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Register a new userMotor proteins traffic regulation by supply-demand balance of resources
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In cells and in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and affecting cytoskeletal transport. In this work we provide a theoretical framework to study, analytically and numerically, how motor density profiles and crowding along cytoskeletal filaments depend on the competition of motors for their binding sites. We propose two models in which finite processive motor proteins actively advance along cytoskeletal filaments and are continuously exchanged with the motor pool. We first look at homogeneous reservoirs and then examine the effects of free motor diffusion in the surrounding medium. We consider as a reference situation recent in vitro experimental setups of kinesin-8 motors binding and moving along microtubule filaments in a flow chamber. We investigate how the crowding of linear motor proteins moving on a filament can be regulated by the balance between supply (concentration of motor proteins in the flow chamber) and demand (total number of polymerised tubulin heterodimers). We present analytical results for the density profiles of bound motors, the reservoir depletion, and propose novel phase diagrams that present the formation of jams of motor proteins on the filament as a function of two tuneable experimental parameters: the motor protein concentration and the concentration of tubulins polymerized into cytoskeletal filaments. Extensive numerical simulations corroborate the analytical results for parameters in the experimental range and also address the effects of diffusion of motor proteins in the reservoir.
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We discuss the problem of proteasomal degradation of proteins. Though proteasomes are important for all aspects of the cellular metabolism, some details of the physical mechanism of the process remain unknown. We introduce a stochastic model of the proteasomal degradation of proteins, which accounts for the protein translocation and the topology of the positioning of cleavage centers of a proteasome from first principles. For this model we develop the mathematical description based on a master-equation and techniques for reconstruction of the cleavage specificity inherent to proteins and the proteasomal translocation rates, which are a property of the proteasome specie, from mass spectroscopy data on digestion patterns. With these properties determined, one can quantitatively predict digestion patterns for new experimental set-ups. Additionally we design an experimental set-up for a synthetic polypeptide with a periodic sequence of amino acids, which enables especially reliable determination of translocation rates.
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F1F0 ATP synthase (ATPase) either facilitates the synthesis of ATP in the mitochondrial membranes and bacterial inner membranes in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F0 and F1, which generate the opposing rotation and compete for control of their shared central gamma-shaft. Here we present a self-consistent physical model of the F1 motor as a simplified two-state Brownian ratchet based on the asymmetry of torsional elastic energy of the coiled-coil gamma-shaft. This stochastic model unifies the physical description of linear and rotary motors and explains the stepped unidirectional rotation of the $gamma$-shaft, in agreement with the `binding-change ideas of Boyer. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the `no-load angular velocity is ca. 400~rad/s anticlockwise at 4 mM ATP, in close agreement with experiment. Increasing the pmf torque exerted by F0 can slow, stop and overcome the torque generated by F1, switching from ATP hydrolysis to synthesis at a very low value of `stall torque. We discuss the matters of the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the `useful outcome is measured in the number of H+ pushed against the chemical gradient in the F1 ATP-driven operation.
In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly incorporated into prices. Because revealed market liquidity is extremely low, large orders to buy or sell can only be traded incrementally, over periods of time as long as months. As a result order flow is a highly persistent long-memory process. Maintaining compatibility with market efficiency has profound consequences on price formation, on the dynamics of liquidity, and on the nature of impact. We review a body of theory that makes detailed quantitative predictions about the volume and time dependence of market impact, the bid-ask spread, order book dynamics, and volatility. Comparisons to data yield some encouraging successes. This framework suggests a novel interpretation of financial information, in which agents are at best only weakly informed and all have a similar and extremely noisy impact on prices. Most of the processed information appears to come from supply and demand itself, rather than from external news. The ideas reviewed here are relevant to market microstructure regulation, agent-based models, cost-optimal execution strategies, and understanding market ecologies.
In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins. Experiments have shown that, following non-specific binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay. Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths. The model is also used to analyze experimental observations of motor-induced depolymerization.
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