We derive an Itô stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a one-dimensional ...drift-diffusion equation, independent of the underlying physical model. This transformation allows us to identify generic properties of entropy production. It also leads to an exact uncertainty equality relating the Fano factor of entropy production and the Fano factor of the random time, which we also generalize to non-steady-state conditions.
Liquid-liquid phase separation in biology Hyman, Anthony A; Weber, Christoph A; Jülicher, Frank
Annual review of cell and developmental biology,
01/2014, Volume:
30
Journal Article
Peer reviewed
Open access
Cells organize many of their biochemical reactions in non-membrane compartments. Recent evidence has shown that many of these compartments are liquids that form by phase separation from the ...cytoplasm. Here we discuss the basic physical concepts necessary to understand the consequences of liquid-like states for biological functions.
We study the hydrodynamics and shape changes of chemically active droplets. In non-spherical droplets, surface tension generates hydrodynamic flows that drive liquid droplets into a spherical shape. ...Here we show that spherical droplets that are maintained away from thermodynamic equilibrium by chemical reactions may not remain spherical but can undergo a shape instability which can lead to spontaneous droplet division. In this case chemical activity acts against surface tension and tension-induced hydrodynamic flows. By combining low Reynolds-number hydrodynamics with phase separation dynamics and chemical reaction kinetics we determine stability diagrams of spherical droplets as a function of dimensionless viscosity and reaction parameters. We determine concentration and flow fields inside and outside the droplets during shape changes and division. Our work shows that hydrodynamic flows tends to stabilize spherical shapes but that droplet division occurs for sufficiently strong chemical driving, sufficiently large droplet viscosity or sufficiently small surface tension. Active droplets could provide simple models for prebiotic protocells that are able to proliferate. Our work captures the key hydrodynamics of droplet division that could be observable in chemically active colloidal droplets.
We generalize the Susceptible-Infected-Removed (SIR) model for epidemics to take into account generic effects of heterogeneity in the degree of susceptibility to infection in the population. We ...introduce a single new parameter corresponding to a power-law exponent of the susceptibility distribution at small susceptibilities. We find that for this class of distributions the gamma distribution is the attractor of the dynamics. This allows us to identify generic effects of population heterogeneity in a model as simple as the original SIR model which is contained as a limiting case. Because of this simplicity, numerical solutions can be generated easily and key properties of the epidemic wave can still be obtained exactly. In particular, we present exact expressions for the herd immunity level, the final size of the epidemic, as well as for the shape of the wave and for observables that can be quantified during an epidemic. In strongly heterogeneous populations, the herd immunity level can be much lower than in models with homogeneous populations as commonly used for example to discuss effects of mitigation. Using our model to analyze data for the SARS-CoV-2 epidemic in Germany shows that the reported time course is consistent with several scenarios characterized by different levels of immunity. These scenarios differ in population heterogeneity and in the time course of the infection rate, for example due to mitigation efforts or seasonality. Our analysis reveals that quantifying the effects of mitigation requires knowledge on the degree of heterogeneity in the population. Our work shows that key effects of population heterogeneity can be captured without increasing the complexity of the model. We show that information about population heterogeneity will be key to understand how far an epidemic has progressed and what can be expected for its future course.
We study the statistics of infima, stopping times, and passage probabilities of entropy production in nonequilibrium steady states, and we show that they are universal. We consider two examples of ...stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches a given state for the first time. Our main results are as follows: (i) The distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann’s constant; (ii) we find exact expressions for the passage probabilities of entropy production; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production; for example, we derive a relation between the maximal excursion of a molecular motor against the direction of an external force and the infimum of the corresponding entropy-production fluctuations. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follow from our universal results for entropy-production infima.
Protein condensates as aging Maxwell fluids Jawerth, Louise; Fischer-Friedrich, Elisabeth; Saha, Suropriya ...
