The Role of Intracellular Interactions in the Collective Polarization of Tissues and its Interplay with Cellular Geometry

Planar cell polarity (PCP), the coherent in-plane polarization of a tissue on multicellular length scales, provides directional information that guides a multitude of developmental processes at cellular and tissue levels. While it is manifest that cells utilize both intracellular and intercellular mechanisms, how the two produce the collective polarization remains an active area of investigation. We study the role of intracellular interactions in the large-scale spatial coherence of cell polarities, and scrutinize the role of intracellular interactions in the emergence of tissue-wide polarization. We demonstrate that nonlocal cytoplasmic interactions are necessary and sufficient for the robust long-range polarization, and are essential to the faithful detection of weak directional signals. In the presence of nonlocal interactions, signatures of geometrical information in tissue polarity become manifest. We investigate the deleterious effects of geometric disorder, and determine conditions on the cytoplasmic interactions that guarantee the stability of polarization. These conditions get progressively more stringent upon increasing the geometric disorder. Another situation where the role of geometrical information might be evident is elongated tissues. Strikingly, our model recapitulates an observed influence of tissue elongation on the orientation of polarity. Eventually, we introduce three classes of mutants: lack of membrane proteins, cytoplasmic proteins, and local geometrical irregularities. We adopt core-PCP as a model pathway, and interpret the model parameters accordingly, through comparing the in silico and in vivo phenotypes. This comparison helps us shed light on the roles of the cytoplasmic proteins in cell-cell communication, and make predictions regarding the cooperation of cytoplasmic and membrane proteins in long-range polarization.Comment: 15 pages Main Text + 8 page Appendi

Charge/mass dynamic structure factors of water and applications to dielectric friction and electroacoustic conversion

We determine time correlation functions and dynamic structure factors of the number and charge density of liquid water from molecular dynamics simulations. Using these correlation functions we consider dielectric friction and electro acoustic coupling effects via linear response theory. From charge-charge correlations, the drag force on a moving point charge is derived and found to be maximal at a velocity of around 300 m/s. Strong deviations in the resulting friction coefficients from approximate theory employing a single Debye relaxation mode are found that are due to non-Debyelike resonances at high frequencies. From charge-mass cross-correlations the ultrasonic vibration potential is derived, which characterizes the conversion of acoustic waves into electric time-varying potentials. Along the dispersion relation for normal sound waves in water, the ultrasonic vibration potential is shown to strongly vary and to increase for larger wavelengths

Persistent fluid flows defined by active matter boundaries

Biological systems achieve precise control over ambient fluids through the self-organization of active protein structures including flagella, cilia, and cytoskeletal networks. In active structures individual proteins consume chemical energy to generate force and motion at molecular length scales. Self-organization of protein components enables the control and modulation of fluid flow fields on micron scales. The physical principles underlying the organization and control of active-matter driven fluid flows are poorly understood. Here, we apply an optically-controlled active-matter system composed of microtubule filaments and light-switchable kinesin motor proteins to analyze the emergence of persistent flow fields in a model active matter system. Using light, we form contractile microtubule networks of varying shape. We analyze the fluid flow fields generated by a wide range of microtubule network geometries and explain the resulting flow fields within a unified theoretical framework. We specifically demonstrate that the geometry of microtubule flux at the boundary of contracting microtubule networks predicts the steady-state fluid flow fields across polygonal network geometries through finite-element simulations. Our work provides a foundation for programming microscopic fluid-flows with controllable active matter and could enable the engineering of versatile and dynamic microfluidic devices

Multifractal Detrended Cross-Correlation Analysis of Sunspot Numbers and River Flow Fluctuations

We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, $(12-24)\leq s\leq 130$ months, is $\lambda = 1.17\pm0.04$ which is almost similar for all underlying rivers at $1\sigma$confidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are $\lambda\in (0.76, 0.85)$ and $\gamma_{\times}\in(0.30, 0.48)$, respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), $\lambda\approx(h_{\rm sun} + h_{\rm river})/2$ is confirmed.Comment: 9 pages, 8 figures and 1 table. V2: Added comments, references, figures and major corrections. Accepted for publication in Physica A: Statistical Mechanics and its Application

