arXiv subjects

Pieter Rein ten Wolde

Publications and source records attributed to Pieter Rein ten Wolde.

At least 37 records · Page 2Linked to original sources

arXiv2019

Diffusible crosslinkers cause superexponential friction forces

The mitotic spindle lies at the heart of the spatio-temporal control over cellular components during cell division. The spindle consists of microtubules, which are not only crosslinked by motor proteins but also by passive binding proteins. These passive crosslinkers stabilize the highly dynamic mitotic spindle by generating friction forces between sliding filaments. However, it remains unclear how the friction coefficient depends on the number of crosslinkers and the size of the overlap between the microtubules. Here, we use theory and computer simulations to study the friction between two filaments that are crosslinked by passive proteins, which can hop between neighboring binding sites while physically excluding each other. The simulations reveal that the movement of one microtubule relative to the other is limited by free-energy barrier crossings, causing rare and discrete jumps of the microtubule that span the distance between adjacent crosslinker binding sites. We derive an exact analytical expression for the free-energy landscape and identify the reaction coordinate that governs the relative movement, which allows us to determine the effective barrier height for the microtubule jumps. Both through simulations and reaction rate theory, we make the experimentally testable prediction that the friction between the microtubules increases superexponentially with the density of crosslinkers.

physics.bio-ph↗

arXiv2019

The behaviour of information flow near criticality

Recent experiments have indicated that many biological systems self-organise near their critical point, which hints at a common design principle. While it has been suggested that information transmission is optimized near the critical point, it remains unclear how information transmission depends on the dynamics of the input signal, the distance over which the information needs to be transmitted, and the distance to the critical point. Here we employ stochastic simulations of a driven 2D Ising system and study the instantaneous mutual information and the information transmission rate between a driven input spin and an output spin. The instantaneous mutual information varies non-monotonically with the temperature, but increases monotonically with the correlation time of the input signal. In contrast, the information transmission rate exhibits a maximum as a function of the input correlation time. Moreover, there exists an optimal temperature that maximizes this maximum information transmission rate. It arises from a tradeoff between the necessity to respond fast to changes in the input so that more information per unit amount of time can be transmitted, and the need to respond to reliably. The optimal temperature lies above the critical point, but moves towards it as the distance between the input and output spin is increased.

cond-mat.stat-mech↗

arXiv2018

The power of being explicit: demystifying work, heat, and free energy in the physics of computation

Interest in the thermodynamics of computation has revived in recent years, driven by developments in science, economics and technology. Given the consequences of the growing demand for computational power, the idea of reducing the energy cost of computations has gained new importance. Simultaneously, many biological networks are now interpreted as information-processing or computational systems constrained by their underlying thermodynamics. Indeed, some suggest that low-cost, high-density biological systems may help to mitigate the rising demand for computational power and the "end" of Moore's law of exponential growth in the density of transistors. In this chapter we address widespread misconceptions about thermodynamics and the thermodynamics of computation. In particular, we will argue against the general perception that a measurement or copy operation can be performed at no cost, against the emphasis placed on the significance of erasure operations, and against the careless discussion of heat and work. While not universal, these misconceptions are sufficiently prevalent (particularly within interdisciplinary contexts) to warrant a detailed discussion. In the process, we will argue that explicitly representing fundamental processes is a useful tool, serving to demystify key concepts. We first give a brief overview of thermodynamics, then the history of the thermodynamics of computation - particularly in terms of copy and measurement operations inherent to classic thought experiments. Subsequently, we analyse these ideas via an explicit biochemical representation of the entire cycle of Szilard's engine. In doing so we show that molecular computation is both a promising engineering paradigm, and a valuable tool in providing fundamental understanding.

