Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately-initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy and of a state-dependent effective diffusion coefficient that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.Comment: 33 pages, submitted to The Journal of Chemical Physic

Biochemical Network Stochastic Simulator (BioNetS): software for stochastic modeling of biochemical networks

BACKGROUND: Intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA) molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks. RESULTS: We have developed the software package Biochemical Network Stochastic Simulator (BioNetS) for efficiently and accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous) for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solves the appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from . BioNetS also can be run as a stand alone package. All the required files are accessible from . CONCLUSIONS: We have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems

A cut-cell method for simulating spatial models of biochemical reaction networks in arbitrary geometries

Cells use signaling networks consisting of multiple interacting proteins to respond to changes in their environment. In many situations, such as chemotaxis, spatial and temporal information must be transmitted through the network. Recent computational studies have emphasized the importance of cellular geometry in signal transduction, but have been limited in their ability to accurately represent complex cell morphologies. We present a finite volume method that addresses this problem. Our method uses Cartesian cut cells and is second order in space and time. We use our method to simulate several models of signaling systems in realistic cell morphologies obtained from live cell images and examine the effects of geometry on signal transduction

Simulating Biochemical Signaling Networks in Complex Moving Geometries

Signaling networks regulate cellular responses to environmental stimuli through cascades of protein interactions. External signals can trigger cells to polarize and move in a specific direction. During migration, spatially localized activity of proteins is maintained. To investigate the effects of morphological changes on intracellular signaling, we developed a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods to simulate the resulting advection-reaction-diffusion system. We then apply the method to several biochemical reaction networks in changing geometries. We found that a Turing instability can develop exclusively by cell deformations that maintain constant area. For a Turing system with a geometry-dependent single or double peak solution, simulations in a dynamically changing geometry suggest that a single peak solution is the only stable one, independent of the oscillation frequency. The method is also applied to a model of a signaling network in a migrating fibroblast

Entropy gives rise to topologically associating domains

We investigate chromosome organization within the nucleus using polymer models whose formulation is closely guided by experiments in live yeast cells. We employ bead-spring chromosome models together with loop formation within the chains and the presence of nuclear bodies to quantify the extent to which these mechanisms shape the topological landscape in the interphase nucleus. By investigating the genome as a dynamical system, we show that domains of high chromosomal interactions can arise solely from the polymeric nature of the chromosome arms due to entropic interactions and nuclear confinement. In this view, the role of bio-chemical related processes is to modulate and extend the duration of the interacting domains

Transient crosslinking kinetics optimize gene cluster interactions

Our understanding of how chromosomes structurally organize and dynamically interact has been revolutionized through the lens of long-chain polymer physics. Major protein contributors to chromosome structure and dynamics are condensin and cohesin that stochastically generate loops within and between chains, and entrap proximal strands of sister chromatids. In this paper, we explore the ability of transient, protein-mediated, gene-gene crosslinks to induce clusters of genes, thereby dynamic architecture, within the highly repeated ribosomal DNA that comprises the nucleolus of budding yeast. We implement three approaches: live cell microscopy; computational modeling of the full genome during G1 in budding yeast, exploring four decades of timescales for transient crosslinks between 5k bp domains in the nucleolus on Chromosome XII; and, temporal network models with automated community detection algorithms applied to the full range of 4D modeling datasets. The data analysis tools detect and track gene clusters, their size, number, persistence time, and their plasticity. Of biological significance, our analysis reveals an optimal mean crosslink lifetime that promotes pairwise and cluster gene interactions through "flexible" clustering. In this state, large gene clusters self-assemble yet frequently interact, marked by gene exchanges between clusters, which in turn maximizes global gene interactions in the nucleolus. This regime stands between two limiting cases each with far less global gene interactions: with shorter crosslink lifetimes, "rigid" clustering emerges with clusters that interact infrequently; with longer crosslink lifetimes, there is a dissolution of clusters. These observations are compared with imaging experiments on a normal yeast strain and two condensin-modified mutant cell strains, applying the same image analysis pipeline to the experimental and simulated datasets

Phosphoregulation provides specificity to biomolecular condensates in the cell cycle and cell polarity

