Searcharxiv⌕ Search

arXiv subjects

David K. Lubensky

Publications and source records attributed to David K. Lubensky.

At least 19 recordsLinked to original sources
arXiv2024

Physical limits on chemical sensing in bounded domains

Cells respond to chemical cues, and the precision with which they can sense these cues is fundamentally limited by the stochastic nature of diffusion and ligand binding. Berg and Purcell famously investigated how well a small sensor in an infinite ligand bath can determine the ligand concentration, and a number of subsequent analyses have refined and built upon their classical estimates. Not all concentration sensing problems, however, occur in such an infinite geometry. At different scales, subcellular sensors and cells in tissues are both often confronted with signals whose diffusion is affected by confining boundaries. It is thus valuable to understand how basic limits on chemosensation depend on the sensor's size and on its position in the domain in which ligand diffuses. Here we compute how sensor size and proximity to reflecting boundaries affect the diffusion-limited precision of chemosensation for various geometries in one and three dimensions. We derive analytical expressions for the sensing limit in these geometries. Among our conclusions is the surprising result that, in certain circumstances, smaller sensors can be more effective than larger sensors. This effect arises from a trade-off between spatial averaging and time averaging that we analyze in detail. We also find that proximity to confining boundaries can degrade a sensor's precision significantly compared to the precision of the same sensor far from any boundaries.

physics.bio-ph↗
arXiv2021

Topological Floppy Modes in Epithelial Tissues

Recent advances in topological mechanics have revealed unusual phenomena such as topologically protected floppy modes and states of self-stress that are exponentially localized at boundaries and interfaces of mechanical networks. In this paper, we explore the topological mechanics of epithelial tissues, where the appearance of these boundary and interface modes could lead to localized soft or stressed spots and play a role in morphogenesis. We consider both a simple vertex model (VM) governed by an effective elastic energy and its generalization to an active tension network (ATN) which incorporates active adaptation of the cytoskeleton. By analyzing spatially periodic lattices at the Maxwell point of mechanical instability, we find topologically polarized phases with exponential localization of floppy modes and states of self-stress in the ATN when cells are allowed to become concave, but not in the VM.

cond-mat.soft↗
arXiv2019

Physical limits to sensing material properties

Constitutive relations describe how materials respond to external stimuli such as forces. All materials respond heterogeneously at small scales, which limits what a localized sensor can discern about the global constitution of a material. In this paper, we quantify the limits of such constitutional sensing by determining the optimal measurement protocols for sensors embedded in disordered media. For an elastic medium, we find that the least fractional uncertainty with which a sensor can determine a material constant $λ_0$ is approximately \begin{equation*} \frac{δλ_0}{λ_0 } \sim \left( \frac{Δ_λ }{ λ_0^2} \right)^{1/2} \left( \frac{ d }{ a } \right)^{D/2} \left( \frac{ ξ}{ a } \right)^{D/2} \end{equation*} for $a \gg d \gg ξ$, $λ_0 \gg Δ_λ^{1/2}$, and $D>1$, where $a$ is the size of the sensor, $d$ is its spatial resolution, $ξ$ is the correlation length of fluctuations in the material constant, $Δ_λ$ is the local variability of the material constant, and $D$ is the dimension of the medium. Our results reveal how one can construct microscopic devices capable of sensing near these physical limits, e.g. for medical diagnostics. We show how our theoretical framework can be applied to an experimental system by estimating a bound on the precision of cellular mechanosensing in a biopolymer network.

cond-mat.dis-nn↗
arXiv2018

Distinguishing Feedback Mechanisms in Clock Models

Biological oscillators are very diverse but can be classified based on dynamical motifs such as the types of feedback loops present. The S. Elongatus circadian clock is a remarkable phosphorylation-based oscillator that can be reconstituted in vitro with only 3 different purified proteins: the clock proteins KaiA, KaiB, and KaiC. Despite a growing body of knowledge about the biochemistry of the Kai proteins, basic questions about how their interactions lead to sustained oscillations remain unanswered. Here, we compare models of this system that make opposing assumptions about whether KaiA sequestration introduces a positive or a negative feedback loop. We find that the two different feedback mechanisms can be distinguished experimentally by the introduction of a protein that binds competitively with KaiA. Understanding the dynamical mechanism responsible for oscillations in the Kai system may shed light on the broader question of what clock architectures have been selected by evolution and why.

