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Register a new userA Stochastic Markov Model for Coordinated Molecular Motors
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Added by
Donatello Materassi
Publication date
2010
fields
Physics
and research's language is
English
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Many cell functions are accomplished thanks to intracellular transport mechanisms of macromolecules along filaments. Molecular motors such as dynein or kinesin are proteins playing a primary role in these processes. The behavior of such proteins is quite well understood when there is only one of them moving a cargo particle. Indeed, numerous in vitro experiments have been performed to derive accurate models for a single molecular motor. However, in vivo macromolecules are often carried by multiple motors. The main focus of this paper is to provide an analysis of the behavior of more molecular motors interacting together in order to improve the understanding of their actual physiological behavior. Previous studies provide analyses based on results obtained from Monte Carlo simulations. Different from these studies, we derive an equipollent probabilistic model to describe the dynamics of multiple proteins coupled together and provide an exact theoretical analysis. We are capable of obtaining the probability density function of the motor protein configurations, thus enabling a deeper understanding of their behavior.
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The performance of a molecular motor, characterized by its power output and energy efficiency, is investigated in the motor design space spanned by the stepping rate function and the motor-track interaction potential. Analytic results and simulations show that a gating mechanism that restricts forward stepping in a narrow window in configuration space is needed for generating high power at physiologically relevant loads. By deriving general thermodynamics laws for nonequilibrium motors, we find that the maximum torque (force) at stall is less than its theoretical limit for any realistic motor-track interactions due to speed fluctuations. Our study reveals a tradeoff for the motor- track interaction: while a strong interaction generates a high power output for forward steps, it also leads to a higher probability of wasteful spontaneous back steps. Our analysis and simulations show that this tradeoff sets a fundamental limit to the maximum motor efficiency in the presence of spontaneous back steps, i.e., loose-coupling. Balancing this tradeoff leads to an optimal design of the motor-track interaction for achieving a maximum efficiency close to 1 for realistic motors that are not perfectly coupled with the energy source.Comparison with existing data and suggestions for future experiments are discussed.
A simple flashing ratchet model in two dimensions is proposed to simulate the hand-over-hand motion of two head molecular motors like kinesin. Extensive Langevin simulations of the model are performed. Good qualitative agreement with the expected behavior is observed. We discuss different regimes of motion and efficiency depending of model parameters.
Cilia and flagella often exhibit synchronized behavior; this includes phase locking, as seen in {it Chlamydomonas}, and metachronal wave formation in the respiratory cilia of higher organisms. Since the observations by Gray and Rothschild of phase synchrony of nearby swimming spermatozoa, it has been a working hypothesis that synchrony arises from hydrodynamic interactions between beating filaments. Recent work on the dynamics of physically separated pairs of flagella isolated from the multicellular alga {it Volvox} has shown that hydrodynamic coupling alone is sufficient to produce synchrony. However, the situation is more complex in unicellular organisms bearing few flagella. We show that flagella of {it Chlamydomonas} mutants deficient in filamentary connections between basal bodies display markedly different synchronization from the wild type. We perform micromanipulation on configurations of flagella and conclude that a mechanism, internal to the cell, must provide an additional flagellar coupling. In naturally occurring species with 4, 8, or even 16 flagella, we find diverse symmetries of basal body positioning and of the flagellar apparatus that are coincident with specific gaits of flagellar actuation, suggesting that it is a competition between intracellular coupling and hydrodynamic interactions that ultimately determines the precise form of flagellar coordination in unicellular algae.
Molecular motors transduce chemical energy obtained from hydrolizing ATP into mechanical work exerted against an external force. We calculate their efficiency at maximum power output for two simple generic models and show that the qualitative behaviour depends crucially on the position of the transition state. Specifically, we find a transition state near the initial state (sometimes characterized as a power stroke) to be most favorable with respect to both high power output and high efficiency at maximum power. In this regime, driving the motor further out of equilibrium by applying higher chemical potential differences can even, counter-intuitively, increase the efficiency.
The ribosome is one of the largest and most complex macromolecular machines in living cells. It polymerizes a protein in a step-by-step manner as directed by the corresponding nucleotide sequence on the template messenger RNA (mRNA) and this process is referred to as `translation of the genetic message encoded in the sequence of mRNA transcript. In each successful chemo-mechanical cycle during the (protein) elongation stage, the ribosome elongates the protein by a single subunit, called amino acid, and steps forward on the template mRNA by three nucleotides called a codon. Therefore, a ribosome is also regarded as a molecular motor for which the mRNA serves as the track, its step size is that of a codon and two molecules of GTP and one molecule of ATP hydrolyzed in that cycle serve as its fuel. What adds further complexity is the existence of competing pathways leading to distinct cycles, branched pathways in each cycle and futile consumption of fuel that leads neither to elongation of the nascent protein nor forward stepping of the ribosome on its track. We investigate a model formulated in terms of the network of discrete chemo-mechanical states of a ribosome during the elongation stage of translation. The model is analyzed using a combination of stochastic thermodynamic and kinetic analysis based on a graph-theoretic approach. We derive the exact solution of the corresponding master equations. We represent the steady state in terms of the cycles of the underlying network and discuss the energy transduction processes. We identify the various possible modes of operation of a ribosome in terms of its average velocity and mean rate of GTP hydrolysis. We also compute entropy production as functions of the rates of the interstate transitions and the thermodynamic cost for accuracy of the translation process.
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