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Pieter Rein ten Wolde

Publications and source records attributed to Pieter Rein ten Wolde.

89 records · Page 5Linked to original sources
arXiv2008

Chance and necessity in chromosomal gene distributions

By analyzing the spacing of genes on chromosomes, we find that transcriptional and RNA-processing regulatory sequences outside coding regions leave footprints on the distribution of intergenic distances. Using analogies between genes on chromosomes and one-dimensional gases, we constructed a statistical null model. We have used this to estimate typical upstream and downstream regulatory sequence sizes in various species. Deviations from this model reveal bi-directional transcriptional regulatory regions in S. cerevisiae and bi-directional terminators in E. coli.

q-bio.GN↗
arXiv2007

Enzyme localization can drastically affect signal amplification in signal transduction pathways

Push-pull networks are ubiquitous in signal transduction pathways in both prokaryotic and eukaryotic cells. They allow cells to strongly amplify signals via the mechanism of zero-order ultrasensitivity. In a push-pull network, two antagonistic enzymes control the activity of a protein by covalent modification. These enzymes are often uniformly distributed in the cytoplasm. They can, however, also be colocalized in space, for instance, near the pole of the cell. Moreover, it is increasingly recognized that these enzymes can also be spatially separated, leading to gradients of the active form of the messenger protein. Here, we investigate the consequences of the spatial distributions of the enzymes for the amplification properties of push-pull networks. Our calculations reveal that enzyme localization by itself can have a dramatic effect on the gain. The gain is maximized when the two enzymes are either uniformly distributed or colocalized in one region in the cell. Depending on the diffusion constants, however, the sharpness of the response can be strongly reduced when the enzymes are spatially separated. We discuss how our predictions could be tested experimentally.

q-bio.MN↗
arXiv2007

Fundamental Limits to Position Determination by Concentration Gradients

Position determination in biological systems is often achieved through protein concentration gradients. Measuring the local concentration of such a protein with a spatially-varying distribution allows the measurement of position within the system. In order for these systems to work effectively, position determination must be robust to noise. Here, we calculate fundamental limits to the precision of position determination by concentration gradients due to unavoidable biochemical noise perturbing the gradients. We focus on gradient proteins with first order reaction kinetics. Systems of this type have been experimentally characterised in both developmental and cell biology settings. For a single gradient we show that, through time-averaging, great precision can potentially be achieved even with very low protein copy numbers. As a second example, we investigate the ability of a system with oppositely directed gradients to find its centre. With this mechanism, positional precision close to the centre improves more slowly with increasing averaging time, and so longer averaging times or higher copy numbers are required for high precision. For both single and double gradients, we demonstrate the existence of optimal length scales for the gradients, where precision is maximized, as well as analyzing how precision depends on the size of the concentration measuring apparatus. Our results provide fundamental constraints on the positional precision supplied by concentration gradients in various contexts, including both in developmental biology and also within a single cell.

q-bio.SC↗
arXiv2007

An allosteric model of KaiC phosphorylation

In a recent series of ground-breaking experiments, Nakajima et al. [Science 308, 414-415 (2005)] showed that the three cyanobacterial clock proteins KaiA, KaiB, and KaiC are sufficient in vitro to generate circadian phosphorylation of KaiC. Here, we present a mathematical model of the Kai system. At its heart is the assumption that KaiC can exist in two conformational states, one favoring phosphorylation and the other dephosphorylation. Each individual KaiC hexamer then has a propensity to be phosphorylated in a cyclic manner. To generate macroscopic oscillations, however, the phosphorylation cycles of the different hexamers must be synchronized. We propose a novel synchronisation mechanism based on differential affinity: KaiA stimulates KaiC phosphorylation, but the limited supply of KaiA dimers binds preferentially to those KaiC hexamers that are falling behind in the oscillation. KaiB sequesters KaiA and stabilizes the dephosphorylating KaiC state. We show that our model can reproduce a wide range of published data, including the observed insensitivity of the oscillation period to variations in temperature, and that it makes nontrivial predictions about the effects of varying the concentrations of the Kai proteins.

q-bio.MN↗
arXiv2006

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

We study by simulation the effect of the diffusive motion of repressor molecules on the noise in mRNA and protein levels in the case of a repressed gene. We find that spatial fluctuations due to diffusion can drastically enhance the noise in gene expression. 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. We also show that the effect of spatial fluctuations can be well described by a two-step kinetic scheme, where formation of an encounter complex by diffusion and the subsequent association reaction are treated separately. Our results also emphasize that power spectra are a highly useful tool for studying the propagation of noise through the different stages of gene expression.

q-bio.MN↗
arXiv2006

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

Understanding cell function requires an accurate description of how noise is transmitted through biochemical networks. We present an analytical result for the power spectrum of the output signal of a biochemical network that takes into account the correlations between the noise in the input signal (the extrinsic noise) and the noise in the reactions that constitute the network (the intrinsic noise). These correlations arise from the fact that the reactions by which biochemical signals are detected necessarily affect the signaling molecules and the detection components of the network simultaneously. We show that anti-correlation between the extrinsic and intrinsic noise enhances the robustness of zero-order ultrasensitive networks to biochemical noise. We discuss the consequences of the correlation between extrinsic and intrinsic noise for a modular description of noise transmission through large biochemical networks in the context of the mitogen-activated protein kinase cascade.

