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Most of our current understanding of phase separation is based on ideas that disregard correlations. Here we illuminate unexpected effects of correlations on the structure and thermodynamics of interfaces and in turn phase separation, which are decisive in systems with strong interactions. Evaluating the continuum limit of the Ising model on the Bethe-Guggenheim level, we derive a Cahn-Hilliard free energy that takes into account pair correlations. For a one-dimensional interface in a strip geometry, these are shown to give rise to an effective interface broadening at interaction strengths near and above the thermal energy, which is verified in the Ising model. Interface broadening is the result of an entropy-driven interface delocalization, which is not accounted for in the widely adopted mean field theory. Pair correlations are required for thermodynamic consistency as they enforce a thermodynamically optimal local configuration of defects and profoundly affect nucleation and spinodal decomposition at strong coupling.

Phase separation has emerged as an essential concept for the spatial organization inside biological cells. However, despite the clear relevance to virtually all physiological functions, we understand surprisingly little about what phases form in a system of many interacting components, like in cells. Here, we introduce a new numerical method based on physical relaxation dynamics to study the coexisting phases in such systems. We use our approach to optimize interactions between components, similar to how evolution might have optimized the interactions of proteins. These evolved interactions robustly lead to a defined number of phases, despite substantial uncertainties in the initial composition, while random or designed interactions perform much worse. Moreover, the optimized interactions are robust to perturbations and they allow fast adaption to new target phase counts. We thus show that genetically encoded interactions of proteins provide versatile control of phase behavior. The phases forming in our system are also a concrete example of a robust emergent property that does not rely on fine-tuning the parameters of individual constituents., Comment: 7 pages, 5 figures, and Supplementary Information

Meiotic crossovers, which are exchanges of genetic material between homologous chromosomes, are more evenly and distantly spaced along chromosomes than expected by chance. This is because the occurrence of one crossover reduces the likelihood of nearby crossover events — a conserved and intriguing phenomenon called crossover interference. Although crossover interference was first described over a century ago, the mechanism allowing coordination of the fate of potential crossover sites half a chromosome away remains elusive. In this review, we discuss the recently published evidence supporting a new model for crossover patterning, coined the coarsening model, and point out the missing pieces that are still needed to complete this fascinating puzzle.

Background Nasal obstruction is a common problem, with significant impact on quality of life. Accurate diagnosis may be challenging because of the complex and dynamic nature of the involved anatomy. Computational fluid dynamics modeling has the ability to identify specific anatomical defects, allowing for a targeted surgical approach. The goal of the current study is to better understand nasal obstruction as it pertains to disease-specific quality of life by way of a novel computational fluid dynamics model of nasal airflow. Methods Fifty-three patients with nasal obstruction underwent computational fluid dynamics modeling based on computed tomographic imaging. Nasal resistance was compared to demographic data and baseline subjective nasal patency based on Nasal Obstructive Symptom Evaluation scores. Results Mean Nasal Obstructive Symptom Evaluation score among all patients was 72.6. Nasal Obstructive Symptom Evaluation score demonstrated a significant association with nasal resistance in patients with static obstruction (p = 0.03). There was a positive correlation between Nasal Obstructive Symptom Evaluation score and nasal resistance in patients with static bilateral nasal obstruction (R2 = 0.32) and poor correlation in patients with dynamic bilateral obstruction caused by nasal valve collapse (R2 = 0.02). Patients with moderate and severe bilateral symptoms had significantly higher nasal resistance compared to those with unilateral symptoms (p = 0.048). Conclusions Nasal obstruction is a multifactorial condition in most patients. This study shows correlation between simulated nasal resistance and Nasal Obstructive Symptom Evaluation score in a select group of patients. There is currently no standardized diagnostic algorithm or gold standard objective measure of nasal airflow; however, computational fluid dynamics may better inform treatment planning and surgical techniques on an individual basis. Clinical question/level of evidence Risk, V.