q-bio.MN↗
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↗
arXiv2017

Spontaneous Chiral Symmetry Breaking in Planar Polarized Epithelia

Most animal body plans have some degree of left-right asymmetry. This chirality at the tissue and organ level is often assumed to originate from the intrinsic handedness of biological molecules. How this handedness might be transferred from molecules to tissues during development, however, is not well understood. Here we explore an alternative paradigm where tissue chirality results from spontaneous symmetry breaking at the cellular scale, with molecular chirality acting only as a weak bias that ensures that one handedness predominates over the other. Specifically, we show that systems capable of generating planar polarity, found in many epithelial tissues, can also generically break left-right symmetry, and we identify the key interaction parameters that must be varied to access the chiral phase. In addition to a chiral polar phase corresponding to one found in liquid crystal films, a two-dimensional chiral nematic phase with no liquid crystal analog is also possible. Our results have clear implications for the interpretation of mutant phenotypes, especially in certain Drosophila epithelia.

q-bio.TO↗
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↗
arXiv2016

Vertex stability and topological transitions in vertex models of foams and epithelia

In computer simulations of dry foams and of epithelial tissues, vertex models are often used to describe the shape and motion of individual cells. Although these models have been widely adopted, relatively little is known about their basic theoretical properties. For example, while fourfold vertices in real foams are always unstable, it remains unclear whether a simplified vertex model description has the same behavior. Here, we study vertex stability and the dynamics of T1 topological transitions in vertex models. We show that, when all edges have the same tension, stationary fourfold vertices in these models do indeed always break up. In contrast, when tensions are allowed to depend on edge orientation, fourfold vertices can become stable, as is observed in some biological systems. More generally, our formulation of vertex stability leads to an improved treatment of T1 transitions in simulations and paves the way for studies of more biologically realistic models that couple topological transitions to the dynamics of regulatory proteins.

q-bio.TO↗
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.

q-bio.MN↗
arXiv2012

Exchange of stability as a function of system size in a nonequilibrium system

In equilibrium systems with short-ranged interactions, the relative stability of different thermodynamic states generally does not depend on system size (as long as this size is larger than the interaction range). Here, we use a large deviations approach to show that, in contrast, different states can exchange stability as system size is varied in a driven, bistable reaction-diffusion system. This striking effect is related to a shift from a spatially uniform to a nonuniform transition state and should generically be possible in a wide range of nonequilibrium physical and biological systems.

cond-mat.stat-mech↗
arXiv2010

Robust circadian clocks from coupled protein modification and transcription-translation cycles

The cyanobacterium Synechococcus elongatus uses both a protein phosphorylation cycle and a transcription-translation cycle to generate circadian rhythms that are highly robust against biochemical noise. We use stochastic simulations to analyze how these cycles interact to generate stable rhythms in growing, dividing cells. We find that a protein phosphorylation cycle by itself is robust when protein turnover is low. For high decay or dilution rates (and co mpensating synthesis rate), however, the phosphorylation-based oscillator loses its integrity. Circadian rhythms thus cannot be generated with a phosphorylation cycle alone when the growth rate, and consequently the rate of protein dilution, is high enough; in practice, a purely post-translational clock ceases to function well when the cell doubling time drops below the 24 hour clock period. At higher growth rates, a transcription-translation cycle becomes essential for generating robust circadian rhythms. Interestingly, while a transcription-translation cycle is necessary to sustain a phosphorylation cycle at high growth rates, a phosphorylation cycle can dramatically enhance the robustness of a transcription-translation cycle at lower protein decay or dilution rates. Our analysis thus predicts that both cycles are required to generate robust circadian rhythms over the full range of growth conditions.

q-bio.MN↗
arXiv2010

Switch and template pattern formation in a discrete reaction diffusion system inspired by the Drosophila eye

