arXiv subjects

Pieter Rein ten Wolde

Publications and source records attributed to Pieter Rein ten Wolde.

At least 55 records · Page 3Linked to original sources

arXiv2015

Optimal Prediction by Cellular Signaling Networks

Living cells can enhance their fitness by anticipating environmental change. We study how accurately linear signaling networks in cells can predict future signals. We find that maximal predictive power results from a combination of input-noise suppression, linear extrapolation, and selective readout of correlated past signal values. Single-layer networks generate exponential response kernels, which suffice to predict Markovian signals optimally. Multilayer networks allow oscillatory kernels that can optimally predict non-Markovian signals. At low noise, these kernels exploit the signal derivative for extrapolation, while at high noise, they capitalize on signal values in the past that are strongly correlated with the future signal. We show how the common motifs of negative feedback and incoherent feed-forward can implement these optimal response functions. Simulations reveal that E. coli can reliably predict concentration changes for chemotaxis, and that the integration time of its response kernel arises from a trade-off between rapid response and noise suppression.

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arXiv2015

Molecular clustering digitizes signaling and increases fidelity

Many membrane-bound molecules in cells form small clusters. It has been hypothesized that these clusters convert an analog extracellular signal into a digital intracellular signal and that this conversion increases signaling fidelity. However, the mechanism by which clusters digitize a signal and the subsequent effects on fidelity remain poorly understood. Here we demonstrate using a stochastic model of cooperative cluster formation that sufficient cooperation leads to digital signaling. We show that despite reducing the number of output states, which decreases fidelity, digitization also reduces noise in the system, which increases fidelity. The tradeoff between these effects leads to an optimal cluster size that agrees with experimental measurements.

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arXiv2015

Discrete gene replication events drive coupling between the cell cycle and circadian clocks

Many organisms possess both a cell cycle to control DNA replication and a circadian clock to anticipate changes between day and night. In some cases, these two rhythmic systems are known to be coupled by specific, cross-regulatory interactions. Here, we use mathematical modeling to show that, additionally, the cell cycle generically influences circadian clocks in a non-specific fashion: The regular, discrete jumps in gene-copy number arising from DNA replication during the cell cycle cause a periodic driving of the circadian clock, which can dramatically alter its behavior and impair its function. A clock built on negative transcriptional feedback either phase locks to the cell cycle, so that the clock period tracks the cell division time, or exhibits erratic behavior. We argue that the cyanobacterium Synechococcus elongatus has evolved two features that protect its clock from such disturbances, both of which are needed to fully insulate it from the cell cycle and give it its observed robustness: a phosphorylation-based protein modification oscillator, together with its accompanying push-pull read-out circuit that responds primarily to the ratios of the different phosphoforms, makes the clock less susceptible to perturbations in protein synthesis; and the presence of multiple, asynchronously replicating copies of the same chromosome diminishes the effect of replicating any single copy of a gene.

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arXiv2015

Fundamental Limits to Cellular Sensing

In recent years experiments have demonstrated that living cells can measure low chemical concentrations with high precision, and much progress has been made in understanding what sets the fundamental limit to the precision of chemical sensing. Chemical concentration measurements start with the binding of ligand molecules to receptor proteins, which is an inherently noisy process, especially at low concentrations. The signaling networks that transmit the information on the ligand concentration from the receptors into the cell have to filter this noise extrinsic to the cell as much as possible. These networks, however, are also stochastic in nature, which means that they will also add noise to the transmitted signal. In this review, we will first discuss how the diffusive transport and binding of ligand to the receptor sets the receptor correlation time, and then how downstream signaling pathways integrate the noise in the receptor state; we will discuss how the number of receptors, the receptor correlation time, and the effective integration time together set a fundamental limit on the precision of sensing. We then discuss how cells can remove the receptor noise while simultaneously suppressing the intrinsic noise in the signaling network. We describe why this mechanism of time integration requires three classes of resources---receptors and their integration time, readout molecules, energy---and how each resource class sets a fundamental sensing limit. We also briefly discuss the scheme of maximum-likelihood estimation, the role of receptor cooperativity, and how cellular copy protocols differ from canonical copy protocols typically considered in the computational literature, explaining why cellular sensing systems can never reach the Landauer limit on the optimal trade-off between accuracy and energetic cost.