Most meiotic crossovers (COs), called class I crossovers, are produced by a conserved pathway catalyzed by the ZMM proteins; COs are limited in number, typically to 1–3 per chromosome, and are prevented from occurring close to one other by crossover interference1-3. In many species, CO number is subject to dimorphism between males and females, and a lower CO number is associated with shorter chromosome axes and stronger interference4. How the patterning of COs is imposed, however, remains poorly understood. Here, we show that overexpression of the ZMM protein HEI10 increases COs and reduces crossover interference but maintains sexual dimorphism; shorter axes length in female meiosis is still associated with fewer COs and stronger interference than in male meiocytes. Disrupting the synaptonemal complex (SC) by mutating ZYP1 also leads to an increase in class I COs but, in contrast, abolishes interference and disrupts the link between chromosome axis length and COs, with female and male meiocytes having the same CO frequency despite different axis lengths. Combining HEI10 overexpression and zyp1 mutation leads to a massive increase in class I COs and absence of interference, while axes lengths are still unaffected. These observations support, and can be effectively predicted by, a recently proposed coarsening model5,6 in which HEI10 diffusion is funneled by the central element of the SC before coarsening into large, well-spaced CO-promoting droplets. Given the conservation of the components, this model may account for CO patterning in many eukaryotes.

Phase separation is the thermodynamic process that explains how droplets form in multicomponent fluids. These droplets can provide controlled compartments to localize chemical reactions, and reactions can also affect the droplets' dynamics. This review focuses on the tight interplay between phase separation and chemical reactions originating from thermodynamic constraints. In particular, simple mass action kinetics cannot describe chemical reactions since phase separation requires non-ideal fluids. Instead, thermodynamics implies that passive chemical reactions reduce the complexity of phase diagrams and provide only limited control over the system's behavior. However, driven chemical reactions, which use external energy input to create spatial fluxes, can circumvent thermodynamic constraints. Such active systems can suppress the typical droplet coarsening, control droplet size, and localize droplets. This review provides an extensible framework for describing active chemical reactions in phase separating systems, which forms a basis for improving control in technical applications and understanding self-organized structures in biological cells., 15 pages, 6 figures, review

Droplets form a cornerstone of the spatiotemporal organization of biomolecules in cells. These droplets are controlled using physical processes like chemical reactions and imposed gradients, which are costly to simulate using traditional approaches, like solving the Cahn-Hilliard equation. To overcome this challenge, we here present an alternative, efficient method. The main idea is to focus on the relevant degrees of freedom, like droplet positions and sizes. We derive dynamical equations for these quantities using analytical solutions to simplified situations. We verify our method against fully-resolved simulations and show that it can describe interacting droplets under the influence of chemical reactions and external gradients using only a fraction of the computational costs of traditional methods. Our method can be extended to include other processes in the future and will thus serve as a relevant platform for understanding the dynamics of droplets in cells., Comment: 7 pages, 6 figures

Biological flow networks adapt their network morphology to optimise flow while being exposed to external stimuli from different spatial locations in their environment. These adaptive flow networks retain a memory of the stimulus location in the network morphology. Yet, what limits this memory and how many stimuli can be stored is unknown. Here, we study a numerical model of adaptive flow networks by applying multiple stimuli subsequently. We find strong memory signals for stimuli imprinted for a long time into young networks. Consequently, networks can store many stimuli for intermediate stimulus duration, which balance imprinting and ageing., Comment: 7 pages, 4 figures, 9 pages of appendix

For billions of years, photosynthetic microbes have evolved under the variable exposure to sunlight in diverse ecosystems and microhabitats all over our planet. Their abilities to dynamically respond to alterations of the luminous intensity, including phototaxis, surface association and diurnal cell cycles, are pivotal for their survival. If these strategies fail in the absence of light, the microbes can still sustain essential metabolic functionalities and motility by switching their energy production from photosynthesis to oxygen respiration. For suspensions of motile C. reinhardtii cells above a critical density, we demonstrate that this switch reversibly controls collective microbial aggregation. Aerobic respiration dominates over photosynthesis in conditions of low light, which causes the microbial motility to sensitively depend on the local availability of oxygen. For dense microbial populations in self-generated oxygen gradients, microfluidic experiments and continuum theory based on a reaction–diffusion mechanism show that oxygen-regulated motility enables the collective emergence of highly localized regions of high and low cell densities.

