncovering fundamental operating constraints, with implications for endogenous and synthetic design of microorganisms.

Estimations of intrinsic and extrinsic noise in models of nonlinear genetic networks

We discuss two methods that can be used to estimate the impact of internal and external variability on nonlinear systems, and demonstrate their utility by comparing two experimentally implemented oscillatory genetic networks with different designs. The methods allow for rapid estimations of intrinsic and extrinsic noise and should prove useful in the analysis of natural genetic networks and when constructing synthetic gene regulatory systems.

Deterministic characterization of stochastic genetic circuits.

For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of deterministic rate equation models. Unfortunately, there are few analytic methods for examining the qualitative behavior of stochastic systems. Here we describe such a method that extends deterministic analysis to include leading-order corrections due to the molecular noise. The method allows the steady-state behavior of the stochastic model to be easily computed, facilitates the mapping of stability phase diagrams that include stochastic effects, and reveals how model parameters affect noise susceptibility in a manner not accessible to numerical simulation. By way of illustration we consider two genetic circuits: a bistable positive-feedback loop and a negative-feedback oscillator. We find in the positive feedback circuit that translational activation leads to a far more stable system than transcriptional control. Conversely, in a negative-feedback loop triggered by a positive-feedback switch, the stochasticity of transcriptional control is harnessed to generate reproducible oscillations.

Estimating the stochastic bifurcation structure of cellular networks.

High throughput measurement of gene expression at single-cell resolution, combined with systematic perturbation of environmental or cellular variables, provides information that can be used to generate novel insight into the properties of gene regulatory networks by linking cellular responses to external parameters. In dynamical systems theory, this information is the subject of bifurcation analysis, which establishes how system-level behaviour changes as a function of parameter values within a given deterministic mathematical model. Since cellular networks are inherently noisy, we generalize the traditional bifurcation diagram of deterministic systems theory to stochastic dynamical systems. We demonstrate how statistical methods for density estimation, in particular, mixture density and conditional mixture density estimators, can be employed to establish empirical bifurcation diagrams describing the bistable genetic switch network controlling galactose utilization in yeast Saccharomyces cerevisiae. These approaches allow us to make novel qualitative and quantitative observations about the switching behavior of the galactose network, and provide a framework that might be useful to extract information needed for the development of quantitative network models.

Growth-dependent bacterial susceptibility to ribosome-targeting antibiotics

Bacterial growth environment strongly influences the efficacy of antibiotic treatment, with slow growth often being associated with decreased susceptibility. Yet in many cases, the connection between antibiotic susceptibility and pathogen physiology remains unclear. We show that for ribosome-targeting antibiotics acting on Escherichia coli, a complex interplay exists between physiology and antibiotic action; for some antibiotics within this class, faster growth indeed increases susceptibility, but for other antibiotics, the opposite is true. Remarkably, these observations can be explained by a simple mathematical model that combines drug transport and binding with physiological constraints. Our model reveals that growth-dependent susceptibility is controlled by a single parameter characterizing the ‘reversibility’ of ribosome-targeting antibiotic transport and binding. This parameter provides a spectrum classification of antibiotic growth-dependent efficacy that appears to correspond at its extremes to existing binary classification schemes. In these limits, the model predicts universal, parameter-free limiting forms for growth inhibition curves. The model also leads to non-trivial predictions for the drug susceptibility of a translation mutant strain of E. coli, which we verify experimentally. Drug action and bacterial metabolism are mechanistically complex; nevertheless, this study illustrates how coarse-grained models can be used to integrate pathogen physiology into drug design and treatment strategies.Bacterial growth environment strongly influences the efficacy of antibiotic treatment, with slow growth often being associated with decreased susceptibility. Yet in many cases, the connection between antibiotic susceptibility and pathogen physiology remains unclear. We show that for ribosome‐targeting antibiotics acting on Escherichia coli, a complex interplay exists between physiology and antibiotic action; for some antibiotics within this class, faster growth indeed increases susceptibility, but for other antibiotics, the opposite is true. Remarkably, these observations can be explained by a simple mathematical model that combines drug transport and binding with physiological constraints. Our model reveals that growth‐dependent susceptibility is controlled by a single parameter characterizing the ‘reversibility’ of ribosome‐targeting antibiotic transport and binding. This parameter provides a spectrum classification of antibiotic growth‐dependent efficacy that appears to correspond at its extremes to existing binary classification schemes. In these limits, the model predicts universal, parameter‐free limiting forms for growth inhibition curves. The model also leads to non‐trivial predictions for the drug susceptibility of a translation mutant strain of E. coli, which we verify experimentally. Drug action and bacterial metabolism are mechanistically complex; nevertheless, this study illustrates how coarse‐grained models can be used to integrate pathogen physiology into drug design and treatment strategies.

