Topological floppy modes in models of 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.

Defect patterns on the curved surface of fish retinae suggest a mechanism of cone mosaic formation.

The outer epithelial layer of zebrafish retinae contains a crystalline array of cone photoreceptors, called the cone mosaic. As this mosaic grows by mitotic addition of new photoreceptors at the rim of the hemispheric retina, topological defects, called "Y-Junctions", form to maintain approximately constant cell spacing. The generation of topological defects due to growth on a curved surface is a distinct feature of the cone mosaic not seen in other well-studied biological patterns like the R8 photoreceptor array in the Drosophila compound eye.

Apical stress fibers enable a scaling between cell mechanical response and area in epithelial tissue.

Biological systems tailor their properties and behavior to their size throughout development and in numerous aspects of physiology. However, such size scaling remains poorly understood as it applies to cell mechanics and mechanosensing. By examining how the pupal dorsal thorax epithelium responds to morphogenetic forces, we found that the number of apical stress fibers (aSFs) anchored to adherens junctions scales with cell apical area to limit larger cell elongation under mechanical stress.

Physical limits to sensing material properties.

All materials respond heterogeneously at small scales, which limits what a sensor can learn. Although previous studies have characterized measurement noise arising from thermal fluctuations, the limits imposed by structural heterogeneity have remained unclear. In this paper, we find that the least fractional uncertainty with which a sensor can determine a material constant λ of an elastic medium is approximately [Formula: see text] for a ≫ d ≫ ξ, [Formula: see text], and D > 1, where a is the size of the sensor, d is its spatial resolution, ξ is the correlation length of fluctuations in λ, Δ is the local variability of λ, and D is the dimension of the medium.

Statistics of noisy growth with mechanical feedback in elastic tissues.

Tissue growth is a fundamental aspect of development and is intrinsically noisy. Stochasticity has important implications for morphogenesis, precise control of organ size, and regulation of tissue composition and heterogeneity. However, the basic statistical properties of growing tissues, particularly when growth induces mechanical stresses that can in turn affect growth rates, have received little attention.

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 24 h 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.

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.

Anisotropic Müller glial scaffolding supports a multiplex lattice mosaic of photoreceptors in zebrafish retina.

Background: The multiplex, lattice mosaic of cone photoreceptors in the adult fish retina is a compelling example of a highly ordered epithelial cell pattern, with single cell width rows and columns of cones and precisely defined neighbor relationships among different cone types. Cellular mechanisms patterning this multiplex mosaic are not understood. Physical models can provide new insights into fundamental mechanisms of biological patterning.

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 approximately one day in different constant environments. The posttranslational 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.

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. Elowitz and Leibler [Nature (London) 403, 335 (2000)NATUAS0028-083610.1038/35002125] 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.

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.

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.

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 nonspecific 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.

Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis.

The orientation of cell division along the long axis of the interphase cell--the century-old Hertwig's rule--has profound roles in tissue proliferation, morphogenesis, architecture and mechanics. In epithelial tissues, the shape of the interphase cell is influenced by cell adhesion, mechanical stress, neighbour topology, and planar polarity pathways. At mitosis, epithelial cells usually adopt a rounded shape to ensure faithful chromosome segregation and to promote morphogenesis.

Patterning the cone mosaic array in zebrafish retina requires specification of ultraviolet-sensitive cones.

Cone photoreceptors in teleost fish are organized in precise, crystalline arrays in the epithelial plane of the retina. In zebrafish, four distinct morphological/spectral cone types occupy specific, invariant positions within a regular lattice. The cone lattice is aligned orthogonal and parallel to circumference of the retinal hemisphere: it emerges as cones generated in a germinal zone at the retinal periphery are incorporated as single-cell columns into the cone lattice.

Participant experiences and facilitators and barriers to pill use among men who have sex with men in the iPrEx pre-exposure prophylaxis trial in San Francisco.

In 2010, the iPrEx study demonstrated efficacy of daily emtricitabine/tenofovir disoproxil fumarate (FTC/TDF) pre-exposure prophylaxis (PrEP) in reducing HIV acquisition among men who have sex with men. Adherence to study product was critical for PrEP efficacy, and varied considerably, with FTC/TDF detection rates highest in the United States. We conducted a qualitative study to gain insights into the experiences of iPrEx participants in San Francisco (SF) where there was high confirmed adherence, to understand individual and contextual factors influencing study product use in this community.

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.

Coupling mechanical deformations and planar cell polarity to create regular patterns in the zebrafish retina.

The orderly packing and precise arrangement of epithelial cells is essential to the functioning of many tissues, and refinement of this packing during development is a central theme in animal morphogenesis. The mechanisms that determine epithelial cell shape and position, however, remain incompletely understood. Here, we investigate these mechanisms in a striking example of planar order in a vertebrate epithelium: The periodic, almost crystalline distribution of cone photoreceptors in the adult teleost fish retina.

A dynamical model of ommatidial crystal formation.

The crystalline photoreceptor lattice in the Drosophila eye is a paradigm for pattern formation during development. During eye development, activation of proneural genes at a moving front adds new columns to a regular lattice of R8 photoreceptors. We present a mathematical model of the governing activator-inhibitor system, which indicates that the dynamics of positive induction play a central role in the selection of certain cells as R8s.

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.

Equilibriumlike behavior in chemical reaction networks far from equilibrium.

In an equilibrium chemical reaction mixture, the number of molecules present obeys a Poisson distribution. We report that, surprisingly, the same is true of a large class of nonequilibrium reaction networks. In particular, we show that certain topological features imply a Poisson distribution, whatever the reaction rates.

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 known to be 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.

An allosteric model of circadian KaiC phosphorylation.

In a recent series of ground-breaking experiments, Nakajima et al. [Nakajima M, Imai K, Ito H, Nishiwaki T, Murayama Y, Iwasaki H, Oyama T, Kondo T (2005) Science 308:414-415] 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.

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.