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Gerbich, T. M., McLaughlin, G. A., Cassidy, K., Gerber, S., Adalsteinsson, D., & Gladfelter, A. S. Phosphoregulation provides specificity to biomolecular condensates in the cell cycle and cell polarity. Journal of Cell Biology, 219(7), (2020): e201910021, doi:10.1083/jcb.201910021.Biomolecular condensation is a way of organizing cytosol in which proteins and nucleic acids coassemble into compartments. In the multinucleate filamentous fungus Ashbya gossypii, the RNA-binding protein Whi3 regulates the cell cycle and cell polarity through forming macromolecular structures that behave like condensates. Whi3 has distinct spatial localizations and mRNA targets, making it a powerful model for how, when, and where specific identities are established for condensates. We identified residues on Whi3 that are differentially phosphorylated under specific conditions and generated mutants that ablate this regulation. This yielded separation of function alleles that were functional for either cell polarity or nuclear cycling but not both. This study shows that phosphorylation of individual residues on molecules in biomolecular condensates can provide specificity that gives rise to distinct functional identities in the same cell.The work was supported by National Institutes of Health grant R01-GM-081506

An internal splash: Levitation of falling spheres in stratified fluids

We experimentally explore the motion of falling spheres in strongly stratified fluids in which the fluid transitions from low density at the top to high density at the bottom and document an internal splash in which the falling sphere may reverse its direction of motion (from falling, to rising, to falling again) as it penetrates a region of strong density transition. We present measurements of the sphere’s velocity and exhibit nonmonotonic sphere velocity profiles connecting the maximum and minimum terminal velocities, matching earlier measurements [J. Fluid Mech. 381, 175 (1999)], but further exhibit the new levitation phenomenon. We give a physical explanation of this motion which necessarily couples the sphere motion with the stratified fluid, and vice versa, and supplement this with a simplified, reduced mathematical model involving a nonlinear system of ordinary differential equations which captures the nonmonotonic transition and agrees with the measuredvelocity profiles at all depths except those in the vicinity of the sharp transition for which the model deviates from the measured speeds. We repeat the experiments adjusting the distance between the camera and falling sphere thereby reducing the optical blur associated with the change in optical refractive index associated with the strong density transition. By directly measuring the residual optical distortion with a center plane, vertical ruler, we exhibit that the measuredvelocity profile within the transition layer is strongly sensitive to the details of the measured optical distortion, and show subsequent improved agreement between the measurement and the model. Through direct measurement of the nonlinear mapping between physical and imaged coordinates we document measuredvelocity error trends which may occur from inaccurately accounting for this optical distortion. We suggest strategies for correcting this localized measurement detail generally

Enrichment of dynamic chromosomal crosslinks drive phase separation of the nucleolus

Regions of highly repetitive DNA, such as those found in the nucleolus, show a self-organization that is marked by spatial segregation and frequent self-interaction. The mechanisms that underlie the sequestration of these sub-domains are largely unknown. Using a stochastic, bead-spring representation of chromatin in budding yeast, we find enrichment of protein-mediated, dynamic chromosomal cross-links recapitulates the segregation, morphology and self-interaction of the nucleolus. Rates and enrichment of dynamic crosslinking have profound consequences on domain morphology. Our model demonstrates the nucleolus is phase separated from other chromatin in the nucleus and predicts that multiple rDNA loci will form a single nucleolus independent of their location within the genome. Fluorescent labeling of budding yeast nucleoli with CDC14-GFP revealed that a split rDNA locus indeed forms a single nucleolus. We propose that nuclear sub-domains, such as the nucleolus, result from phase separations within the nucleus, which are driven by the enrichment of protein-mediated, dynamic chromosomal crosslinks

Prevalence of Bourbon and Heartland viruses in field collected ticks at an environmental field station in St. Louis County, Missouri, USA

Heartland and Bourbon viruses are pathogenic tick-borne viruses putatively transmitted by Amblyomma americanum, an abundant tick species in Missouri. To assess the prevalence of these viruses in ticks, we collected 2778 ticks from eight sampling sites at Tyson Research Center, an environmental field station within St. Louis County and close to the City of St. Louis, from May - July in 2019 and 2021. Ticks were pooled according to life stage and sex, grouped by year and sampling site to create 355 pools and screened by RT-qPCR for Bourbon and Heartland viruses. Overall, 14 (3.9%) and 27 (7.6%) of the pools were positive for Bourbon virus and Heartland virus respectively. In 2019, 11 and 23 pools were positive for Bourbon and Heartland viruses respectively. These positives pools were of males, females and nymphs. In 2021, there were 4 virus positive pools out of which 3 were positive for both viruses and were comprised of females and nymphs. Five out of the 8 sampling sites were positive for at least one virus. This included a site that was positive for both viruses in both years. Detection of these viruses in an area close to a relatively large metropolis presents a greater public health threat than previously thought