arXiv subjects

Andrew Mugler

Publications and source records attributed to Andrew Mugler.

At least 55 records · Page 3Linked to original sources

arXiv2015

Role of spatial averaging in multicellular gradient sensing

Gradient sensing underlies important biological processes including morphogenesis, polarization, and cell migration. The precision of gradient sensing increases with the length of a detector (a cell or group of cells) in the gradient direction, since a longer detector spans a larger range of concentration values. Intuition from analyses of concentration sensing suggests that precision should also increase with detector length in the direction transverse to the gradient, since then spatial averaging should reduce the noise. However, here we show that, unlike for concentration sensing, the precision of gradient sensing decreases with transverse length for the simplest gradient sensing model, local excitation--global inhibition (LEGI). The reason is that gradient sensing ultimately relies on a subtraction of measured concentration values. While spatial averaging indeed reduces the noise in these measurements, which increases precision, it also reduces the covariance between the measurements, which results in the net decrease in precision. We demonstrate how a recently introduced gradient sensing mechanism, regional excitation--global inhibition (REGI), overcomes this effect and recovers the benefit of transverse averaging. Using a REGI-based model, we compute the optimal two- and three-dimensional detector shapes, and argue that they are consistent with the shapes of naturally occurring gradient-sensing cell populations.

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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

Stochastic modeling of gene expression, protein modification, and polymerization

Many fundamental cellular processes involve small numbers of molecules. When numbers are small, fluctuations dominate, and stochastic models, which account for these fluctuations, are required. In this chapter, we describe minimal stochastic models of three fundamental cellular processes: gene expression, protein modification, and polymerization. We introduce key analytic tools for solving each model, including the generating function, eigenfunction expansion, and operator methods, and we discuss how these tools are extended to more complicated models. These analytic tools provide an elegant, efficient, and often insightful alternative to stochastic simulation.

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arXiv2015

Noise expands the response range of the Bacillus subtilis competence circuit

Gene regulatory circuits must contend with intrinsic noise that arises due to finite numbers of proteins. While some circuits act to reduce this noise, others appear to exploit it. A striking example is the competence circuit in Bacillus subtilis, which exhibits much larger noise in the duration of its competence events than a synthetically constructed analog that performs the same function. Here, using stochastic modeling and fluorescence microscopy, we show that this larger noise allows cells to exit terminal phenotypic states, which expands the range of stress levels to which cells are responsive and leads to phenotypic heterogeneity at the population level. This is an important example of how noise confers a functional benefit in a genetic decision-making circuit.

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arXiv2015

Cell-cell communication enhances the capacity of cell ensembles to sense shallow gradients during morphogenesis

Collective cell responses to exogenous cues depend on cell-cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and, little is known about how multicellular signal processing modulates single cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored if cell-cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow Epidermal Growth Factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells.

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arXiv2015

Limits to the precision of gradient sensing with spatial communication and temporal integration

Gradient sensing requires at least two measurements at different points in space. These measurements must then be communicated to a common location to be compared, which is unavoidably noisy. While much is known about the limits of measurement precision by cells, the limits placed by the communication are not understood. Motivated by recent experiments, we derive the fundamental limits to the precision of gradient sensing in a multicellular system, accounting for communication and temporal integration. The gradient is estimated by comparing a "local" and a "global" molecular reporter of the external concentration, where the global reporter is exchanged between neighboring cells. Using the fluctuation-dissipation framework, we find, in contrast to the case when communication is ignored, that precision saturates with the number of cells independently of the measurement time duration, since communication establishes a maximum lengthscale over which sensory information can be reliably conveyed. Surprisingly, we also find that precision is improved if the local reporter is exchanged between cells as well, albeit more slowly than the global reporter. The reason is that while exchange of the local reporter weakens the comparison, it decreases the measurement noise. We term such a model "regional excitation--global inhibition" (REGI). Our results demonstrate that fundamental sensing limits are necessarily sharpened when the need to communicate information is taken into account.

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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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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

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

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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arXiv2011

Membrane clustering and the role of rebinding in biochemical signaling

In many cellular signaling pathways, key components form clusters at the cell membrane. Although much work has focused on the mechanisms behind such cluster formation, the implications for downstream signaling remain poorly understood. Here, motivated by recent experiments, we study via particle-based simulation a covalent modification network in which the activating component is either clustered or randomly distributed on the membrane. We find that while clustering reduces the response of a single-modification network, clustering can enhance the response of a double-modification network. The reduction is a bulk effect: a cluster presents a smaller effective target to a substrate molecule in the bulk. The enhancement, on the other hand, is a local effect: a cluster promotes the rapid rebinding and second activation of singly active substrate molecules. As such, the enhancement relies upon frequent collisions on a short timescale, which leads to a diffusion coefficient at which the enhancement is optimal. We complement simulation with analytic results at both the mean-field and first-passage distribution levels. Our results emphasize the importance of spatially resolved models, showing that significant effects of spatial correlations persist even in spatially averaged quantities such as response curves.

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arXiv2010

A statistical method for revealing form-function relations in biological networks

Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question "how does function follow form" is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.

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arXiv2010

Analytic methods for modeling stochastic regulatory networks

The past decade has seen a revived interest in the unavoidable or intrinsic noise in biochemical and genetic networks arising from the finite copy number of the participating species. That is, rather than modeling regulatory networks in terms of the deterministic dynamics of concentrations, we model the dynamics of the probability of a given copy number of the reactants in single cells. Most of the modeling activity of the last decade has centered on stochastic simulation of individual realizations, i.e., Monte-Carlo methods for generating stochastic time series. Here we review the mathematical description in terms of probability distributions, introducing the relevant derivations and illustrating several cases for which analytic progress can be made either instead of or before turning to numerical computation.

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arXiv2010

Telling time with an intrinsically noisy clock

Intracellular transmission of information via chemical and transcriptional networks is thwarted by a physical limitation: the finite copy number of the constituent chemical species introduces unavoidable intrinsic noise. Here we provide a method for solving for the complete probabilistic description of intrinsically noisy oscillatory driving. We derive and numerically verify a number of simple scaling laws. Unlike in the case of measuring a static quantity, response to an oscillatory driving can exhibit a resonant frequency which maximizes information transmission. Further, we show that the optimal regulatory design is dependent on the biophysical constraints (i.e., the allowed copy number and response time). The resulting phase diagram illustrates under what conditions threshold regulation outperforms linear regulation.

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arXiv2009

Network motifs come in sets: correlations in the randomization process

The identification of motifs--subgraphs that appear significantly more often in a particular network than in an ensemble of randomized networks--has become a ubiquitous method for uncovering potentially important subunits within networks drawn from a wide variety of fields. We find that the most common algorithms used to generate the ensemble from the real network change subgraph counts in a highly correlated manner, so that one subgraph's status as a motif may not be independent from the statuses of the other subgraphs. We demonstrate this effect for the problem of 3- and 4-node motif identification in the transcriptional regulatory networks of E. coli and S. cerevisiae in which randomized networks are generated via an edge-swapping algorithm (Milo et al., Science 298:824, 2002). We show that correlations among 3-node subgraphs are easily interpreted, and we present an information-theoretic tool that may be used to identify correlations among subgraphs of any size.

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