When liquid droplets nucleate and grow in a polymer network, compressive stresses can significantly increase their internal pressure, reaching values that far exceed the Laplace pressure. When droplets have grown in a polymer network with a stiffness gradient, droplets in relatively stiff regions of the network tend to dissolve, favoring growth of droplets in softer regions. Here, we show that this elastic ripening can be strong enough to reverse the direction of Ostwald ripening: large droplets can shrink to feed the growth of smaller ones. To numerically model these experiments, we generalize the theory of elastic ripening to account for gradients in solubility alongside gradients in mechanical stiffness., Soft Matter, 16 (25), ISSN:1744-683X, ISSN:1744-6848

Meiotic recombination is highly regulated to ensure precise segregation of homologous chromosomes. Evidence from diverse organisms indicates that the synaptonemal complex (SC), which assembles between paired chromosomes, plays essential roles in crossover formation and patterning. Several additional “pro-crossover” proteins are also required for recombination intermediates to become crossovers. These typically form multiple foci or recombination nodules along SCs, and later accumulate at fewer, widely spaced sites. Here we report that in C. elegans CDK-2 is required to stabilize all crossover intermediates and stabilizes interactions among pro-crossover factors by phosphorylating MSH-5. Additionally, we show that the conserved RING domain proteins ZHP-3/4 diffuse along the SC and remain dynamic following their accumulation at recombination sites. Based on these and previous findings we propose a model in which recombination nodules arise through spatially restricted biomolecular condensation and then undergo a regulated coarsening process, resulting in crossover interference.

Biomolecular condensates are small droplets forming spontaneously in biological cells through phase separation. They play a role in many cellular processes, but it is unclear how cells control them. Cellular regulation often relies on post-translational modifications of proteins. For biomolecular condensates, such chemical modifications could alter the molecular interaction of key condensate components. Here, we test this idea using a theoretical model based on non-equilibrium thermodynamics. In particular, we describe the chemical reactions using transition-state theory, which accounts for the non-ideality of phase separation. We identify that fast control, as in cell signalling, is only possible when external energy input drives the reaction out of equilibrium. If this reaction differs inside and outside the droplet, it is even possible to control droplet sizes. Such an imbalance in the reaction could be created by enzymes localizing to the droplet. Since this situation is typical inside cells, we speculate that our proposed mechanism is used to stabilize multiple droplets with independently controlled size and count. Our model provides a novel and thermodynamically consistent framework for describing droplets subject to non-equilibrium chemical reactions.

The continuous adaptation of networks like our vasculature ensures optimal network performance when challenged with changing loads. Here, we show that adaptation dynamics allow a network to memorize the position of an applied load within its network morphology. We identify that the irreversible dynamics of vanishing network links encode memory. Our analytical theory successfully predicts the role of all system parameters during memory formation, including parameter values which prevent memory formation. We thus provide analytical insight on the theory of memory formation in disordered systems.

Biological cells use droplets to separate components and spatially control their interior. Experiments demonstrate that the complex, crowded cellular environment affects the droplet arrangement and their sizes. To understand this behavior, we here construct a theoretical description of droplets growing in an elastic matrix, which is motivated by experiments in synthetic systems where monodisperse emulsions form during a temperature decrease. We show that large droplets only form when they break the surrounding matrix in a cavitation event. The energy barrier associated with cavitation stabilizes small droplets on the order of the mesh size and diminishes the stochastic effects of nucleation. Consequently, the cavitated droplets have similar sizes and highly correlated positions. In particular, we predict the density of cavitated droplets, which increases with faster cooling, as in the experiments. Our model also suggests how adjusting the cooling protocol and the density of nucleation sites affects the droplet size distribution. In summary, our theory explains how elastic matrices affect droplets in the synthetic system, and it provides a framework for understanding the biological case.

