text: The molecular motor myosin V transports cargo by stepping on actin filaments, executing a random diffusive search for actin binding sites at each step. A recent experiment suggests that the joint between the myosin lever arms may not rotate freely, as assumed in earlier studies, but instead has a preferred angle giving rise to structurally constrained diffusion. We address this controversy through comprehensive analytical and numerical modeling of myosin V diffusion and stepping. When the joint is constrained, our model reproduces the experimentally observed diffusion, allowing us to estimate bounds on the constraint energy. We also test the consistency between the constrained diffusion model and previous measurements of step size distributions and the load dependence of various observable quantities. The theory lets us address the biological significance of the constrained joint and provides testable predictions of new myosin behaviors, including the stomp distribution and the run length under off-axis force.
  All the data for the figures in the study (Fig. 3-8), along with the corresponding code to process the data and produce the figures, is included in the source data file uploaded with the submission.
  - David Hathcock
  - Dave Thirumalai
  The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
  © 2020, Hathcock et al.
  This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.
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  Planar cell polarity (PCP) – tissue-scale alignment of the direction of asymmetric localization of proteins at the cell-cell interface – is essential for embryonic development and physiological functions. Abnormalities in PCP can result in developmental imperfections, including neural tube closure defects and misaligned hair follicles. Decoding the mechanisms responsible for PCP establishment and maintenance remains a fundamental open question. While the roles of various molecules – broadly classified into ‘global’ and ‘local’ modules – have been well-studied, their necessity and sufficiency in explaining PCP and connecting their perturbations to experimentally observed patterns have not been examined. Here, we develop a minimal model that captures the proposed features of PCP establishment – a global tissue-level gradient and local asymmetric distribution of protein complexes. The proposed model suggests that while polarity can emerge without a gradient, the gradient not only acts as a global cue but also increases the robustness of PCP against stochastic perturbations. We also recapitulated and quantified the experimentally observed features of swirling patterns and domineering non-autonomy, using only three free model parameters - rate of protein binding to membrane, the concentration of PCP proteins, and the gradient steepness. We explain how self-stabilizing asymmetric protein localizations in the presence of tissue-level gradient can lead to robust PCP patterns and reveal minimal design principles for a polarized system.
  Many proteins have been recently shown to undergo a process of phase separation that leads to the formation of biomolecular condensates. Intriguingly, it has been observed that some of these proteins form dense droplets of sizeable dimensions already below the critical concentration, which is the concentration at which phase separation occurs. To understand this phenomenon, which is not readily compatible with classical nucleation theory, we investigated the properties of the droplet size distributions as a function of protein concentration. We found that these distributions can be described by a scale-invariant log-normal function with an average that increases progressively as the concentration approaches the critical concentration from below. The results of this scaling analysis suggest the existence of a universal behaviour independent of the sequences and structures of the proteins undergoing phase separation. While we refrain from proposing a theoretical model here, we suggest that any model of protein phase separation should predict the scaling exponents that we reported here from the fitting of experimental measurements of droplet size distributions. Furthermore, based on these observations, we show that it is possible to use the scale invariance to estimate the critical concentration for protein phase separation.