Science (American Association for the Advancement of Science),
12/2020, Volume:
370, Issue:
6522
Journal Article
Peer reviewed
Protein condensates are complex fluids that can change their material properties with time. However, an appropriate rheological description of these fluids remains missing. We characterize the ...time-dependent material properties of in vitro protein condensates using laser tweezer-based active and microbead-based passive rheology. For different proteins, the condensates behave at all ages as viscoelastic Maxwell fluids. Their viscosity strongly increases with age while their elastic modulus varies weakly. No significant differences in structure were seen by electron microscopy at early and late ages. We conclude that protein condensates can be soft glassy materials that we call Maxwell glasses with age-dependent material properties. We discuss possible advantages of glassy behavior for modulation of cellular biochemistry.
In eukaryotes, DNA is packed inside the cell nucleus in the form of chromatin, which consists of DNA, proteins such as histones, and RNA. Euchromatin, which is permissive for transcription, is ...spatially organized into transcriptionally inactive domains interspersed with pockets of transcriptional activity. While transcription and RNA have been implicated in euchromatin organization, it remains unclear how their interplay forms and maintains transcription pockets. Here we combine theory and experiment to analyze the dynamics of euchromatin organization as pluripotent zebrafish cells exit mitosis and begin transcription. We show that accumulation of RNA induces formation of transcription pockets which displace transcriptionally inactive chromatin. We propose that the accumulating RNA recruits RNA-binding proteins that together tend to separate from transcriptionally inactive euchromatin. Full phase separation is prevented because RNA remains tethered to transcribed euchromatin through RNA polymerases. Instead, smaller scale microphases emerge that do not grow further and form the typical pattern of euchromatin organization.
Studying how epithelia respond to mechanical stresses is key to understanding tissue shape changes during morphogenesis. Here, we study the viscoelastic properties of the Drosophila wing epithelium ...during pupal morphogenesis by quantifying mechanical stress and cell shape as a function of time. We find a delay of 8 h between maximal tissue stress and maximal cell elongation, indicating a viscoelastic deformation of the tissue. We show that this viscoelastic behavior emerges from the mechanosensitivity of endocytic E-cadherin turnover. The increase in E-cadherin turnover in response to stress is mediated by mechanosensitive relocalization of the E-cadherin binding protein p120-catenin (p120) from cell junctions to cytoplasm. Mechanosensitivity of E-cadherin turnover is lost in p120 mutant wings, where E-cadherin turnover is constitutively high. In this mutant, the relationship between mechanical stress and stress-dependent cell dynamics is altered. Cells in p120 mutant deform and undergo cell rearrangements oriented along the stress axis more rapidly in response to mechanical stress. These changes imply a lower viscosity of wing epithelium. Taken together, our findings reveal that p120-dependent mechanosensitive E-cadherin turnover regulates viscoelastic behavior of epithelial tissues.
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•Mechanical stress releases p120-catenin from apical junctions•Loss of p120-catenin increases endocytic E-cadherin turnover•Loss of p120 speeds stress-dependent remodeling of the junctional network•Mechanical stress dependence of E-cadherin turnover sets tissue viscoelasticity
How epithelial junctional networks remodel in response to tissue stress is key to morphogenesis. Iyer et al. show that mechanical stress increases endocytic turnover of E-cadherin by depleting the E-cadherin binding protein p120 from cell junctions. This speeds remodeling of the junctional network and decreases cell shape viscosity.
Asymmetric cell divisions are essential for the development of multicellular organisms. To proceed, they require an initially symmetric cell to polarize. In Caenorhabditis elegans zygotes, ...anteroposterior polarization is facilitated by a large-scale flow of the actomyosin cortex, which directs the asymmetry of the first mitotic division. Cortical flows appear in many contexts of development, but their underlying forces and physical principles remain poorly understood. How actomyosin contractility and cortical tension interact to generate large-scale flow is unclear. Here we report on the subcellular distribution of cortical tension in the polarizing C. elegans zygote, which we determined using position- and direction-sensitive laser ablation. We demonstrate that cortical flow is associated with anisotropies in cortical tension and is not driven by gradients in cortical tension, which contradicts previous proposals. These experiments, in conjunction with a theoretical description of active cortical mechanics, identify two prerequisites for large-scale cortical flow: a gradient in actomyosin contractility to drive flow and a sufficiently large viscosity of the cortex to allow flow to be long-ranged. We thus reveal the physical requirements of large-scale intracellular cortical flow that ensure the efficient polarization of the C. elegans zygote.
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