Biomedical subjects

Pieter Rein ten Wolde

Publications and source records attributed to Pieter Rein ten Wolde.

14 recordsLinked to original sources

PubMed2006

Transcriptional regulation by competing transcription factor modules.

Gene regulatory networks lie at the heart of cellular computation. In these networks, intracellular and extracellular signals are integrated by transcription factors, which control the expression of transcription units by binding to cis-regulatory regions on the DNA. The designs of both eukaryotic and prokaryotic cis-regulatory regions are usually highly complex. They frequently consist of both repetitive and overlapping transcription factor binding sites. To unravel the design principles of these promoter architectures, we have designed in silico prokaryotic transcriptional logic gates with predefined input-output relations using an evolutionary algorithm. The resulting cis-regulatory designs are often composed of modules that consist of tandem arrays of binding sites to which the transcription factors bind cooperatively. Moreover, these modules often overlap with each other, leading to competition between them. Our analysis thus identifies a new signal integration motif that is based upon the interplay between intramodular cooperativity and intermodular competition. We show that this signal integration mechanism drastically enhances the capacity of cis-regulatory domains to integrate signals. Our results provide a possible explanation for the complexity of promoter architectures and could be used for the rational design of synthetic gene circuits.

Algorithms↗

PubMed2006

Exact results for noise power spectra in linear biochemical reaction networks.

We present a simple method for determining the exact noise power spectra and related statistical properties for linear chemical reaction networks. The method is applied to reaction networks which are representative of biochemical processes such as gene expression. We find, for example, that a post-translational modification reaction can reduce the noise associated with gene expression. Our results also indicate how to coarse grain networks by the elimination of fast reactions. In this context we have discovered a breakdown of the sum rule which relates the noise power spectrum to the total noise. The breakdown can be quantified by a sum rule deficit, which is found to be universal, and can be attributed to the high-frequency noise in the fast reactions.

Gene Expression Regulation, Bacterial↗

PubMed2006

Diffusion of transcription factors can drastically enhance the noise in gene expression.

We study by Green's Function Reaction Dynamics the effect of the diffusive motion of repressor molecules on the noise in mRNA and protein levels for a gene that is under the control of a repressor. We find that spatial fluctuations due to diffusion can drastically enhance the noise in gene expression. After dissociation from the operator, a repressor can rapidly rebind to the DNA. Our results show that the rebinding trajectories are so short that, on this timescale, the RNA polymerase (RNAP) cannot effectively compete with the repressor for binding to the promoter. As a result, a dissociated repressor molecule will on average rebind many times, before it eventually diffuses away. These rebindings thus lower the effective dissociation rate, and this increases the noise in gene expression. Another consequence of the timescale separation between repressor rebinding and RNAP association is that the effect of spatial fluctuations can be described by a well-stirred, zero-dimensional, model by renormalizing the reaction rates for repressor-DNA (un) binding. Our results thus support the use of well-stirred, zero-dimensional models for describing noise in gene expression. We also show that for a fixed repressor strength, the noise due to diffusion can be minimized by increasing the number of repressors or by decreasing the rate of the open complex formation. Lastly, our results emphasize that power spectra are a highly useful tool for studying the propagation of noise through the different stages of gene expression.

Algorithms↗

PubMed2006

Signal detection, modularity, and the correlation between extrinsic and intrinsic noise in biochemical networks.

We present an expression for the power spectrum of the output signal of a biochemical network, which reveals that the reactions that allow a network to detect biochemical signals, induce correlations between the extrinsic noise of the input signals and the intrinsic noise of the reactions that form the network. We show that anticorrelations between the extrinsic and intrinsic noise enhance the robustness of zero-order ultrasensitive networks to biochemical noise. We discuss the consequences for a modular description of noise transmission using the mitogen-activated protein kinase cascade.

Biochemistry↗

PubMed2006

Forward flux sampling-type schemes for simulating rare events: efficiency analysis.

We analyze the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems in or out of equilibrium. We derive analytical expressions for the computational cost of using these methods and for the statistical error in the final estimate of the rate constant for a given computational cost. These expressions can be used to determine which method to use for a given problem, to optimize the choice of parameters, and to evaluate the significance of the results obtained. We apply the expressions to the two-dimensional nonequilibrium rare event problem proposed by Maier and Stein [Phys. Rev. E 48, 931 (1993)]. For this problem, our analysis gives accurate quantitative predictions for the computational efficiency of the three methods.

Journal Article↗

PubMed2006

Simulating rare events in equilibrium or nonequilibrium stochastic systems.

We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase-space density and are suitable for equilibrium or nonequilibrium systems in stationary state. All the methods use a series of interfaces in phase space, between the initial and final states, to generate transition paths as chains of connected partial paths, in a ratchetlike manner. No assumptions are made about the distribution of paths at the interfaces. The three methods differ in the way that the transition path ensemble is generated. We apply the algorithms to kinetic Monte Carlo simulations of a genetic switch and to Langevin dynamics simulations of intermittently driven polymer translocation through a pore. We find that the three methods are all of comparable efficiency, and that all the methods are much more efficient than brute-force simulation.

Journal Article↗

PubMed2005

Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space.