Liquid-liquid phase separation is an important mechanism for compartmentalizing the cell's cytoplasm, allowing the dynamic organization of the components necessary for survival. However, it is not clear how phase separation is affected by the complex viscoelastic environment inside the cell. Here, we study theoretically how stiffness gradients influence droplet growth and arrangement. We show that stiffness gradients imply concentration gradients in the dilute phase, which transport droplet material from stiff to soft regions. Consequently, droplets dissolve in the stiff region, creating a dissolution front. Using a mean-field theory, we predict that the front emerges where the curvature of the elasticity profile is large and that it propagates diffusively. This elastic ripening can occur at much faster rates than classical Ostwald ripening, thus driving the dynamics. Our work shows how gradients in elastic properties control the size and arrangement of droplets, which has potential applications in soft matter physics and plays a role inside biological cells.

Liquid–liquid phase separation is a key organizational principle in eukaryotic cells, on par with intracellular membranes. It allows cells to concentrate specific proteins into condensates, increasing reaction rates and achieving switch-like regulation. We propose two active mechanisms that can explain how cells regulate condensate formation and size. In both, the cell regulates the activity of an enzyme, often a kinase, that adds post-translational modifications to condensate proteins. In enrichment inhibition, the enzyme enriches in the condensate and weakens interactions, as seen in stress granules (SGs), Cajal bodies, and P granules. In localization-induction, condensates form around immobilized enzymes that strengthen interactions, as observed in DNA repair, transmembrane signaling, and microtubule assembly. These models can guide studies into the many emerging roles of biomolecular condensates.

Liquid-liquid phase separation is a key organizational principle in eukaryotic cells, on par with intracellular membranes. It allows cells to concentrate specific proteins into condensates, increasing reaction rates and achieving switch-like regulation. However, it is unclear how cells trigger condensate formation or dissolution and regulate their sizes. We predict from first principles two mechanisms of active regulation by post-translational modifications such as phosphorylation: In enrichment-inhibition, the regulating modifying enzyme enriches in condensates and the modifications of proteins inhibit their interactions. Stress granules, Cajal bodies, P granules, splicing speckles, and synapsin condensates obey this model. In localization-induction, condensates form around an immobilized modifying enzyme, whose modifications strengthen protein interactions. Spatially targeted condensates formed during transmembrane signaling, microtubule assembly, and actin polymerization conform to this model. The two models make testable predictions that can guide studies into the many emerging roles of biomolecular condensates.

Phase separating systems that are maintained away from thermodynamic equilibrium via molecular processes represent a class of active systems, which we call active emulsions. These systems are driven by external energy input for example provided by an external fuel reservoir. The external energy input gives rise to novel phenomena that are not present in passive systems. For instance, concentration gradients can spatially organise emulsions and cause novel droplet size distributions. Another example are active droplets that are subject to chemical reactions such that their nucleation and size can be controlled and they can spontaneously divide. In this review we discuss the physics of phase separation and emulsions and show how the concepts that governs such phenomena can be extended to capture the physics of active emulsions. This physics is relevant to the spatial organisation of the biochemistry in living cells, for the development novel applications in chemical engineering and models for the origin of life., Review article about passive and active emulsions