cond-mat.stat-mech↗

arXiv2018

Non-equilibrium correlations in minimal dynamical models of polymer copying

Living systems produce "persistent" copies of information-carrying polymers, in which template and copy sequences remain correlated after physically decoupling. We identify a general measure of the thermodynamic efficiency with which these non-equilibrium states are created, and analyze the accuracy and efficiency of a family of dynamical models that produce persistent copies. For the weakest chemical driving, when polymer growth occurs in equilibrium, both the copy accuracy and, more surprisingly, the efficiency vanish. At higher driving strengths, accuracy and efficiency both increase, with efficiency showing one or more peaks at moderate driving. Correlations generated within the copy sequence, as well as between template and copy, store additional free energy in the copied polymer and limit the single-site accuracy for a given chemical work input. Our results provide insight in the design of natural self-replicating systems and can aid the design of synthetic replicators.

cond-mat.stat-mech↗

arXiv2018

Theory of circadian metabolism

Many organisms repartition their proteome in a circadian fashion in response to the daily nutrient changes in their environment. A striking example is provided by cyanobacteria, which perform photosynthesis during the day to fix carbon. These organisms not only face the challenge of rewiring their proteome every 12 hours, but also the necessity of storing the fixed carbon in the form of glycogen to fuel processes during the night. In this manuscript, we extend the framework developed by Hwa and coworkers (Scott et al., Science 330, 1099 (2010)) for quantifying the relatinship between growth and proteome composition to circadian metabolism. We then apply this framework to investigate the circadian metabolism of the cyanobacterium Cyanothece, which not only fixes carbon during the day, but also nitrogen during the night, storing it in the polymer cyanophycin. Our analysis reveals that the need to store carbon and nitrogen tends to generate an extreme growth strategy, in which the cells predominantly grow during the day, as observed experimentally. This strategy maximizes the growth rate over 24 hours, and can be quantitatively understood by the bacterial growth laws. Our analysis also shows that the slow relaxation of the proteome, arising from the slow growth rate, puts a severe constraint on implementing this optimal strategy. Yet, the capacity to estimate the time of the day, enabled by the circadian clock, makes it possible to anticipate the daily changes in the environment and mount a response ahead of time. This significantly enhances the growth rate by counteracting the detrimental effects of the slow proteome relaxation.

q-bio.MN↗

arXiv2018

Robustness of clocks to input noise

To estimate the time, many organisms, ranging from cyanobacteria to animals, employ a circadian clock which is based on a limit-cycle oscillator that can tick autonomously with a nearly 24h period. Yet, a limit-cycle oscillator is not essential for knowing the time, as exemplified by bacteria that possess an 'hourglass': a system that when forced by an oscillatory light input exhibits robust oscillations from which the organism can infer the time, but that in the absence of driving relaxes to a stable fixed point. Here, using models of the Kai system of cyanobacteria, we compare a limit- cycle oscillator with two hourglass models, one that without driving relaxes exponentially and one that does so in an oscillatory fashion. In the limit of low input-noise, all three systems are equally informative on time, yet in the regime of high input-noise the limit-cycle oscillator is far superior. The same behavior is found in the Stuart-Landau model, indicating that our result is universal.

q-bio.MN↗

arXiv2018

Quantifying fluctuations in reversible enzymatic cycles and clocks

Biochemical reactions are fundamentally noisy at a molecular scale. This limits the precision of reaction networks, but also allows fluctuation measurements which may reveal the structure and dynamics of the underlying biochemical network. Here, we study non-equilibrium reaction cycles, such as the mechanochemical cycle of molecular motors, the phosphorylation cycle of circadian clock proteins, or the transition state cycle of enzymes. Fluctuations in such cycles may be measured using either of two classical definitions of the randomness parameter, which we show to be equivalent in general microscopically reversible cycles. We define a stochastic period for reversible cycles and present analytical solutions for its moments. Furthermore, we associate the two forms of the randomness parameter with the thermodynamic uncertainty relation, which sets limits on the timing precision of the cycle in terms of thermodynamic quantities. Our results should prove useful also for the study of temporal fluctuations in more general networks.