We have developed a new numerical technique, called Green's-function reaction dynamics (GFRD), that makes it possible to simulate biochemical networks at the particle level and in both time and space. In this scheme, a maximum time step is chosen such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equation can be solved analytically using Green's functions. The main idea of GFRD is to exploit the exact solution of the Smoluchoswki equation to set up an event-driven algorithm, which combines in one step the propagation of the particles in space with the reactions between them. The event-driven nature allows GFRD to make large jumps in time and space when the particles are far apart from each other. Here, we apply the technique to a simple model of gene expression. The simulations reveal that spatial fluctuations can be a major source of noise in biochemical networks. The calculations also show that GFRD is highly efficient. Under biologically relevant conditions, GFRD is up to five orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space. GFRD is not limited to biochemical networks. It can also be applied to a large number of other reaction-diffusion problems.

Algorithms↗

PubMed2005

Finding the center reliably: robust patterns of developmental gene expression.

We investigate a mechanism for the robust identification of the center of a developing biological system. We assume the existence of two morphogen gradients, an activator emanating from the anterior, and a corepressor from the posterior. The corepressor inhibits the action of the activator in switching on target genes. We apply this system to Drosophila embryos, where we predict the existence of a hitherto undetected posterior corepressor. Using mathematical modeling, we show that a symmetric activator-corepressor model can quantitatively explain the precise midembryo expression boundary of the hunchback gene, and the scaling of this pattern with embryo size.

Animals↗

PubMed2005

Interplay between structure and size in a critical crystal nucleus.

We study the kinetics of crystal nucleation of an undercooled Lennard-Jones liquid using various path-sampling methods. We obtain the rate constant and elucidate the pathways for crystal nucleation. Analysis of the path ensemble reveals that crystal nucleation occurs along many different pathways, in which critical solid nuclei can be small, compact, and face centered cubic, but also large, less ordered, and more body centered cubic. The reaction coordinate thus includes, besides the cluster size, also the quality of the crystal structure.

Journal Article↗

PubMed2005

Chemical models of genetic toggle switches.

We study by mean-field analysis and stochastic simulations chemical models for genetic toggle switches formed from pairs of genes that mutually repress each other. To determine the stability of the genetic switches, we make a connection with reactive flux theory and transition state theory. The switch stability is characterized by a well-defined lifetime tau. We find that tau grows exponentially with the mean number N of transcription factor molecules involved in the switching. In the regime accessible to direct numerical simulations, the growth law is well-characterized by tau approximately N(alpha) exp(bN), where alpha and b are parameters. The switch stability is decreased by phenomena that increase the noise in gene expression, such as the production of multiple copies of a protein from a single mRNA transcript (shot noise) and fluctuations in the number of proteins produced per transcript. However, robustness against biochemical noise can be drastically enhanced by arranging the transcription factor binding domains on the DNA such that competing transcription factors mutually exclude each other on the DNA. We also elucidate the origin of the enhanced stability of the exclusive switch with respect to that of the general switch; while the kinetic prefactor is roughly the same for both switches, the "barrier" for flipping the switch is significantly higher for the exclusive switch than that for the general switch.

Animals↗

PubMed2005

Simulating biochemical networks at the particle level and in time and space: Green's function reaction dynamics.

We present a technique, called Green's function reaction dynamics (GFRD), for particle-based simulations of reaction-diffusion systems. GFRD uses a maximum time step such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equations are solved analytically using Green's functions, which are used to set up an event-driven algorithm. We apply the technique to a model of gene expression. Under biologically relevant conditions, GFRD is up to 5 orders of magnitude faster than conventional particle-based schemes.

Algorithms↗

PubMed2004

Enhancement of the stability of genetic switches by overlapping upstream regulatory domains.

We study genetic switches formed from pairs of mutually repressing operons. The switch stability is characterized by a well-defined lifetime, which grows very rapidly, albeit subexponentially, with the number of copies of the most-expressed transcription factor. The switch stability can be drastically enhanced by overlapping the upstream regulatory domains such that competing regulatory molecules mutually exclude each other. Our results suggest that robustness against biochemical noise can provide a selection pressure that drives operons together in the course of evolution.

Computer Simulation↗

PubMed2002

Drying-induced hydrophobic polymer collapse.

We have used computer simulation to study the collapse of a hydrophobic chain in water. We find that the mechanism of collapse is much like that of a first-order phase transition. The evaporation of water in the vicinity of the polymer provides the driving force for collapse, and the rate limiting step is the nucleation of a sufficiently large vapor bubble. The study is made possible through the application of transition path sampling and a coarse-grained treatment of liquid water. Relevance of our findings to understanding the folding and assembly of proteins is discussed.

Computer Simulation↗

PubMed2001

Model of a fluid at small and large length scales and the hydrophobic effect.

We present a statistical field theory to describe large length scale effects induced by solutes in a cold and otherwise placid liquid. The theory divides space into a cubic grid of cells. The side length of each cell is of the order of the bulk correlation length of the bulk liquid. Large length scale states of the cells are specified with an Ising variable. Finer length scale effects are described with a Gaussian field, with mean and variance affected by both the large length scale field and by the constraints imposed by solutes. In the absence of solutes and corresponding constraints, integration over the Gaussian field yields an effective lattice-gas Hamiltonian for the large length scale field. In the presence of solutes, the integration adds additional terms to this Hamiltonian. We identify these terms analytically. They can provoke large length scale effects, such as the formation of interfaces and depletion layers. We apply our theory to compute the reversible work to form a bubble in liquid water, as a function of the bubble radius. Comparison with molecular simulation results for the same function indicates that the theory is reasonably accurate. Importantly, simulating the large length scale field involves binary arithmetic only. It thus provides a computationally convenient scheme to incorporate explicit solvent dynamics and structure in simulation studies of large molecular assemblies.

Journal Article↗