Centrosomes are major microtubule-organizing centers composed of centrioles surrounded by an extensive proteinacious layer called the pericentriolar material (PCM). In Caenorhabditis elegans embryos, the mitotic PCM expands by Polo-like kinase 1 (PLK-1) phosphorylation-accelerated assembly of SPD-5 molecules into supramolecular scaffolds. However, how PLK-1 phosphorylation regulates SPD-5 assembly is not known. We found that a mutant version of SPD-5 that is insensitive to PLK-1 phosphorylation (SPD-54A) could localize to PCM but was unable to rescue the reduction in PCM size and density when wild-type SPD-5 levels were decreased. In vitro, purified SPD-54A self-assembled into functional supramolecular scaffolds over long time scales, suggesting that phosphorylation only controls the rate of SPD-5 scaffold assembly. Furthermore, the SPD-5 scaffold, once assembled, remained intact and supported microtubule nucleation in the absence of PLK-1 activity in vivo. We conclude that PLK-1 is required for rapid assembly of the PCM scaffold but not for scaffold maintenance or function. Based on this idea, we developed a theoretical model that adequately predicted PCM growth rates in different mutant conditions in vivo. We propose that PLK-1 phosphorylation-dependent conversion of SPD-5 into an assembly-competent form underlies PCM formation in vivo and that the rate of this conversion determines final PCM size and density., Summary: Polo-like kinase phosphorylation determines proper centrosome scaffold size and density, but not function or maintenance, in Caenorhabditis elegans embryos.

Phase separation is a central concept of materials physics [1-3] and has recently emerged as an important route to compartmentalization within living cells [4-6]. Biological phase separation features activity [7], complex compositions [8], and elasticity [9], which reveal important gaps in our understanding of this universal physical phenomenon. Here, we explore the impact of elasticity on phase separation in synthetic polymer networks. We show that compressive stresses in a polymer network can suppress phase separation of the solvent that swells it, stabilizing mixtures well beyond the liquid-liquid phase separation boundary. Network stresses also drive a new form of ripening, driven by transport of solute down stiffness gradients. This elastic ripening can be much faster than conventional surface tension driven Ostwald ripening.

Chemically active droplets are nonequilibrium systems that combine phase separation with chemical reactions. We here investigate how the activity introduced by the chemical reactions influences solid particles inside such droplets. We find that passive particles are centered in active droplets governed by first-order reactions. In autocatalytic active droplets, only catalytically active particles can be centered. An example of such systems in biology are centrosomes. Our study can account for the observed positioning of centrioles and provides a general mechanism to control the position of particles within chemically active droplets.

The nasal cavity is a vital component of the respiratory system that heats and humidifies inhaled air in all vertebrates. Despite this common function, the shapes of nasal cavities vary widely across animals. To understand this variability, we here connect nasal geometry to its function by theoretically studying the airflow and the associated scalar exchange that describes heating and humidification. We find that optimal geometries, which have minimal resistance for a given exchange efficiency, have a constant gap width between their side walls, while their overall shape can adhere to the geometric constraints imposed by the head. Our theory explains the geometric variations of natural nasal cavities quantitatively, and we hypothesize that the trade-off between high exchange efficiency and low resistance to airflow is the main driving force shaping the nasal cavity. Our model further explains why humans, whose nasal cavities evolved to be smaller than expected for their size, become obligate oral breathers in aerobically challenging situations.

It has been proposed that during the early steps in the origin of life, small droplets could have formed via the segregation of molecules from complex mixtures by phase separation. These droplets could have provided chemical reaction centres. However, whether these droplets could divide and propagate is unclear. Here we examine the behaviour of droplets in systems that are maintained away from thermodynamic equilibrium by an external supply of energy. In these systems, droplets grow by the addition of droplet material generated by chemical reactions. Surprisingly, we find that chemically driven droplet growth can lead to shape instabilities that trigger the division of droplets into two smaller daughters. Therefore, chemically active droplets can exhibit cycles of growth and division that resemble the proliferation of living cells. Dividing active droplets could serve as a model for prebiotic protocells, where chemical reactions in the droplet play the role of a prebiotic metabolism. Droplets are an appealing picture for protocells in origin-of-life studies, but it’s unclear how they would have propagated by growth and division. Theory suggests that chemically active droplets spontaneously split into equal daughter droplets.