physics.bio-ph↗

arXiv2017

eGFRD in all dimensions

Biochemical reactions typically occur at low copy numbers, but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. However, while particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers, the algorithms used to simulate them oftentimes imply trade-offs between computational efficiency and accuracy. eGFRD (enhanced Green's Function Reaction Dynamics) is an exact algorithm that evades such trade-offs by partitioning the N-particle system into M<N analytically tractable one- and two-particle systems; the analytical solutions (Green's functions) then are used to implement an event-driven particle-based scheme that allows particles to make large jumps in time and space while retaining access to their state variables at any moment. Here we present "eGFRD2", a new eGFRD version that implements the principle of eGFRD in all dimensions, enabling efficient simulation of biochemical reaction-diffusion processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D elongated cylinders representative of, e.g., cytoskeletal tracks or DNA; in 1D, it also incorporates convective motion used to model active transport. We find that, for low particle densities, eGFRD2 is up to 3 orders of magnitude faster than optimized Brownian Dynamics. We exemplify the capabilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport on microtubules, and autophosphorylation on the membrane, confirming recent results on this system and demonstrating that it can efficiently operate under genuinely stochastic conditions.

q-bio.MN↗

arXiv2017

Period Robustness and Entrainability of the Kai System to Changing Nucleotide Concentrations

Circadian clocks must be able to entrain to time-varying signals to keep their oscillations in phase with the day-night rhythm. On the other hand, they must also exhibit input compensation: their period must remain about one day in different constant environments. The post-translational oscillator of the Kai system can be entrained by transient or oscillatory changes in the ATP fraction, yet is insensitive to constant changes in this fraction. We study in three different models of this system how these two seemingly conflicting criteria are met: the Van Zon model (Van Zon et al., PNAS, 2007), the Rust model (Phong et al., PNAS, 2013), and our new model (Paijmans et al., arXiv:1612.02715). We find that the new model exhibits the best trade-off between input compensation and entrainability: on the footing of equal phase-response curves, it exhibits the strongest input compensation. Performing stochastic simulations at the level of individual hexamers allows us to identify a new mechanism, which is employed by the new model to achieve input compensation: At lower ATP fraction, the individual hexamers make a shorter cycle in the phosphorylation state space, which compensates for the slower pace at which they traverse the cycle.

physics.bio-ph↗

arXiv2017

Optimal entrainment of circadian clocks in the presence of noise

Circadian clocks are biochemical oscillators that allow organisms to estimate the time of the day. These oscillators are inherently noisy due to the discrete nature of the reactants and the stochastic character of their interactions. To keep these oscillators in sync with the daily day-night rhythm in the presence of noise, circadian clocks must be coupled to the dark-light cycle. In this manuscript, we study the entrainment of phase oscillators as a function of the intrinsic noise in the system. Using stochastic simulations, we compute the optimal coupling strength, intrinsic frequency and shape of the phase-response curve, that maximize the mutual information between the phase of the clock and time. We show that the optimal coupling strength and intrinsic frequency increase with the noise, but that the shape of the phase-response curve varies non-monotonically with the noise: in the low-noise regime, it features a deadzone that increases in width as the noise increases, while in the high-noise regime, the width decreases with the noise. These results arise from a trade-off between maximizing stability -noise suppression - and maximizing linearity of the input-output, i.e. time- phase, relation. We also show that three analytic approximations -the linear-noise approximation, the phase-averaging method, and linear-response theory- accurately describe different regimes of the coupling strength and the noise.