The competing benefits of noise and heterogeneity in neural coding

Noise and heterogeneity are both known to benefit neural coding. Stochastic resonance describes how noise, in the form of random fluctuations in a neurons membrane voltage, can improve neural representations of an input signal. Neuronal heterogeneity refers to variation in any one of a number of neuron parameters and is also known to increase the information content of a population. We explore the interaction between noise and heterogeneity and find that their benefits to neural coding are not independent. Specifically, a neuronal population better represents an input signal when either noise or heterogeneity is added, but adding both does not always improve representation further. To explain this phenomenon, we propose that noise and heterogeneity operate using two shared mechanisms: (1) temporally desynchronizing the firing of neurons in the population and (2) linearizing the response of a population to a stimulus. We first characterize the effects of noise and heterogeneity on the information content of populations of either leaky integrate-and-fire or FitzHugh-Nagumo neurons. We then examine how the mechanisms of desynchronization and linearization produce these effects, and find that they work to distribute information equally across all neurons in the population in terms of both signal timing (desynchronization) and signal amplitude (linearization). Without noise or heterogeneity, all neurons encode the same aspects of the input signal; adding noise or heterogeneity allows neurons to encode complementary aspects of the input signal, thereby increasing information content. The simulations detailed in this letter highlight the importance of heterogeneity and noise in population coding, demonstrate their complex interactions in terms of the information content of neurons, and explain these effects in terms of underlying mechanisms.

Approximating intrinsic noise in continuous multispecies models

In small-scale chemical reaction networks, the local density of molecules is changed by discrete jumps owing to reactive collisions, and through transport. A systematic perturbation scheme is developed to analytically characterize these non-equilibrium intrinsic fluctuations in a multispecies spatially varying system. The method is illustrated on a variety of model systems. In all cases, the continuous approximation method is corroborated with extensive stochastic simulation. As an example of our technique applied to a spatially varying steady state, we demonstrate that a model for embryonic patterning mediated by regulatory mRNA is surprisingly robust to intrinsic fluctuations.

The role of Stern layer in the interplay of dielectric saturation and ion steric effects for the capacitance of graphene in aqueous electrolytes

Nano-scale devices continue to challenge our theoretical understanding of microscopic systems. Of particular interest is the characterization of the interface electrochemistry of graphene-based sensors. Typically operated in a regime of high ion concentration and high surface charge density, dielectric saturation and ion crowding become non-negligible at the interface, complicating continuum treatments based upon the Poisson-Boltzmann equation. Using the Poisson-Boltzmann equation, modified with the Bikerman-Freise model to account for non-zero ion size and the Booth model to account for dielectric saturation at the interface, we characterize the diffuse layer capacitance of both metallic and graphene electrodes immersed in an aqueous electrolyte. We find that the diffuse layer capacitance exhibits two peaks when the surface charge density of the electrode is increased, in contrast with experimental results. We propose a self-consistent (and parameter-free) method to include the Stern layer which eliminat...

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

Long delay times in reaction rates increase intrinsic fluctuations.

In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a probabilistic description. The coupling of delayed rates with stochastic dynamics leads to a probability conservation equation characterizing a non-Markovian process. A systematic approximation is derived that incorporates the effect of delayed rates on the characterization of molecular noise valid in the limit of long delay time. By way of a simple example, we show that delayed reaction dynamics can only increase intrinsic fluctuations about the steady state. The method is general enough to accommodate nonlinear transition rates allowing characterization of fluctuations around a delay-induced limit cycle.