Polarons and Mobile Impurities Near a Quantum Phase Transition

This dissertation aims at improving the current understanding of the physics of mobile impurities in highly correlated liquid-like phases of matter. Impurity problems pose challenging and intricate questions in different realms of many-body physics. For instance, the problem of ''solvation'' of charged solutes in polar solvents, has been the subject of longstanding debates among chemical physicists. The significant role of quantum fluctuations of the solvent, as well as the break down of linear response theory, render the ordinary treatments intractable. Inspired by this complicated problem, we first attempt to understand the role of non-specific quantum fluctuations in the solvation process. To this end, we calculate the dynamic structure factor of a model polar liquid, using the classical Molecular Dynamics (MD) simulations. We verify the failure of linear response approximation in the vicinity of a hydrated electron, by comparing the outcomes of MD simulations with the predictions of linear response theory. This nonlinear behavior is associated with the pronounced peaks of the structure factor, which reflect the strong fluctuations of the local modes. A cavity picture is constructed based on heuristic arguments, which suggests that the electron, along with the surrounding polarization cloud, behave like a frozen sphere, for which the linear response theory is broken inside and valid outside. The inverse radius of the spherical region serves as a UV momentum cutoff for the linear response approximation to be applicable.The problem of mobile impurities in polar liquids can be also addressed in the framework of the ''polaron'' problem. Polaron is a quasiparticle that typically acquires an extended state at weak couplings, and crossovers to a self-trapped state at strong couplings. Using the analytical fits to the numerically obtained charge-charge structure factor, a phenomenological approach is proposed within the Leggett's influence functional formalism, which derives the effective Euclidean action from the classical equation of motion. We calculate the effective mass of the polaron in the model polar liquid at zero and finite temperatures. The self-trapping transition of this polaron turns out to be discontinuous in certain regions of the phase diagram.In order to systematically investigate the role of quantum fluctuations on the polaron properties, we adopt a quantum field theory which supports nearly-critical local modes: the quantum Landau-Brazovskii (QLB) model, which exhibits fluctuation-induced first order transition (weak crystallization). In the vicinity of the phase transition, the quantum fluctuations are strongly correlated; one can in principle tune the strength of these fluctuations, by adjusting the parameters close to or away from the transition point. Furthermore, sufficiently close to the transition, the theory accommodates ``soliton'' solutions, signaling the nonlinear response of the system. Therefore, the model seems to be a promising candidate for studying the effects of strong quantum fluctuations and also failure of linear response theory, in the polaron problem. We observe that at zero temperature, and away from the Brazovskii transition where the linear response approximation is valid, the localization transition of the polaron is discontinuous. Upon enhancing fluctuations|of either thermal or quantum nature|the gap of the effective mass closes at distinct second-order critical points. Sufficiently close to the Brazovskii transition where the nonlinear contributions of the field are significantly large, a new state appears in addition to extended and self-trapped polarons: an impurity-induced soliton. We interpret this as the break-down of linear response, reminiscent of what we observe in a polar liquid. Quantum LB model has been proposed to be realizable in ultracold Bose gases in cavities. We thus discuss the experimental feasibility, and propose a setup which is believed to exhibit the aforementioned polaronic and solitonic states. We eventually generalize the polaron formalism to the case of impurities that couple quadratically to a nearly-critical field; hence called the ''quadratic polaron''. The Hertz-Millis field theory and its generalization to the case of magnetic transition in helimagnets, is taken as a toy model. The phase diagram of the bare model contains both second-order and fluctuation-induced first-order quantum phase transitions. We propose a semi-classical scenario in which the impurity and the field couple quadratically. The polaron properties in the vicinity of these transitions are calculated in different dimensions. We observe that the quadratic coupling in three dimensions, even in the absence of the critical modes with finite wavelength, leads to a jump-like localization of the polaron. In lower dimensions, the transition behavior remains qualitatively similar to those in the case of linear coupling, namely the critical modes must have a finite wavelength to localize the particle

Persistent fluid flows defined by active matter boundaries

Biological systems achieve precise control over ambient fluids through the self-organization of active protein structures including flagella, cilia, and cytoskeletal networks. In active structures individual proteins consume chemical energy to generate force and motion at molecular length scales. Self-organization of protein components enables the control and modulation of fluid flow fields on micron scales. The physical principles underlying the organization and control of active-matter driven fluid flows are poorly understood. Here, we apply an optically-controlled active-matter system composed of microtubule filaments and light-switchable kinesin motor proteins to analyze the emergence of persistent flow fields in a model active matter system. Using light, we form contractile microtubule networks of varying shape. We analyze the fluid flow fields generated by a wide range of microtubule network geometries and explain the resulting flow fields within a unified theoretical framework. We specifically demonstrate that the geometry of microtubule flux at the boundary of contracting microtubule networks predicts the steady-state fluid flow fields across polygonal network geometries through finite-element simulations. Our work provides a foundation for programming microscopic fluid-flows with controllable active matter and could enable the engineering of versatile and dynamic microfluidic devices

Multifractal detrended cross-correlation analysis of temporal and spatial seismic data

We use Multi-Fractal Detrended Cross-Correlation Analysis (MF-DXA) method to investigate the cross-correlation of temporal and spatial inter-events seismic data, which expected to be correlated. The mentioned data are the California earthquakes' data which are simultaneously recorded, over an extended period of time. We get the cross-correlation exponent 0.76 ± 0.01. We determine generalized Hurst exponent and singularity spectrum and find that these sequences are joined in various scales and have a multifractality behavior. It means that the correlation in small scales of the sequences (the earthquakes which are close together in space and time) are different from in the large ones. We also find that in spite of the multifractal behavior of temporal and spatial time series, their cross series shows fractal behavior, meaning that the statistical properties of the cross series are invariant under the change of scale

Author Correction: Stem cell-derived synthetic embryos self-assemble by exploiting cadherin codes and cortical tension.

Funder: Wellcome Trust (207415/Z/17/Z), the ERC advanced grant (669198), the NIH R01 (HD100456-01A1) grant, the NIH Pioneer Award (DP1 HD104575-01), Tianqiao and Chrissy Chen Institute for Neuroscience, and Shurl and Kay Curci Foundatio