Centrosomes are major microtubule-organizing centers composed of centrioles surrounded by an extensive proteinacious layer called the pericentriolar material (PCM). In C. elegans embryos, the mitotic PCM expands by Polo-kinase (PLK-1) phosphorylation-accelerated assembly of SPD-5 molecules into supramolecular scaffolds. However, how PLK-1 phosphorylation regulates SPD-5 assembly is not known. We found that a mutant version of SPD-5 that is insensitive to PLK-1 phosphorylation (SPD-54A) could localize to PCM but was unable to rescue the reduction in PCM size and density when wild-type SPD-5 levels were decreased. In vitro, purified SPD-54A self-assembled into functional supramolecular scaffolds over long time scales, suggesting that phosphorylation only controls the rate of SPD-5 scaffold assembly. Furthermore, the SPD-5 scaffold, once assembled, remained intact and supported microtubule nucleation in the absence of PLK-1 activity in vivo. We conclude that Polo Kinase is required for rapid assembly of the PCM scaffold but not for scaffold maintenance or function. Based on this idea, we developed a theoretical model that adequately predicted PCM growth rates in different mutant conditions in vivo. We propose that PLK-1 phosphorylation-dependent conversion of SPD-5 into an assembly-competent form underlies PCM formation in vivo and that the rate of this conversion determines final PCM size and density.

Developing validated objective measures of nasal airflow is paramount for improving the management of nasal obstruction. Nasal airflow can be studied objectively by simulating the flow in the computer. This requires a faithful reconstruction of the nasal geometry since the simulated airflow is sensitive to small variations of the complex shape of the nasal cavity. We here show that altering the geometry by less than 1 mm can change the airflow two-fold. We also show that a faithful reconstruction of the nasal geometry is possible with a threshold-based segmentation. Utilizing the known geometry of a CT phantom, we determine an optimal segmentation threshold of -450 HU. Changing this threshold by 100 HU alters the geometry by only about 0.1 mm. We use this verified segmentation to extract nasal geometries of three patients and simulate the respective airflows using the Lattice Boltzmann method. Using a simple model, we can predict how the reconstruction threshold affects the resistance to airflow. Since the segmentation and the simulation can be automated completely, this is an important step toward an objective analysis of nasal airflow based on CT scans.

The Hubbard model on a cube was revisited and extended by both nearest-neighbor (nn) Coulomb correlation and {nearest-neighbor} Heisenberg exchange. The complete eigensystem was computed exactly for all electron occupancies and all model parameters ranging from minus infinity to plus infinity. For two electrons on the cluster the eigensystem is given in analytical form. For six electrons and infinite on-site correlation U we determinded the groundstate and the groundstate energy of the pure Hubbard model analytically. For fixed electron numbers we found a multitude of ground state level crossings in dependence on the various model parameters. Furthermore the groundstates of the pure Hubbard model in dependence on a magnetic field h coupled to the spins are shown for the complete U-h plane. For the cubic cluster gas we calculated the density $n(\mu,T,h)$ and the thermodynamical density of states from the grand potential. The ground states and the various spin-spin correlation functions are studied for both attractive and repulsive values of the three interaction constants. The anomalous degeneration lines are calculated. For the cases where these lines end in triple points we give the related parameter values. The influence of the nn-exchange and the nn-Coulomb correlation onto the anomalous degeneration is discussed., Comment: 31 pages, 13 figures,2 tables. Main text at pages 1-17. Pages 18-31 contain the analytical solution for two electrons

