INSTITUTE OF PHYSICS PUBLISHING PHYSICAL BIOLOGY Phys. Biol. 2 (2005) S137–S147 doi:10.1088/1478-3975/2/4/S08 Protein flexibility using constraints from molecular dynamics simulations Tatyana Mamonova 1 , Brandon Hespenheide 2 , Rachel Straub 1 , M F Thorpe 2 and Maria Kurnikova 1 1 Chemistry Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA 2 Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287, USA E-mail: Kurnikova@cmu.edu Received 4 July 2005 Accepted for publication 22 August 2005 Published 9 November 2005 Online at stacks.iop.org/PhysBio/2/S137 Abstract Proteins are held together in the native state by hydrophobic interactions, hydrogen bonds and interactions with the surrounding water, whose strength as well as spatial and temporal distribution affects protein flexibility and hence function. We study these effects using 10 ns molecular dynamics simulations of pure water and of two proteins, the glutamate receptor ligand binding domain and barnase. We find that most of the noncovalent interactions flicker on and off over typically nanoseconds, and so we can obtain good statistics from the molecular dynamics simulations. Based on this information, a topological network of rigid bonds corresponding to a protein structure with covalent and noncovalent bonds is constructed, with account being taken of the influence of the flickering hydrogen bonds. We define the duty cycle for the noncovalent interactions as the percentage of time a given interaction is present, which we use as an input to investigate flexibility/rigidity patterns, in the algorithm FIRST which constructs and analyses topological networks. 1. Introduction It has been long recognized that molecular flexibility is as critical for protein function as its structure [1–15]. For example, the binding of a ligand, a substrate or another protein may change protein flexibility in addition to changing its conformation [3, 4, 9, 10], with, e.g., possible implications for functionality and allosteric pathways. Another example of the functional importance of protein flexibility is that the dynamic synchronization of positioning of the substrates in an enzyme active site and the subsequent prompt release of products may be critically important for enzymatic catalysis. Understanding, predicting and manipulating protein function (e.g. in drug design) therefore requires not only understanding of protein structure but also protein flexibility and how it relates to function on a molecular basis. Protein dynamics spans a range of time scales and may exhibit a variety of amplitudes of characteristic fluctuations as reflected, e.g., in B-factors of x-ray structures, an ensemble of structures typically produced in nuclear magnetic resonance (NMR) refinement, time resolved NMR [16, 17], Fourier transform infrared spectroscopy (FTIR) [18–20] and other emerging experimental techniques [7, 10, 21, 22]. While in recent years, rapid progress in time-resolved techniques for studying protein dynamics has been made, the spatial and temporal resolution for such measurements remains limited and often insufficient to characterize functionally important dynamic processes. Molecular dynamics (MD) simulations can provide a fairly realistic description of a protein and solvent dynamics and have proved useful for assessing protein flexibility and dynamics on a nanosecond time scale [23]. One obstacle on the route of extending classical MD simulations to mesoscopic (here hundreds of nanoseconds through microsecond to millisecond) time scales is that the basic time step used in the simulation is limited to resolving the fastest motions in the system. These are often vibrations involving covalent bonds, which occur on the pico-second time scale, and hence require femto-second time steps in the MD for sufficient accuracy. Clearly, the slower the dynamics of functionally important transitions, the less important for its characterization are the fast degrees of freedom such as valence bond and angle vibrational motions, rotation of torsion angles and libration of small chemical groups constituting the amino acid side chains. Based on these and similar observations, 1478-3975/05/040137+11$30.00 © 2005 IOP Publishing Ltd Printed in the UK S137