Dual-Ring SNAREpin Machinery Tuning for Fast Synaptic Vesicle Fusion.

During neurotransmission, neurotransmitters are released less than a millisecond after the arrival of the action potential. To achieve this ultra-fast event, the synaptic vesicle must be pre-docked to the plasma membrane. In this primed state, SNAREpins, the protein-coiled coils whose assembly provides the energy to trigger fusion, are partly zippered and clamped like a hairpin and held open and ready to snap close when the clamp is released. Recently, it was suggested that three types of regulatory factors, synaptophysin, synaptotagmins, and complexins act cooperatively to organize two concentric rings, a central and a peripheral ring, containing up to six SNAREpins each. We used a mechanical model of the SNAREpins with two separate states, half-zippered and fully zippered, and determined the energy landscape according to the number of SNAREpins in each ring. We also performed simulations to estimate the fusion time in each case. The presence of the peripheral SNAREpins generally smoothens the energy landscape and accelerates the fusion time. With the predicted physiological numbers of six central and six peripheral SNAREpins, the fusion time is accelerated at least 100 times by the presence of the peripheral SNAREpins, and fusion occurs in less than 10 µs, which is well within the physiological requirements.

Varying thin filament activation in the framework of the Huxley'57 model.

Muscle contraction is triggered by the activation of the actin sites of the thin filament by calcium ions. It results that the thin filament activation level varies over time. Moreover, this activation process is also used as a regulation mechanism of the developed force. Our objective is to build a model of varying actin site activation level within the classical Huxley'57 two-state framework. This new model is obtained as an enhancement of a previously proposed formulation of the varying thick filament activation within the same framework. We assume that the state of an actin site depends on whether it is activated and whether it forms a cross-bridge with the associated myosin head, which results in four possible states. The transitions between the actin site states are controlled by the global actin sites activation level and the dynamics of these transitions is coupled with the attachment-detachment process. A preliminary calibration of the model with experimental twitch contraction data obtained at varying sarcomere lengths is performed.

Hierarchical modeling of force generation in cardiac muscle.

Performing physiologically relevant simulations of the beating heart in clinical context requires to develop detailed models of the microscale force generation process. These models, however, may reveal difficult to implement in practice due to their high computational costs and complex calibration. We propose a hierarchy of three interconnected muscle contraction models-from the more refined to the more simplified-that are rigorously and systematically related to each other, offering a way to select, for a specific application, the model that yields a good trade-off between physiological fidelity, computational cost and calibration complexity. The three model families are compared to the same set of experimental data to systematically assess what physiological indicators can be reproduced or not and how these indicators constrain the model parameters. Finally, we discuss the applicability of these models for heart simulation.

SNARE machinery is optimized for ultrafast fusion.

SNARE proteins zipper to form complexes (SNAREpins) that power vesicle fusion with target membranes in a variety of biological processes. A single SNAREpin takes about 1 s to fuse two bilayers, yet a handful can ensure release of neurotransmitters from synaptic vesicles much faster: in a 10th of a millisecond. We propose that, similar to the case of muscle myosins, the ultrafast fusion results from cooperative action of many SNAREpins. The coupling originates from mechanical interactions induced by confining scaffolds. Each SNAREpin is known to have enough energy to overcome the fusion barrier of 25-[Formula: see text]; however, the fusion barrier only becomes relevant when the SNAREpins are nearly completely zippered, and from this state, each SNAREpin can deliver only a small fraction of this energy as mechanical work. Therefore, they have to act cooperatively, and we show that at least three of them are needed to ensure fusion in less than a millisecond. However, to reach the prefusion state collectively, starting from the experimentally observed half-zippered metastable state, the SNAREpins have to mechanically synchronize, which takes more time as the number of SNAREpins increases. Incorporating this somewhat counterintuitive idea in a simple coarse-grained model results in the prediction that there should be an optimum number of SNAREpins for submillisecond fusion: three to six over a wide range of parameters. Interestingly, in situ cryoelectron microscope tomography has very recently shown that exactly six SNAREpins participate in the fusion of each synaptic vesicle. This number is in the range predicted by our theory.

Stochastic modeling of chemical-mechanical coupling in striated muscles.

We propose a chemical-mechanical model of myosin heads in sarcomeres, within the classical description of rigid sliding filaments. In our case, myosin heads have two mechanical degrees-of-freedom (dofs)-one of which associated with the so-called power stroke-and two possible chemical states, i.e., bound to an actin site or not. Our major motivations are twofold: (1) to derive a multiscale coupled chemical-mechanical model and (2) to thus account-at the macroscopic scale-for mechanical phenomena that are out of reach for classical muscle models. This model is first written in the form of Langevin stochastic equations, and we are then able to obtain the corresponding Fokker-Planck partial differential equations governing the probability density functions associated with the mechanical dofs and chemical states. This second form is important, as it allows to monitor muscle energetics and also to compare our model with classical ones, such as the Huxley'57 model to which our equations are shown to reduce under two different types of simplifying assumptions. This provides insight and gives a Langevin form for Huxley'57. We then show how we can calibrate our model based on experimental data-taken here for skeletal muscles-and numerical simulations demonstrate the adequacy of the model to represent complex physiological phenomena, in particular the fast isometric transients in which the power stroke is known to have a crucial role, thus circumventing a limitation of many classical models.