Lorenzo Marcucci

Switching of myosin-V motion between the lever-arm swing and Brownian search-and-catch

Motor proteins are force-generating nanomachines that are highly adaptable to their ever-changing biological environments and have a high energy conversion efficiency. Here we constructed an imaging system that uses optical tweezers and a DNA handle to visualize elementary mechanical processes of a nanomachine under load. We apply our system to myosin-V, a well-known motor protein that takes 72 nm hand-over-hand steps composed of a lever-arm swing and a brownian search-and-catch. We find that the lever-arm swing generates a large proportion of the force at low load (<0.5 pN), resulting in 3 k(B)T of work. At high load (1.9 pN), however, the contribution of the brownian search-and-catch increases to dominate, reaching 13 k(B)T of work. We believe the ability to switch between these two force-generation modes facilitates myosin-V function at high efficiency while operating in a dynamic intracellular environment.

From Single Molecule Fluctuations to Muscle Contraction: A Brownian Model of A.F. Huxley's Hypotheses

Muscular force generation in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion. However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations reported in the literature. We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a Brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios.

Including Thermal Fluctuations in Actomyosin Stable States Increases the Predicted Force per Motor and Macroscopic Efficiency in Muscle Modelling.

Muscle contractions are generated by cyclical interactions of myosin heads with actin filaments to form the actomyosin complex. To simulate actomyosin complex stable states, mathematical models usually define an energy landscape with a corresponding number of wells. The jumps between these wells are defined through rate constants. Almost all previous models assign these wells an infinite sharpness by imposing a relatively simple expression for the detailed balance, i.e., the ratio of the rate constants depends exponentially on the sole myosin elastic energy. Physically, this assumption corresponds to neglecting thermal fluctuations in the actomyosin complex stable states. By comparing three mathematical models, we examine the extent to which this hypothesis affects muscle model predictions at the single cross-bridge, single fiber, and organ levels in a ceteris paribus analysis. We show that including fluctuations in stable states allows the lever arm of the myosin to easily and dynamically explore all possible minima in the energy landscape, generating several backward and forward jumps between states during the lifetime of the actomyosin complex, whereas the infinitely sharp minima case is characterized by fewer jumps between states. Moreover, the analysis predicts that thermal fluctuations enable a more efficient contraction mechanism, in which a higher force is sustained by fewer attached cross-bridges.

Titin-mediated thick filament activation, through a mechanosensing mechanism, introduces sarcomere-length dependencies in mathematical models of rat trabecula and whole ventricle

Recent experimental evidence in skeletal muscle demonstrated the existence of a thick-filament mechanosensing mechanism, acting as a second regulatory system for muscle contraction, in addition to calcium-mediated thin filament regulation. These two systems cooperate to generate force, but the extent to which their interaction is relevant in physiologically contracting muscle was not yet assessed experimentally. Therefore, we included both regulatory mechanisms in a mathematical model of rat trabecula and whole ventricle. No additional regulatory mechanisms were considered in our model. Our simulations suggested that mechanosensing regulation is not limited to the initial phases of contraction but, instead, is crucial during physiological contraction. An important consequence of this finding is that titin mediated thick filament activation can account for several sarcomere length dependencies observed in contracting muscle. Under the hypothesis that a similar mechanism is acting on cardiac muscle, and within the limits of a finite element left ventricle model, we predict that these two regulatory mechanisms are crucial for the molecular basis of the Frank-Starling law of the heart.

A 3D diffusional-compartmental model of the calcium dynamics in cytosol, sarcoplasmic reticulum and mitochondria of murine skeletal muscle fibers

Variations of free calcium concentration ([Ca2+]) are powerful intracellular signals, controlling contraction as well as metabolism in muscle cells. To fully understand the role of calcium redistribution upon excitation and contraction in skeletal muscle cells, the local [Ca2+] in different compartments needs to be taken into consideration. Fluorescent probes allow the determination of [Ca2+] in the cytosol where myofibrils are embedded, the lumen of the sarcoplasmic reticulum (SR) and the mitochondrial matrix. Previously, models have been developed describing intracellular calcium handling in skeletal and cardiac muscle cells. However, a comprehensive model describing the kinetics of the changes in free calcium concentration in these three compartments is lacking. We designed a new 3D compartmental model of the half sarcomere with radial symmetry, which accounts for diffusion of Ca2+ into the three compartments and simulates its dynamics at rest and at various rates of stimulation in mice skeletal muscle fibers. This model satisfactorily reproduces both the amplitude and time course of the variations of [Ca2+] in the three compartments in mouse fast fibers. As an illustration of the applicability of the model, we investigated the effects of Calsequestrin (CSQ) ablation. CSQ is the main Ca2+ buffer in the SR, localized in close proximity of its calcium release sites and near to the mitochondria. CSQ knock-out mice muscles still preserve a near-normal contractile behavior, but it is unclear whether this is caused by additional SR calcium buffering or a significant contribution of calcium entry from extracellular space, via stored-operated calcium entry (SOCE). The model enabled quantitative assessment of these two scenarios by comparison to measurements of local calcium in the cytosol, the SR and the mitochondria. In conclusion, the model represents a useful tool to investigate the impact of protein ablation and of pharmacological interventions on intracellular calcium dynamics in mice skeletal muscle.

Attached Molecular Motor in Trapped Single Molecule Assay as a Bi-Dimensional Brownian Multi-Stable System

To elucidate the physical properties of the force generation mechanism in molecular motors, we have obtained an analytical solution of the bidimensional Fokker-Plank equation which describes a common setup used in single molecule experiments. As a first application of this general result, we have shown that the size of the trapping system affects the dwell time of a multistable particle linearly. A quantitative application to skeletal actomyosin complex, using direct observation of force generation dynamics in the literature, shows that the size of the trapping system used was important for increasing the dwell time of the myosin head stable states to an observable time scale.

From Single Molecule Fluctuation to Muscle Contraction: A Brownian Model of A.F. Huxley's Hypotheses

Adaptive force generation of muscle in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion (Huxley, 1957; Huxley & Simmons, 1971). However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations (Kitamura, et al. Nature 1999, BIOPHYSICS, 2005; Iwaki et al. Nat. Chem Biol. 2009). We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a Brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios (Lorenzo & Yanagida, PloS One, 2012).