q-bio.MN↗
arXiv2006

Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis

We analyse 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 non-equilibrium rare event problem proposed by Maier and Stein. For this problem, our analysis gives accurate quantitative predictions for the computational efficiency of the three methods.

cond-mat.other↗
arXiv2005

Exact results for noise power spectra in linear biochemical reaction networks

We present a simple method for determining the exact noise power spectra in linear chemical reaction networks. We apply the method to networks which are representative of biochemical processes such as gene expression and signal detection. Our results clarify how noise is transmitted by signal detection motifs, and indicate how to coarse-grain networks by the elimination of fast reactions.

q-bio.SC↗
arXiv2005

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 co-repressor from the posterior. The co-repressor 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 co-repressor. Using mathematical modelling, we show that a symmetric activator-co-repressor model can quantitatively explain the precise mid-embryo expression boundary of the hunchback gene, and the scaling of this pattern with embryo size.

q-bio.TO↗
arXiv2005

Simulating rare events in equilibrium or non-equilibrium 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 non-equilibrium 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 ratchet-like 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.

cond-mat.soft↗
arXiv2004

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. In order to determine the stability of the genetic switches, we make a connection with reactive flux theory and transition state theory. The switch stability is characterised by a well defined lifetime $τ$. We find that $τ$ grows exponentially with the mean number $\Nmean$ of transcription factor molecules involved in the switching. In the regime accessible to direct numerical simulations, the growth law is well characterised by $τ\sim\Nmean{}^α\exp(b\Nmean)$, where $α$ 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 for the general switch.

q-bio.MN↗
arXiv2004

Green's Function Reaction Dynamics: a new approach to simulate biochemical networks at the particle level and in time and space

Biochemical networks are the analog computers of life. They allow living cells to control a large number of biological processes, such as gene expression and cell signalling. In biochemical networks, the concentrations of the components are often low. This means that the discrete nature of the reactants and the stochastic character of their interactions have to be taken into account. Moreover, the spatial distribution of the components can be of crucial importance. However, the current numerical techniques for simulating biochemical networks either ignore the particulate nature of matter or treat the spatial fluctuations in a mean-field manner. We have developed a new 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. This allows GFRD to make large jumps in time 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 the scheme is highly efficient. Under biologically relevant conditions, GFRD is up to six orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space.

q-bio.MN↗
arXiv2004

Sampling rare switching events in biochemical networks

Bistable biochemical switches are ubiquitous in gene regulatory networks and signal transduction pathways. Their switching dynamics, however, are difficult to study directly in experiments or conventional computer simulations, because switching events are rapid, yet infrequent. We present a simulation technique that makes it possible to predict the rate and mechanism of flipping of biochemical switches. The method uses a series of interfaces in phase space between the two stable steady states of the switch to generate transition trajectories in a ratchet-like manner. We demonstrate its use by calculating the spontaneous flipping rate of a symmetric model of a genetic switch consisting of two mutually repressing genes. The rate constant can be obtained orders of magnitude more efficiently than using brute-force simulations. For this model switch, we show that the switching mechanism, and consequently the switching rate, depends crucially on whether the binding of one regulatory protein to the DNA excludes the binding of the other one. Our technique could also be used to study rare events and non-equilibrium processes in soft condensed matter systems.

q-bio.MN↗
arXiv2003

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 characterised by a well defined lifetime which grows sub-exponentially with the number of copies of the most-expressed transcription factor, in the regime accessible by our numerical simulations. The stability can be markedly enhanced by a suitable choice of overlap between the upstream regulatory domains. Our results suggest that robustness against biochemical noise can provide a selection pressure that drives operons, that regulate each other, together in the course of evolution.

q-bio.MN↗
arXiv2002

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.

cond-mat.soft↗
arXiv2002

Hydrophobic interactions: an overview

We present an overview of the recent progress that has been made in understanding the origin of hydrophobic interactions. We discuss the different character of the solvation behavior of apolar solutes at small and large length scales. We emphasize that the crossover in the solvation behavior arises from a collective effect, which means that implicit solvent models should be used with care. We then discuss a recently developed explicit solvent model, in which the solvent is not described at the atomic level, but rather at the level of a density field. The model is based upon a lattice-gas model, which describes density fluctuations in the solvent at large length scales, and a Gaussian model, which describes density fluctuations at smaller length scales. By integrating out the small length scale field, a Hamiltonian is obtained, which is a function of the binary, large-length scale field only. This makes it possible to simulate much larger systems than hitherto possible as demonstrated by the application of the model to the collapse of an ideal hydrophobic polymer. The results show that the collapse is dominated by the dynamics of the solvent, in particular the formation of a vapor bubble of critical size. Implications of these findings to the understanding of pressure denaturation of proteins are discussed.

cond-mat.soft↗