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arXiv2014

The robustness of proofreading to crowding-induced pseudo-processivity in the MAPK pathway

Double phosphorylation of protein kinases is a common feature of signalling cascades. This motif may reduce cross-talk between signalling pathways, as the second phosphorylation site allows for proofreading, especially when phosphorylation is distributive rather than processive. Recent studies suggest that phosphorylation can be `pseudo-processive' in the crowded cellular environment, as rebinding after the first phosphorylation is enhanced by slow diffusion. Here, we use a simple model with unsaturated reactants to show that specificity for one substrate over another drops as rebinding increases and pseudo-processive behavior becomes possible. However, this loss of specificity with increased rebinding is typically also observed if two distinct enzyme species are required for phosphorylation, i.e. when the system is necessarily distributive. Thus the loss of specificity is due to an intrinsic reduction in selectivity with increased rebinding, which benefits inefficient reactions, rather than pseudo-processivity itself. We also show that proofreading can remain effective when the intended signalling pathway exhibits high levels of rebinding-induced pseudo-processivity, unlike other proposed advantages of the dual phosphorylation motif.

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arXiv2014

Positive feedback can lead to dynamic nanometer-scale clustering on cell membranes

Clustering of molecules on biological membranes is a widely observed phenomenon. In some cases, such as the clustering of Ras proteins on the membranes of mammalian cells, proper cell signaling is critically dependent on the maintenance of these clusters. Yet, the mechanism by which clusters form and are maintained in these systems remains unclear. Recently, it has been discovered that activated Ras promotes further Ras activation. Here we show using particle-based simulation that this positive feedback is sufficient to produce persistent clusters of active Ras molecules at the nanometer scale via a dynamic nucleation mechanism. Furthermore, we find that our cluster statistics are consistent with experimental observations of the Ras system. Interestingly, we show that our model does not support a Turing regime of macroscopic reaction-diffusion patterning, and therefore that the clustering we observe is a purely stochastic effect, arising from the coupling of positive feedback with the discrete nature of individual molecules. These results underscore the importance of stochastic and dynamic properties of reaction diffusion systems for biological behavior.

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arXiv2014

The lower bound on the precision of transcriptional regulation

The diffusive arrival of transcription factors at the promoter sites on the DNA sets a lower bound on how accurately a cell can regulate its protein levels. Using results from the literature on diffusion-influenced reactions, we derive an analytical expression for the lower bound on the precision of transcriptional regulation. In our theory, transcription factors can perform multiple rounds of 1D diffusion along the DNA and 3D diffusion in the cytoplasm before binding to the promoter. Comparing our expression for the lower bound on the precision against results from Green's Function Reaction Dynamics simulations shows that the theory is highly accurate under biologically relevant conditions. Our results demonstrate that, to an excellent approximation, the promoter switches between the transcription-factor bound and unbound state in a Markovian fashion. This remains true even in the presence of sliding, i.e. with 1D diffusion along the DNA. This has two important implications: (1) minimizing the noise in the promoter state is equivalent to minimizing the search time of transcription factors for their promoters; (2) the complicated dynamics of 3D diffusion in the cytoplasm and 1D diffusion along the DNA can be captured in a well-stirred model by renormalizing the promoter association and dissociation rates, making it possible to efficiently simulate the promoter dynamics using Gillespie simulations. Based on the recent experimental observation that sliding can speed up the promoter search by a factor of 4, our theory predicts that sliding can enhance the precision of transcriptional regulation by a factor of 2.

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arXiv2014

How biochemical resources determine fundamental limits in cellular sensing

Living cells deploy many resources to sense their environments, including receptors, downstream signaling molecules, time and fuel. However, it is not known which resources fundamentally limit the precision of sensing, like weak links in a chain, and which can compensate each other, leading to trade-offs between them. We show by modeling that in equilibrium systems the precision is limited by the number of receptors; the downstream network can never increase precision. This limit arises from a trade-off between the removal of extrinsic noise in the receptor and intrinsic noise in the downstream network. Non-equilibrium systems can lift this trade-off by storing the receptor state over time in chemical modification states of downstream molecules. As we quantify for a push-pull network, this requires i) time and receptors; ii) downstream molecules; iii) energy (fuel turnover) to drive modification. These three resource classes cannot compensate each other, and it is the limiting class which sets the fundamental sensing limit. Within each class, trade-offs are possible. Energy allows a power-speed trade-off, while time can be traded against receptors.