Natural odors typically consist of many molecules at different concentrations. It is unclear how the numerous odorant molecules and their possible mixtures are discriminated by relatively few olfactory receptors. Using an information-theoretic model, we show that a receptor array is optimal for this task if it achieves two possibly conflicting goals: (i) each receptor should respond to half of all odors and (ii) the response of different receptors should be uncorrelated when averaged over odors presented with natural statistics. We use these design principles to predict statistics of the affinities between receptors and odorant molecules for a broad class of odor statistics. We also show that optimal receptor arrays can be tuned to either resolve concentrations well or distinguish mixtures reliably. Finally, we use our results to predict properties of experimentally measured receptor arrays. Our work can thus be used to better understand natural olfaction and it also suggests ways to improve artificial sensor arrays., Comment: 8 pages, 6 figures

Emulsions consisting of droplets immersed in a fluid are typically unstable since they coarsen over time. One important coarsening process is Ostwald ripening, which is driven by the surface tension of the droplets. Stability of emulsions is relevant not only in complex fluids but also in biological cells, which contain liquidlike compartments, e.g., germ granules, Cajal bodies, and centrosomes. Such cellular systems are driven away from equilibrium, e.g., by chemical reactions, and thus can be called active emulsions. In this paper, we study such active emulsions by developing a coarse-grained description of the droplet dynamics, which we analyze for two different chemical reaction schemes. We first consider the simple case of first-order reactions, which leads to stable, monodisperse emulsions in which Ostwald ripening is suppressed within a range of chemical reaction rates. We then consider autocatalytic droplets, which catalyze the production of their own droplet material. Spontaneous nucleation of autocatalytic droplets is strongly suppressed and their emulsions are typically unstable. We show that autocatalytic droplets can be nucleated reliably and their emulsions stabilized by the help of chemically active cores, which catalyze the production of droplet material. In summary, different reaction schemes and catalytic cores can be used to stabilize emulsions and to control their properties.

Centrosomes are highly dynamic, spherical organelles without a membrane. Their physical nature and their assembly are not understood. Using the concept of phase separation, we propose a theoretical description of centrosomes as liquid droplets. In our model, centrosome material occurs in a form soluble in the cytosol and a form that tends to undergo phase separation from the cytosol. We show that an autocatalytic chemical transition between these forms accounts for the temporal evolution observed in experiments. Interestingly, the nucleation of centrosomes can be controlled by an enzymatic activity of the centrioles, which are present at the core of all centrosomes. This nonequilibrium feature also allows for multiple stable centrosomes, a situation that is unstable in equilibrium phase separation. Our theory explains the growth dynamics of centrosomes for all cell sizes down to the eight-cell stage of the Caenorhabditis elegans embryo, and it also accounts for data acquired in experiments with aberrant numbers of centrosomes and altered cell volumes. Furthermore, the model can describe unequal centrosome sizes observed in cells with perturbed centrioles. We also propose an interpretation of the molecular details of the involved proteins in the case of C. elegans. Our example suggests a general picture of the organization of membraneless organelles.

Measuring the exact path of molecular motors, such as cytoskeletal motor proteins, on their tracks has proven to be difficult without knowing the precise location of the filaments. Up to now, off-axis stepping has therefore mostly been inferred from the tracked positions of the motors with respect to the fitted path of the motors instead of determining the filament centerline. Obviously, this limits the precision of the measurements and may lead to errors due to the sometimes complex three-dimensional structure of the filaments. We developed a filament tracking algorithm to determine the centerline position of fluorescently labeled filaments with nanometer precision. This allowed us to observe the non-parallel movement of kinesin-1 motors with respect to the microtubule centerline, which is consistent with kinesin-1 following a protofilament of a supertwisted microtubule. Combined with methods to measure nanometer heights above substrate surfaces, such as fluorescence interference contrast or parallax, our algorithm presents a promising tool for optical 3D-nanometry.