physics.bio-ph↗

arXiv2017

Spatial-Stochastic Simulation of Reaction-Diffusion Systems

Biochemical networks play a crucial role in biological systems, implementing a broad range of vital functions. They normally operate at low copy numbers and in spatial settings, but this is often ignored and well-stirred conditions are assumed. Yet, it is increasingly becoming clear that even microscopic spatial inhomogeneities oftentimes can induce significant differences on the macroscopic level. Since experimental observation of single-molecule behavior is extremely challenging, theoretical modeling of biochemical reactions on the single-particle level is an important tool for understanding spatial effects in biochemical systems. While purely analytical models quickly become intractable here, spatial-stochastic simulations can capture a wide range of biochemical processes with the necessary levels of detail. Here we discuss different techniques for spatial-stochastic simulation of reaction-diffusion systems, and explain important precautions required to make them biochemically accurate and efficient. We illustrate non-negligible accuracy issues arising even in the most simple approaches to biochemical simulation, and present methods to deal with them. We first explain how Brownian Dynamics, a widely used particle-based diffusion simulation technique with fixed propagation time, can be adapted to incorporate chemical reactions, and portray a range of schemes that elaborate on this idea. We then introduce event-driven spatial-stochastic simulation methods, in which system updates are performed asynchronously with situation-dependent, varying time steps; here we particularly focus on eGFRD, a computationally efficient particle-based algorithm that makes use of analytical functions to accurately sample interparticle reactions and diffusive motion with large jumps in time and space. We end by briefly presenting recent developments in the field of spatial-stochastic biochemical simulation.

q-bio.MN↗

arXiv2017

Fundamental costs in the production and destruction of persistent polymer copies

Living cells use readout molecules to record the state of receptor proteins, similar to measurements or copies in typical computational devices. But is this analogy rigorous? Can cells be optimally efficient, and if not, why? We show that, as in computation, a canonical biochemical readout network generates correlations; extracting no work from these correlations sets a lower bound on dissipation. For general input, the biochemical network cannot reach this bound, even with arbitrarily slow reactions or weak thermodynamic driving. It faces an accuracy-dissipation trade-off that is qualitatively distinct from and worse than implied by the bound, and more complex steady-state copy processes cannot perform better. Nonetheless, the cost remains close to the thermodynamic bound unless accuracy is extremely high. Additionally, we show that biomolecular reactions could be used in thermodynamically optimal devices under exogenous manipulation of chemical fuels, suggesting an experimental system for testing computational thermodynamics.

cond-mat.stat-mech↗

arXiv2017

The thermodynamics of computational copying in biochemical systems

q-bio.MN↗

arXiv2016

Robustness of synthetic oscillators in growing and dividing cells

Synthetic biology sets out to implement new functions in cells, and to develop a deeper understanding of biological design principles. In 2000, Elowitz and Leibler showed that by rational design of the reaction network, and using existing biological components, they could create a network that exhibits periodic gene expression, dubbed the repressilator (Elowitz and Leibler, Nature, 2000). More recently, Stricker et al. presented another synthetic oscillator, called the dual-feedback oscillator (Stricker et al., 2008), which is more stable. How the stability of these oscillators is affected by the intrinsic noise of the interactions between the components and the stochastic expression of their genes, has been studied in considerable detail. However, as all biological oscillators reside in growing and dividing cells, an important question is how these oscillators are perturbed by the cell cycle. In previous work we showed that the periodic doubling of the gene copy numbers due to DNA replication can couple not only natural, circadian oscillators to the cell cycle (Paijmans et al., PNAS, \textbf{113}, 4063, (2016)), but also these synthetic oscillators. Here we expand this study. We find that the strength of the locking between oscillators depends not only on the positions of the genes on the chromosome, but also on the noise in the timing of gene replication: noise tends to weaken the coupling. Yet, even in the limit of high levels of noise in the replication times of the genes, both synthetic oscillators show clear signatures of locking to the cell cycle. This work enhances our understanding of the design of robust biological oscillators inside growing and diving cells.

physics.bio-ph↗

arXiv2016

A Thermodynamically consistent model of the post-translational Kai circadian clock

