First-Principle Coarse-Graining Framework for Scale-Free Bell-Like Association and Dissociation Rates in Thermal and Active Systems - Janeš, Josip Augustin; Monzel, Cornelia; Schmidt, Daniel; Merkel, Rudolf; Seifert, Udo; Sengupta, Kheya; Smith, Ana-Suncana (Physical Review X, 2022)
Fluctuations of surfaces that harbor reactive molecules interacting across the intervening space strongly influence the reaction kinetics. One such paradigmatic system is the cell membrane, with associated proteins, binding to an interior or an exterior scaffold - for example, the cytoskeleton in the former and the extracellular matrix in the latter case. Given that membrane fluctuations are significant and regulated by the activity of the cell, we hypothesize that these active fluctuations can be tuned to influence ligand-receptor-mediated adhesion. However, a comprehensive model, deriving both binding and unbinding rates from first principles, has not yet been established, and as such, the effect of the membrane activity on the rates remains an open problem. Here, we solve this issue by establishing a systematic coarse graining procedure, providing a cascade of expressions for rates appropriate for the observed timescale, and present a scale-free formulation of rates. In the first step, we introduce a minimal model to recover the so-called Bell-Dembo rates from first principles, where the binding and unbinding rates depend on the instantaneous position of the membrane. We then derive the analytical coarse-grained rates for thermal fluctuations, recovering a result that has previously been successfully used in the literature. Finally, we expand this framework to account for active fluctuations of the membrane. In this step, we develop a mechanical model that convolutes Gauss and Laplace distributed noise. This choice may have universal features and is motivated by our analysis of measurements in two very different cell types, namely, human macrophages and red blood cells. We find that cell activation enables the formation of bonds at much larger separations between the cell and the target. This effect is significantly greater for binding to a surface on the extracellular compared to the intracellular side. We thus show that active fluctuations directly influence protein association and dissociation rates, which may have clear physiological implications that are yet to be explored.
CRIS-Team Scopus Importer:2022-09-16

Statistical Mechanics of an Elastically Pinned Membrane: Equilibrium Dynamics and Power Spectrum - Janeš, Josip Augustin; Schmidt, Daniel; Blackwell, Robert; Seifert, Udo; Smith, Ana-Suncana (Biophysical Journal, 2019)
In biological settings, membranes typically interact locally with other membranes: the extracellular matrix in the exterior or internal cellular structures such as the cytoskeleton, locally pinning the membrane. Characterizing the dynamical properties of such interactions presents a difficult task. Significant progress has been achieved through simulations and experiments, yet analytical progress in modeling pinned membranes has been impeded by the complexity of governing equations. Here, we circumvent these difficulties by calculating analytically the time-dependent Green's function of the operator governing the dynamics of an elastically pinned membrane in a hydrodynamic surrounding and subject to external forces. This enables us to calculate the equilibrium power spectral density for an overdamped membrane pinned by an elastic, permanently attached spring subject to thermal excitations. By considering the effects of the finite experimental resolution on the measured spectra, we show that the elasticity of the pinning can be extracted from the experimentally measured spectrum. Membrane fluctuations can thus be used as a tool to probe mechanical properties of the underlying structures. Such a tool may be particularly relevant in the context of cell mechanics, in which the elasticity of the membrane's attachment to the cytoskeleton could be measured.
CRIS-Team Scopus Importer:2019-08-06

Statistical Mechanics of an Elastically Pinned Membrane: Static Profile and Correlations - Janeš, Josip Augustin; Stumpf, Henning; Schmidt, Daniel; Seifert, Udo; Smith, Ana-Suncana (Biophysical Journal, 2019)
The relation between thermal fluctuations and the mechanical response of a free membrane has been explored in great detail, both theoretically and experimentally. However, understanding this relationship for membranes locally pinned by proteins is significantly more challenging. Given that the coupling of the membrane to the cell cytoskeleton, to the extracellular matrix, and to other internal structures is crucial for the regulation of a number of cellular processes, understanding the role of the pinning is of great interest. In this manuscript, we consider a single protein (elastic spring of a finite rest length) pinning a membrane modeled in the Monge gauge. First, we determine the Green's function for the system and complement this approach by the calculation of the mode-coupling coefficients for the plane wave expansion and the orthonormal fluctuation modes, in turn building a set of tools for numerical and analytic studies of a pinned membrane. Furthermore, we explore static correlations of the free and the pinned membrane, as well as the membrane shape, showing that all three are mutually interdependent and have an identical long-range behavior characterized by the correlation length. Interestingly, the latter displays a nonmonotonic behavior as a function of membrane tension. Importantly, exploiting these relations allows for the experimental determination of the elastic parameters of the pinning. Last but not least, we calculate the interaction potential between two pinning sites and show that even in the absence of the membrane deformation, the pinnings will be subject to an attractive force because of changes in membrane fluctuations.
CRIS-Team Scopus Importer:2019-06-07