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arXiv2013

Prediction and Dissipation in Biochemical Sensing

Cells sense and predict their environment via energy-dissipating pathways. However, it is unclear whether dissipation helps or harms prediction. Here we study dissipation and prediction for a minimal sensory module of receptors that reversibly bind ligand. We find that the module performs short-term prediction optimally when operating in an adiabatic regime where dissipation vanishes. In contrast, beyond a critical forecast interval, prediction becomes most precise in a regime of maximal dissipation, suggesting that dissipative sensing in biological systems can serve to enhance prediction performance.

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arXiv2013

The importance of crowding in signaling, genetic, and metabolic networks

It is now well established that the cell is a highly crowded environment. Yet, the effects of crowding on the dynamics of signaling pathways, gene regulation networks and metabolic networks are still largely unknown. Crowding can alter both molecular diffusion and the equilibria of biomolecular reactions. In this review, we first discuss how diffusion can affect biochemical networks. Diffusion of transcription factors can increase noise in gene expression, while diffusion of proteins between intracellular compartments or between cells can reduce concentration fluctuations. In push-pull networks diffusion can impede information transmission, while in multi-site protein modification networks diffusion can qualitatively change the macroscopic response of the system, such as the loss or emergence of bistability. Moreover, diffusion can directly change the metabolic flux. We describe how crowding affects diffusion, and thus how all these phenomena are influenced by crowding. Yet, a potentially more important effect of crowding on biochemical networks is mediated via the shift in the equilibria of bimolecular reactions, and we provide computational evidence that supports this idea. Finally, we discuss how the effects of crowding can be incorporated in models of biochemical networks.

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arXiv2013

Multiplexing oscillatory biochemical signals

In recent years it is increasingly being recognized that biochemical signals are not necessarily constant in time and that the temporal dynamics of a signal can be the information carrier. Moreover, it is now well established that components are often shared between signaling pathways. Here we show by mathematical modeling that living cells can multiplex a constant and an oscillatory signal: they can transmit these two signals through the same signaling pathway simultaneously, and yet respond to them specifically and reliably. We find that information transmission is reduced not only by noise arising from the intrinsic stochasticity of biochemical reactions, but also by crosstalk between the different channels. Yet, under biologically relevant conditions more than 2 bits of information can be transmitted per channel, even when the two signals are transmitted simultaneously. These observations suggest that oscillatory signals are ideal for multiplexing signals.

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arXiv2013

Spatial partitioning improves the reliability of biochemical signaling

Spatial heterogeneity is a hallmark of living systems, even at the molecular scale in individual cells. A key example is the partitioning of membrane-bound proteins via lipid domain formation or cytoskeleton-induced corralling. Yet the impact of this spatial heterogeneity on biochemical signaling processes is poorly understood. Here we demonstrate that partitioning improves the reliability of biochemical signaling. We exactly solve a stochastic model describing a ubiquitous motif in membrane signaling. The solution reveals that partitioning improves signaling reliability via two effects: it moderates the non-linearity of the switching response, and it reduces noise in the response by suppressing correlations between molecules. An optimal partition size arises from a trade-off between minimizing the number of proteins per partition to improve signaling reliability and ensuring sufficient proteins per partition to maintain signal propagation. The predicted optimal partition size agrees quantitatively with experimentally observed systems. These results persist in spatial simulations with explicit diffusion barriers. Our findings suggest that molecular partitioning is not merely a consequence of the complexity of cellular substructures, but also plays an important functional role in cell signaling.

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arXiv2012

Fundamental Limits on Sensing Chemical Concentrations with Linear Biochemical Networks

Living cells often need to extract information from biochemical signals that are noisy. We study how accurately cells can measure chemical concentrations with signaling networks that are linear. For stationary signals of long duration, they can reach, but not beat, the Berg-Purcell limit, which relies on uniformly averaging in time the fluctuations in the input signal. For short times or nonstationary signals, however, they can beat the Berg-Purcell limit, by non-uniformly time-averaging the input. We derive the optimal weighting function for time averaging and use it to provide the fundamental limit of measuring chemical concentrations with linear signaling networks.