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., main text: 7 pages including 5 figures, supplementary information: 13 pages including 9 figures

A comprehensive study on the migration of di- and tri-interstitials in silicon is performed using classical molecular dynamics simulations with the Stillinger-Weber potential. At first the structure and energetics of the di- and the tri-interstitial are investigated, and the accuracy of the interatomic potential is tested by comparing the results with literature data obtained by tight-binding and density-functional-theory calculations. Then the migration is investigated for temperatures between 800 and 1600 K. Very long simulation times, large computational cells and different initial conditions are considered. The defect diffusivity, the self-diffusion coefficient per defect and the corresponding effective migration barriers are calculated. Compared to the mono-interstitial, the di-interstitial migrates faster, whereas the tri-interstitial diffuses slower. The mobility of the di- and the mono-interstitial is higher than the mobility of the lattice atoms during the diffusion of these defects. On the other hand, the tri-interstitial mobility is lower than the corresponding atomic mobility. The migration mechanism of the di-interstitial shows a pronounced dependence on the temperature. At low temperature a high mobility on zig-zag-like lines along a $⟨110⟩$ axis within a {110} plane is found, whereas the change between equivalent $⟨110⟩$ directions or equivalent {110} planes occurs seldom and requires a long time. At high temperature a frequent change between equivalent $⟨110⟩$ directions or {110} planes is observed. During the diffusion within {110} planes the di-interstitial moves like a wave packet so that the atomic mobility is lower than that of the defect. On the other hand, the change between equivalent {110} migration planes is characterized by frequent atomic rearrangements. The visual analysis of the tri-interstitial diffusion reveals complex migration mechanisms and a high atomic mobility. The diffusivities and effective migration barriers obtained are compared with the few data from the literature. The implications of the present results for the explanation of experimental data on defect evolution and migration are discussed.

Small self-interstitial clusters play an important role in the evolution of radiation damage in Si during post-implantation annealing. These small clusters can be formed by two different processes: (i) fast relaxation of highly disordered cascade regions immediately after ion impact and (ii) clustering of diffusing self-interstitials in the first stage of the annealing process. The structure and energetics of the small self-interstitial clusters have been investigated by different theoretical methods. However, there are only few data on their mobility and migration mechanisms. They have been mainly obtained by static potential energy calculations. This work presents results of a systematic molecular dynamics study of the migration of di- and tri-interstitials. A classical potential approach is employed since it allows the investigation of defect migration under relatively realistic conditions, by considering large computational cells, long periods and different initial conditions. The di- and tri-interstitial configurations with the lowest formation energies are determined, and the results are compared with literature data. Then, the migration of di- and tri-interstitials is followed for 10 – 30 ns, at temperatures between 800 and 1600 K. Defect diffusivity and self-diffusion coefficient per defect are obtained by the Wigner-Seitz cell analysis and the Guinan method as well as from the mean square displacements of all atoms. The effective migration energies are determined and compared with the data from literature. The elementary migration mechanisms are discussed in detail by the analysis of movies and snapshots of defect trajectories and atomic rearrangements.

Recent developments in image processing have greatly advanced our understanding of biomolecular processes in vitro and in vivo. In particular, using Gaussian models to fit the intensity profiles of nanometer-sized objects have enabled their two-dimensional localization with a precision in the one-nanometer range. Here, we present an algorithm to precisely localize curved filaments whose structures are characterized by subresolution diameters and micrometer lengths. Using surface-immobilized microtubules, fluorescently labeled with rhodamine, we demonstrate positional precisions of ∼2 nm when determining the filament centerline and ∼9 nm when localizing the filament tips. Combined with state-of-the-art single particle tracking we apply the algorithm 1), to motor-proteins stepping on immobilized microtubules, 2), to depolymerizing microtubules, and 3), to microtubules gliding over motor-coated surfaces.

Previous work in the Gulf of St. Lawrence has yielded an unusually high upper-mantle compressional velocity. In the Gaspé area a more recent determination has yielded a value of 8.75 ± 0.20 km/s for an unreversed profile. The arrival time at a station on the north shore of the St. Lawrence River suggests that there is no major difference in velocity and depth relative to the south shore.