We examine a spatially discrete reaction diffusion model based on the interactions that create a periodic pattern in the Drosophila eye imaginal disc. This model is capable of generating a regular hexagonal pattern of gene expression behind a moving front, as observed in the fly system. In order to better understand the novel switch and template mechanism behind this pattern formation, we present here a detailed study of the model's behavior in one dimension, using a combination of analytic methods and numerical searches of parameter space. We find that patterns are created robustly provided that there is an appropriate separation of timescales and that self-activation is sufficiently strong, and we derive expressions in this limit for the front speed and the pattern wavelength. Moving fronts in pattern-forming systems near an initial linear instability generically select a unique pattern, but our model operates in a strongly nonlinear regime where the final pattern depends on the initial conditions as well as on parameter values. Our work highlights the important role that cellularization and cell-autonomous feedback can play in biological pattern formation.

q-bio.MN↗
arXiv2008

Equilibrium-like behavior in far-from-equilibrium chemical reaction networks

In an equilibrium chemical reaction mixture, the number of molecules present obeys a Poisson distribution. We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain an essentially complete answer. In particular, we show that networks with certain topological features must have a Poisson distribution, whatever the reaction rates. Such driven systems also obey an analog of the fluctuation-dissipation theorem. Our results may be relevant to biological systems and to the larger question of how equilibrium concepts might apply to nonequilibrium systems.

cond-mat.stat-mech↗
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↗
arXiv2004

Dynamics of Molecular Motors with Finite Processivity on Heterogeneous Tracks

The dynamics of molecular motors which occasionally detach from a heterogeneous track like DNA or RNA is considered. Motivated by recent single molecule experiments, we study a simple model for a motor moving along a disordered track using chemical energy while an external force opposes its motion. The motors also have finite processivity, i.e., they can leave the track with a position dependent rate. We show that the response of the system to disorder in the hopping off rate depends on the value of the external force. For most values of the external force, strong disorder causes the motors which survive for long times on the track to be localized at preferred positions. However, near the stall force, localization occurs for any amount of disorder. Existence of localized states near the top of the band implies a stretched exponential contribution to the decay of the survival probability. To obtain these results, we study the complex eigenvalue spectrum of the time evolution operator. A similar spectral analysis also provides a very efficient method for studying the dynamics of motors with infinite processivity.

cond-mat.stat-mech↗
arXiv2004

Dynamics of Molecular Motors and Polymer Translocation with Sequence Heterogeneity

The effect of sequence heterogeneity on polynucleotide translocation across a pore and on simple models of molecular motors such as helicases, DNA polymerase/exonuclease and RNA polymerase is studied in detail. Pore translocation of RNA or DNA is biased due to the different chemical environments on the two sides of the membrane, while the molecular motor motion is biased through a coupling to chemical energy. An externally applied force can oppose these biases. For both systems we solve lattice models exactly both with and without disorder. The models incorporate explicitly the coupling to the different chemical environments for polymer translocation and the coupling to the chemical energy (as well as nucleotide pairing energies) for molecular motors. Using the exact solutions and general arguments we show that the heterogeneity leads to anomalous dynamics. Most notably, over a range of forces around the stall force (or stall tension for DNA polymerase/exonuclease systems) the displacement grows sublinearly as t^μwith μ<1. The range over which this behavior can be observed experimentally is estimated for several systems and argued to be detectable for appropriate forces and buffers. Similar sequence heterogeneity effects may arise in the packing of viral DNA.

cond-mat.stat-mech↗
arXiv2003

Unzipping Kinetics of Double-Stranded DNA in a Nanopore

We studied the unzipping kinetics of single molecules of double-stranded DNA by pulling one of their two strands through a narrow protein pore. PCR analysis yielded the first direct proof of DNA unzipping in such a system. The time to unzip each molecule was inferred from the ionic current signature of DNA traversal. The distribution of times to unzip under various experimental conditions fit a simple kinetic model. Using this model, we estimated the enthalpy barriers to unzipping and the effective charge of a nucleotide in the pore, which was considerably smaller than previously assumed.

cond-mat.soft↗