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arXiv2012

Signalling noise enhances chemotactic drift of E. coli

Noise in transduction of chemotactic stimuli to the flagellar motor of E. coli will affect the random run-and-tumble motion of the cell and the ability to perform chemotaxis. Here we use numerical simulations to show that an intermediate level of noise in the slow methylation dynamics enhances drift while not compromising localisation near concentration peaks. A minimal model shows how such an optimal noise level arises from the interplay of noise and the dependence of the motor response on the network output. Our results suggest that cells can exploit noise to improve chemotactic performance.

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arXiv2012

The macroscopic effects of microscopic heterogeneity

Over the past decade, advances in super-resolution microscopy and particle-based modeling have driven an intense interest in investigating spatial heterogeneity at the level of single molecules in cells. Remarkably, it is becoming clear that spatiotemporal correlations between just a few molecules can have profound effects on the signaling behavior of the entire cell. While such correlations are often explicitly imposed by molecular structures such as rafts, clusters, or scaffolds, they also arise intrinsically, due strictly to the small numbers of molecules involved, the finite speed of diffusion, and the effects of macromolecular crowding. In this chapter we review examples of both explicitly imposed and intrinsic correlations, focusing on the mechanisms by which microscopic heterogeneity is amplified to macroscopic effect.

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arXiv2012

Protein logic: a statistical mechanical study of signal integration at the single-molecule level

Information processing and decision making is based upon logic operations, which in cellular networks has been well characterized at the level of transcription. In recent years however, both experimentalists and theorists have begun to appreciate that cellular decision making can also be performed at the level of a single protein, giving rise to the notion of protein logic. Here we systematically explore protein logic using a well known statistical mechanical model. As an example system, we focus on receptors which bind either one or two ligands, and their associated dimers. Notably, we find that a single heterodimer can realize any of the 16 possible logic gates, including the XOR gate, by variation of biochemical parameters. We then introduce the novel idea that a set of receptors with fixed parameters can encode functionally unique logic gates simply by forming different dimeric combinations. An exhaustive search reveals that the simplest set of receptors (two single-ligand receptors and one double-ligand receptor) can realize several different groups of three unique gates, a result for which the parametric analysis of single receptors and dimers provides a clear interpretation. Both results underscore the surprising functional freedom readily available to cells at the single-protein level.

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arXiv2012

Mutual Repression enhances the Steepness and Precision of Gene Expression Boundaries

Embryonic development is driven by spatial patterns of gene expression that determine the fate of each cell in the embryo. While gene expression is often highly erratic, embryonic development is usually exceedingly precise. In particular, gene expression boundaries are robust not only against intrinsic noise from gene expression and protein diffusion, but also against embryo-to-embryo variations in the morphogen gradients, which provide positional information to the differentiating cells. How development is robust against intra- and inter-embryonic variations is not understood. A common motif in the gene regulation networks that control embryonic development is mutual repression between pairs of genes. To assess the role of mutual repression in the robust formation of gene expression patterns, we have performed large-scale stochastic simulations of a minimal model of two mutually repressing gap genes in Drosophila, hunchback (hb) and knirps (kni). Our model includes not only mutual repression between hb and kni, but also the stochastic and cooperative activation of hb by the anterior morphogen Bicoid (Bcd) and of kni by the posterior morphogen Caudal (Cad), as well as the diffusion of Hb and Kni. Our analysis reveals that mutual repression can markedly increase the steepness and precision of the gap gene expression boundaries. In contrast to spatial averaging and cooperative gene activation, mutual repression thus allows for gene-expression boundaries that are both steep and precise. Moreover, mutual repression dramatically enhances their robustness against embryo-to-embryo variations in the morphogen levels. Finally, our simulations reveal that gap protein diffusion plays a critical role not only in reducing the width of gap gene expression boundaries via spatial averaging, but also in repairing patterning errors that could arise due to the bistability induced by mutual repression.

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arXiv2012

Reliability of frequency- and amplitude-decoding in gene regulation

In biochemical signaling, information is often encoded in oscillatory signals. However, the advantages of such a coding strategy over an amplitude encoding scheme of constant signals remain unclear. Here we study the dynamics of a simple model gene promoter in response to oscillating and constant transcription factor signals. We find that in biologically-relevant parameter regimes an oscillating input can produce a more constant protein level than a constant input. Our results suggest that oscillating signals may be used to minimize noise in gene regulation.

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