Mechanical coupling in flashing ratchets

We consider the transport of rigid objects with internal structure in a flashing ratchet potential by investigating the overdamped behavior of a rod-like chain of evenly spaced point particles. In 1D, analytical arguments show that the velocity can reverse direction multiple times in response to changing the size of the chain or the temperature of the heat bath. The physical reason is that the effective potential experienced by the mechanically coupled objects can have a different symmetry than that of individual objects. All analytical predictions are confirmed by Brownian dynamics simulations. These results may provide a route to simple, coarse-grained models of molecular motor transport that incorporate an object's size and rotational degrees of freedom into the mechanism of transport.Comment: 9 pages, 10 figure

Chaperone-assisted translocation of flexible polymers in three dimensions

Polymer translocation through a nanometer-scale pore assisted by chaperones binding to the polymer is a process encountered in vivo for proteins. Studying the relevant models by computer simulations is computationally demanding. Accordingly, previous studies are either for stiff polymers in three dimensions or flexible polymers in two dimensions. Here, we study chaperone-assisted translocation of flexible polymers in three dimensions using Langevin dynamics. We show that differences in binding mechanisms, more specifically, whether a chaperone can bind to a single or multiple sites on the polymer, lead to substantial differences in translocation dynamics in three dimensions. We show that the single-binding mode leads to dynamics that is very much like that in the constant-force driven translocation and accordingly mainly determined by tension propagation on the cis side. We obtain $\beta \approx 1.26$ for the exponent for the scaling of the translocation time with polymer length. This fairly low value can be explained by the additional friction due to binding particles. The multiple-site binding leads to translocation whose dynamics is mainly determined by the trans side. For this process we obtain $\beta \approx 1.36$. This value can be explained by our derivation of $\beta = 4/3$ for constant-bias translocation, where translocated polymer segments form a globule on the trans side. Our results pave the way for understanding and utilizing chaperone-assisted translocation where variations in microscopic details lead to rich variations in the emerging dynamics.Comment: 10 pages, 12 figure

Structure of the substrate-engaged SecA-SecY protein translocation machine.

The Sec61/SecY channel allows the translocation of many proteins across the eukaryotic endoplasmic reticulum membrane or the prokaryotic plasma membrane. In bacteria, most secretory proteins are transported post-translationally through the SecY channel by the SecA ATPase. How a polypeptide is moved through the SecA-SecY complex is poorly understood, as structural information is lacking. Here, we report an electron cryo-microscopy (cryo-EM) structure of a translocating SecA-SecY complex in a lipid environment. The translocating polypeptide chain can be traced through both SecA and SecY. In the captured transition state of ATP hydrolysis, SecAs two-helix finger is close to the polypeptide, while SecAs clamp interacts with the polypeptide in a sequence-independent manner by inducing a short β-strand. Taking into account previous biochemical and biophysical data, our structure is consistent with a model in which the two-helix finger and clamp cooperate during the ATPase cycle to move a polypeptide through the channel

Diffusion of MMPs on the Surface of Collagen Fibrils: The Mobile Cell Surface – Collagen Substratum Interface

Remodeling of the extracellular matrix catalyzed by MMPs is central to morphogenetic phenomena during development and wound healing as well as in numerous pathologic conditions such as fibrosis and cancer. We have previously demonstrated that secreted MMP-2 is tethered to the cell surface and activated by MT1-MMP/TIMP-2-dependent mechanism. The resulting cell-surface collagenolytic complex (MT1-MMP)2/TIMP-2/MMP-2 can initiate (MT1-MMP) and complete (MMP-2) degradation of an underlying collagen fibril. The following question remained: What is the mechanism of substrate recognition involving the two structures of relatively restricted mobility, the cell surface enzymatic complex and a collagen fibril embedded in the ECM? Here we demonstrate that all the components of the complex are capable of processive movement on a surface of the collagen fibril. The mechanism of MT1-MMP movement is a biased diffusion with the bias component dependent on the proteolysis of its substrate, not adenosine triphosphate (ATP) hydrolysis. It is similar to that of the MMP-1 Brownian ratchet we described earlier. In addition, both MMP-2 and MMP-9 as well as their respective complexes with TIMP-1 and -2 are capable of Brownian diffusion on the surface of native collagen fibrils without noticeable dissociation while the dimerization of MMP-9 renders the enzyme immobile. Most instructive is the finding that the inactivation of the enzymatic activity of MT1-MMP has a detectable negative effect on the cell force developed in miniaturized 3D tissue constructs. We propose that the collagenolytic complex (MT1-MMP)2/TIMP-2/MMP-2 represents a Mobile Cell Surface – Collagen Substratum Interface. The biological implications of MT1-MMP acting as a molecular ratchet tethered to the cell surface in complex with MMP-2 suggest a new mechanism for the role of spatially regulated peri-cellular proteolysis in cell-matrix interactions

Structure and dynamics of the integrin LFA-1 I-domain in the inactive state underlie its inside-out/outside-in signaling and allosteric mechanisms.

