Models of single-molecule experiments with periodic perturbations reveal hidden dynamics in RNA folding

Revisiting kinetic Monte Carlo algorithms for time-dependent processes: From open-loop control to feedback control

Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system's dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to time-dependent stochastic systems. Based on this analysis, we revisit several time-dependent kinetic Monte Carlo (KMC) algorithms designed for systems under open-loop-control protocols. Our analysis provides a unified alternative proof to these algorithms, summarized into a pedagogical tutorial. Moreover, with the trajectory probability analysis, we present a novel feedback-controlled KMC algorithm that accurately captures the dynamics systems controlled by an external signal based on the measurements of the system's state. Our method correctly captures the system dynamics and avoids the artificial Zeno effect that arises from incorrectly applying the direct Gillespie algorithm to feedback-controlled systems. This work provides a unified perspective on existing open-loop-control KMC algorithms and also offers a powerful and accurate tool for simulating stochastic systems with feedback control.

Phase resetting reveals network dynamics underlying a bacterial cell cycle

Genomic and proteomic methods yield networks of biological regulatory interactions but do not provide direct insight into how those interactions are organized into functional modules, or how information flows from one module to another. In this work we introduce an approach that provides this complementary information and apply it to the bacterium Caulobacter crescentus, a paradigm for cell-cycle control. Operationally, we use an inducible promoter to express the essential transcriptional regulatory gene ctrA in a periodic, pulsed fashion. This chemical perturbation causes the population of cells to divide synchronously, and we use the resulting advance or delay of the division times of single cells to construct a phase resetting curve. We find that delay is strongly favored over advance. This finding is surprising since it does not follow from the temporal expression profile of CtrA and, in turn, simulations of existing network models. We propose a phenomenological model that suggests that the cell-cycle network comprises two distinct functional modules that oscillate autonomously and couple in a highly asymmetric fashion. These features collectively provide a new mechanism for tight temporal control of the cell cycle in C. crescentus. We discuss how the procedure can serve as the basis for a general approach for probing network dynamics, which we term chemical perturbation spectroscopy (CPS).

During the cell cycle, the cell progresses through a series of stages that are associated with various cell cycle events such as replication of genetic materials. Genetic and molecular dissections have revealed that the cell cycle is regulated by a network of interacting molecules that produces oscillatory dynamics. The major cell cycle regulators have been identified previously in different species and the activity of these regulators oscillates. However, the question of how cell cycle regulators coordinate different cell cycle events during the cell cycle remains controversial. Here, we investigate this question in a model bacterial system for cell cycle, Caulobacter crescentus. We perturb the expression of the master cell cycle regulator ctrA in a pulsatile fashion and quantify the response of the cell cycle to such perturbations. The measured response is contradictory to the existing mechanism of Caulobacter cell cycle control, which views the cell cycle progression as a sequential activation/inhibition process. We propose a new model that involves coupling of multiple oscillators and show the quantitative agreement between this new model and our measurements. We expect this procedure to be generalized and applied to a broad range of systems to obtain information that complements that obtained from other methods.

Flow-Dependent Unfolding and Refolding of an RNA by Nonequilibrium Umbrella Sampling

Nonequilibrium experiments of single biomolecules such as force-induced unfolding reveal details about a few degrees of freedom of a complex system. Molecular dynamics simulations can provide complementary information, but exploration of the space of possible configurations is often hindered by large barriers in phase space that separate metastable regions. To solve this problem, enhanced sampling methods have been developed that divide a phase space into regions and integrate trajectory segments in each region. These methods boost the probability of passage over barriers and facilitate parallelization since integration of the trajectory segments does not require communication, aside from their initialization and termination. Here, we present a parallel version of an enhanced sampling method suitable for systems driven far from equilibrium: nonequilibrium umbrella sampling (NEUS). We apply this method to a coarse-grained model of a 262-nucleotide RNA molecule that unfolds and refolds in an explicit flow field modeled with stochastic rotation dynamics. Using NEUS, we are able to observe extremely rare unfolding events that have mean first passage times as long as 45 s (1.1 × 10(15) dynamics steps). We examine the unfolding process for a range of flow rates of the medium, and we describe two competing pathways in which different intramolecular contacts are broken.

Defining cooperativity in gene regulation locally through intrinsic noise

Regulatory networks in cells may comprise a variety of types of molecular interactions. The most basic are pairwise interactions, in which one species controls the behaviour of another (e.g. a transcription factor activates or represses a gene). Higher-order interactions, while more subtle, may be important for determining the function of networks. Here, the authors systematically expand a simple master equation model for a gene to derive an approach for robustly assessing the cooperativity (effective copy number) with which a transcription factor acts. The essential idea is that moments of a joint distribution of protein copy numbers determine the Hill coefficient of a cis-regulatory input function without non-linear fitting. The authors show that this method prescribes a definition of cooperativity that is meaningful even in highly complex situations in which the regulation does not conform to a simple Hill function. To illustrate the utility of the method, the authors measure the cooperativity of the transcription factor CI in simulations of phage- and show how the cooperativity accurately reflects the behaviour of the system. The authors numerically assess the effects of deviations from ideality, as well as possible sources of error. The relationship to other definitions of cooperativity and issues for experimentally realising the procedure are discussed.