The principal pacemaker of the circadian clock of the cyanobacterium S. elongatus is a protein phosphorylation cycle consisting of three proteins, KaiA, KaiB and KaiC. KaiC forms a homohexamer, with each monomer consisting of two domains, CI and CII. Both domains can bind and hydrolyze ATP, but only the CII domain can be phosphorylated, at two residues, in a well-defined sequence. While this system has been studied extensively, how the clock is driven thermodynamically has remained elusive. Inspired by recent experimental observations and building on ideas from previous mathematical models, we present a new, thermodynamically consistent, statistical-mechanical model of the clock. At its heart are two main ideas: i) ATP hydrolysis in the CI domain provides the thermodynamic driving force for the clock, switching KaiC between an active conformational state in which its phosphorylation level tends to rise and an inactive one in which it tends to fall; ii) phosphorylation of the CII domain provides the timer for the hydrolysis in the CI domain. The model also naturally explains how KaiA, by acting as a nucleotide exchange factor, can stimulate phosphorylation of KaiC, and how the differential affinity of KaiA for the different KaiC phosphoforms generates the characteristic temporal order of KaiC phosphorylation. As the phosphorylation level in the CII domain rises, the release of ADP from CI slows down, making the inactive conformational state of KaiC more stable. In the inactive state, KaiC binds KaiB, which not only stabilizes this state further, but also leads to the sequestration of KaiA, and hence to KaiC dephosphorylation. Using a dedicated kinetic Monte Carlo algorithm, we show that the model can describe a wealth of experimental data.

physics.bio-ph↗

arXiv2016

Multiscale simulations of anisotropic particles combining Brownian Dynamics and Green's Function Reaction Dynamics

The modeling of complex reaction-diffusion processes in, for instance, cellular biochemical networks or self-assembling soft matter can be tremendously sped up by employing a multiscale algorithm which combines the mesoscopic Green's Function Reaction Dynamics (GFRD) method with explicit stochastic Brownian, Langevin, or deterministic Molecular Dynamics to treat reactants at the microscopic scale [A. Vijaykumar, P.G. Bolhuis and P.R. ten Wolde, J. Chem. Phys. {\bf 43}, 21: 214102 (2015)]. Here we extend this multiscale BD-GFRD approach to include the orientational dynamics that is crucial to describe the anisotropic interactions often prevalent in biomolecular systems. We illustrate the novel algorithm using a simple patchy particle model. After validation of the algorithm we discuss its performance. The rotational BD-GFRD multiscale method will open up the possibility for large scale simulations of e.g. protein signalling networks.

q-bio.MN↗

arXiv2016

Biochemical machines for the interconversion of mutual information and work

We propose a physically-realisable biochemical device that is coupled to a biochemical reservoir of mutual information, fuel molecules and a chemical bath. Mutual information allows work to be done on the bath even when the fuel molecules appear to be in equilibrium; alternatively, mutual information can be created by driving from the fuel or the bath. The system exhibits diverse behaviour, including a regime in which the information, despite increasing during the reaction, enhances the extracted work. We further demonstrate that a modified device can function without the need for external manipulation, eliminating the need for a complex and potentially costly control.

cond-mat.stat-mech↗

arXiv2016

The accuracy of telling time via oscillatory signals

Circadian clocks are the central timekeepers of life, allowing cells to anticipate changes between day and night. Experiments in recent years have revealed that circadian clocks can be highly stable, raising the question how reliably they can be read out. Here, we combine mathematical modeling with information theory to address the question how accurately a cell can infer the time from an ensemble of protein oscillations, which are driven by a circadian clock. We show that the precision increases with the number of oscillations and their amplitude relative to their noise. Our analysis also reveals that their exists an optimal phase relation that minimizes the error in the estimate of time, which depends on the relative noise levels of the protein oscillations. Lastly, our work shows that cross-correlations in the noise of the protein oscillations can enhance the mutual information, which suggests that cross-regulatory interactions between the proteins that read out the clock can be beneficial for temporal information transmission.

q-bio.MN↗