Lymphocyte function-associated antigen 1 (LFA-1) is an integrin that transmits information in two directions across the plasma membrane of leukocytes, in so-called outside-in and inside-out signaling mechanisms. To investigate the structural basis of these mechanisms, we studied the conformational space of the apo I-domain using replica-averaged metadynamics simulations in combination with nuclear magnetic resonance chemical shifts. We thus obtained a free energy landscape that reveals the existence of three conformational substates of this domain. The three substates include conformations similar to existing crystallographic structures of the low-affinity I-domain, the inactive I-domain with an allosteric antagonist inhibitor bound underneath α helix 7, and an intermediate affinity state of the I-domain. The multiple substates were validated with residual dipolar coupling measurements. These results suggest that the presence of three substates in the apo I-domain enables the precise regulation of the binding process that is essential for the physiological function of LFA-1.This study was supported by the Wellcome Trust and the BBSRC.This is the final version of the article. It first appeared from Cell Press via http://dx.doi.org/10.1016/j.str.2014.12.02

Numerical modeling of F-.Actin bundles interacting with cell membranes

Actin is one of the most aboundant proteins in eukaryotic cells, where it forms a dendridic network (cytoskeleton) beneath the cell membrane providing mechanical stability and performing fundamental tasks in several functions, including cellular motility. The first step in cell locomotion is the protrusion of a leading edge, for which a significant deformation of the membrane is required: this step relies essentially on the forces generated by actin polymerization pushing the plasma membrane outward. Different types of structures can emerge from the plasma membrane, like lamellipodia (quasi-2d actin mesh) and filopodia (parallel actin bundles). The main topic of the research project is the dynamics of bundles of parallel actin filaments growing against barriers, either rigid (a wall) or flexible (a membrane). In the first part of the thesis, the dynamic behavior of bundles of actin filaments growing against a loaded wall is investigated through a generalized version of the standard multi filaments Brownian Ratchet model in which the (de)polymerizing filaments are treated not as rigid rods but as semi-flexible discrete wormlike chains with a realistic value of the persistence length. A Statistical Mechanics framework is built for bundles of actin filaments growing in optical trap apparatus (harmonic external load) and several equilibrium properties are derived from it, like the maximum force that the filaments can exert (stalling force) or the number of filaments in contact with the wall. Besides, Stochastic Dynamic simulations are employed to study the non-equilibrium relaxation of the bundle of filaments growing in the same optical trap apparatus, interpreting the system evolution by a suitable Markovian approach. Thanks to the observed time scale separation between the wall motion and the filament size relaxation, the optical trap set-up allows to extract the full velocity-load curve V(F) -- the velocity at which the obstacle moves when subject to the combined action of the polymerizing filaments and the external load F -- from a single experiment. The main finding is the observation of a systematic evolution of steady non-equilibrium states over three regimes of bundle lengths L. A first threshold length Λ marks the transition between the rigid dynamic regime (L Λ), where the velocity V(F,L) is an increasing function of the bundle length L at fixed load F, the enhancement being the result of an improved level of work sharing among the filaments induced by flexibility. A second critical length corresponds to the beginning of an unstable regime characterized by a high probability to develop escaping filaments which start growing laterally and thus do not participate anymore to the generation of the polymerization force. This phenomenon prevents the bundle from reaching at this critical length the limit behavior corresponding to Perfect Load Sharing. In the second part of the thesis, filaments growing against a flexible, deformable membrane are studied by means of Langevin dynamics simulations; the membrane is discretized into a dynamically triangulated network of tethered beads, while the filaments are described as chains of bonded monomers. Both the monomers in the filaments and the membrane beads, which interact with each other via a purely repulsive potential, are followed in space and time integrating its equations of motion with a second order accurate scheme. The elastic properties of the membrane are studied in detail via several methods, showing an unprecedentent level of agreement among them. The onset of filopodial protrusions is observed for N>1 filaments growing from beneath the membrane and pushing it upwards, with a velocity which is systematically larger for flexible filaments than for rigid ones. Since filaments are wrapped by the membrane in the protrusion, escaping filaments are not predicted nor observed in this case

A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales

In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps. An important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved, partially resolved, or fully resolved while retaining a good level of accuracy. Error estimates in each of these regimes are given for the method. A number of theoretical and numerical checks are furthermore performed to assess its physical fidelity. For a conservative force, the method is found to simulate particles with the correct Boltzmann equilibrium statistics. It is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters. The method is also shown to reproduce a well-known hydrodynamic effect of a Brownian particle in which the velocity autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times. A few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method.Comment: 52 pages, 11 figures, published in journal of computational physic

Field-control, phase-transitions, and life's emergence

Instances of critical-like characteristics in living systems at each organizational level as well as the spontaneous emergence of computation (Langton), indicate the relevance of self-organized criticality (SOC). But extrapolating complex bio-systems to life's origins, brings up a paradox: how could simple organics--lacking the 'soft matter' response properties of today's bio-molecules--have dissipated energy from primordial reactions in a controlled manner for their 'ordering'? Nevertheless, a causal link of life's macroscopic irreversible dynamics to the microscopic reversible laws of statistical mechanics is indicated via the 'functional-takeover' of a soft magnetic scaffold by organics (c.f. Cairns-Smith's 'crystal-scaffold'). A field-controlled structure offers a mechanism for bootstrapping--bottom-up assembly with top-down control: its super-paramagnetic components obey reversible dynamics, but its dissipation of H-field energy for aggregation breaks time-reversal symmetry. The responsive adjustments of the controlled (host) mineral system to environmental changes would bring about mutual coupling between random organic sets supported by it; here the generation of long-range correlations within organic (guest) networks could include SOC-like mechanisms. And, such cooperative adjustments enable the selection of the functional configuration by altering the inorganic network's capacity to assist a spontaneous process. A non-equilibrium dynamics could now drive the kinetically-oriented system towards a series of phase-transitions with appropriate organic replacements 'taking-over' its functions.Comment: 54 pages, pdf fil