Molecular machines

Multiscale Approaches to Protein Modeling, 2010

In proteins and enzymes the necessity that the native state is thermodynamically stable must be appropriately balanced by the capability of the structure to sustain conformational changes and efficiently interconvert among different functionally relevant conformers. This subtle equilibrium reverberates in the complexity of the free-energy landscape which is endowed by a variety of local minima of varying depth and breadth corresponding to the salient structural states of the molecules. In this chapter we will present some concepts and computational algorithms that can be used to characterize the internal dynamics of proteins and relate it to their "functional mechanics." We will apply these concepts to the analysis of a molecular dynamics simulation of adenylate kinase, a protein for which the structural rearrangement is known to be crucial for the accomplishment of its biological function. We will show that, despite the structural heterogeneity of the explored conformational ensemble, the generalized directions accounting for conformational fluctuations within and across the visited conformational substates are robust and can be described by a limited set of collective coordinates. Finally, as a term of comparison, we will show that in the case of HIV-1 Trans-Activator of Transcription (TAT), a naturally unstructured protein, the lack of any hierarchical organization of the free-energy minima results in a poor consistency of the essential dynamical spaces sampled during the dynamical evolution of the system.

Biophysical Chemistry, 2012

We propose a biochemical model providing the kinetic and energetic descriptions of the processivity dynamics of kinesin and dinein molecular motors. Our approach is a modified version of a well known model describing kinesin dynamics and considers the presence of a competitive inhibition reaction by ADP. We first first reconstruct a continuous free-energy landscape of the cycle catalyst process that allows us to calculate the number of steps given by a single molecular motor. Then, we calculate an analytical expression associated to the translational velocity and the stopping time of the molecular motor in terms of time and ATP concentration. An energetic interpretation of motor processivity is discussed in quantitative form by using experimental data. We also predict a time duration of collective processes that agrees with experimental reports.

Motor proteins, sometimes referred to as mechanoenzymes, are a group of proteins that maintain a large part of intracellular motion. Being enzymes, they undergo chemical reactions leading to energy conversion and changes of their conformation. Being mechanodevices, they use the chemical energy to perform mechanical work, leading to the phenomena of motion. Over the past 20 years a series of novel experiments (e.g. single molecule observations) has been performed to gain the deeper knowledge about chemical states of molecular motors as well as their dynamics in the presence or absence of an external force. At the same time, many theoretical models have been proposed, offering various insights into the nano-world dynamics. They can be divided into three main categories: mechanochemical models, ratchet models and molecular dynamics simulations. We demonstrate that by combining those complementary approaches a deeper understanding of the dynamics and chemistry of the motor proteins can be achieved. As a working example, we choose kinesin -a motor protein responsible for directed transport of organelles and vesicles along microtubule tracts.

Protein Conformational Dynamics

Biomolecular machines can achieve physiological functions precisely and efficiently, though they always operate under fluctuations and noises. We review two types of simple machinery that we have recently studied. The machinery can be regarded as molecular motors. They transform chemical free energy from NTP hydrolysis to mechanical work. One type belongs to small monomeric helicases that move directionally along single-stranded nucleic acid, and may further unwind the duplex part for gene replication or repair. The other type belongs to ring-shaped NTPase motors that also move or transport nucleic acid or protein substrate in a directional manner, such as for genome packaging or protein degradation. The central issue in this review is on how the machinery coordinates essential degrees of freedom during the mechanochemical coupling process. Further concerns include how the coordination and control are manifested in experiments, and how they can be captured well in modeling and computational research. We employed atomistic molecular dynamics simulations, coarse-grained analyses, and stochastic modeling techniques to examine the molecular machines at multiple resolutions and timescales. Detailed descriptions on how the protein interacts with its substrate at interface, as well as how multiple protein subunits are coordinated are summarized.

Biophysical Journal, 2006

Force-induced changes in protein conformation are thought to be responsible for certain cellular responses to mechanical force. Changes in conformation subsequently initiate a biochemical response by alterations in, for example, binding affinity to another protein or enzymatic activity. Here, a model of protein extension under external forcing is created inspired by Kramers' theory for reaction rate kinetics in liquids. The protein is assumed to have two distinct conformational states: a relaxed state, C 1 , preferred in the absence of external force, and an extended state, C 2 , favored under force application. In the context of mechanotransduction, the extended state is a conformation from which the protein can initiate signaling. Appearance and persistence of C 2 are assumed to lead to transduction of the mechanical signal into a chemical one. The protein energy landscape is represented by two harmonic wells of stiffness k 1 and k 2 , whose minima correspond to conformations C 1 and C 2 . First passage time t f from C 1 to C 2 is determined from the Fokker-Plank equation employing several different approaches found in the literature. These various approaches exhibit significant differences in behavior as force increases. Although the level of applied force and the energy difference between states largely determine equilibrium, the dominant influence on t f is the height of the transition state. Distortions in the energy landscape due to force can also have a significant influence, however, exhibiting a weaker force dependence than exponential as previously reported, approaching a nearly constant value at a level of force that depends on the ratio k 1 /k 2 . Two model systems are used to demonstrate the utility of this approach: a short a-helix undergoing a transition between two well-defined states and a simple molecular motor.

Journal of Statistical Physics, 2007

Protein motors play a central role in many cellular functions. Due to the small size of these molecular motors, their motion is dominated by high viscous friction and large thermal fluctuations. There are many levels of modeling molecular motors: from simple chemical kinetic models with a small number of discrete states to all atom molecular dynamics simulations. Here we describe

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Current Opinion in Structural Biology, 2012

The past decade has produced an avalanche of experimental data on the structure and dynamics of the ribosome. Groundbreaking studies in structural biology and kinetics have placed important constraints on ribosome structural dynamics. However, a gulf remains between static structures and time dependent data. In particular, x-ray crystallography and cryo-EM studies produce static models of the ribosome in various states, but lack dynamic information. Single molecule studies produce information on the rates of transitions between these states but do not have highresolution spatial information. Computational studies have aided in bridging this gap by providing atomic resolution simulations of structural fluctuations and transitions between configurations.