PROTEINS: Structure, Function, and Bioinformatics 65:347–361 (2006) Pump-Probe Molecular Dynamics as a Tool for Studying Protein Motion and Long Range Coupling Kim Sharp* and John J. Skinner Department of Biochemistry and Biophysics, University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania 19104 ABSTRACT A new method for analyzing the mation provided by these simulations is enormous. Ana- dynamics of proteins is developed and tested. The lyzing the fluctuations in a useful way and relating them method, pump-probe molecular dynamics, excites to specific experiments is nontrivial. selected atoms or residues with a set of oscillating An important class of methods for studying protein forces, and the transmission of the impulse to other motion is based on frequency analysis. An early example parts of the protein is probed using Fourier trans- is the now classic method of normal mode (harmonic) form of the atomic motions. From this analysis, a analysis,3 which decomposes the possible motions of a coupling profile can be determined which quanti- protein around a minimum conformation into harmonic, fies the degree of interaction between pump and orthogonal modes. An important insight from this analy- probe residues. Various physical properties of the sis is that the lowest frequency modes represent the soft- method such as reciprocity and speed of transmis- est, most thermodynamically accessible ways a protein sion are examined to establish the soundness of could change its conformation (the stiffness being propor- the method. The coupling strength can be used to tional to the square of the frequency). These modes in- address questions such as the degree of interaction volve long range, concerted motions because they are low between different residues at the level of dynamics, frequency, i.e. they have a large effective mass, and hence and identify propagation of influence of one part of involve many atoms.4 A related method is the quasi-har- the protein on another via ‘‘pathways’’ through the monic method that uses coordinate fluctuation covariance protein. The method is illustrated by analysis of matrices obtained from MD to model modes of conforma- coupling between different secondary structure ele- tional change.5–8 This allows for a limited amount of an- ments in the allosteric protein calmodulin, and by harmonicity. The coordinate covariance matrices may analysis of pathways of residue–residue interaction then be analyzed in terms of eigen-vectors and subjected in the PDZ domain protein previously elucidated by to the same frequency analysis as with normal modes. genomics and mutational studies. Proteins 2006;65: Principle component and essential dynamics analysis 347–361. VC 2006 Wiley-Liss, Inc. also use effective modes obtained from coordinate fluctua- tion covariances.9–11 However, extracting, interpreting, Key words: molecular dynamics; protein motion; and using the modes obtained by this kind of frequency residue coupling; correlation analysis; analysis is not easy.12–15 Alternatively, coupling between allostery different atoms, residues, or segments may be analyzed directly using the covariance terms.16 Another approach is to use simplified harmonic models (Elastic network or Tirion type potentials17,18) that can be combined with INTRODUCTION other treatments of large anharmonic motion19 and Proteins are dynamic objects, and motions of a protein sequence/mutation data.20 Fourier transformation (FT) play an important part in their function. Functionally im- and filtering of frequencies can be used to simplify and portant conformational changes in proteins are typically analyze MD trajectories.21,22 Removal of high frequency driven by energies of only a few kT, provided, for example, motions allows clearer analysis of the putatively more by the binding of ligands or other proteins. Techniques interesting, or at least large scale, low frequency motions. such as NMR and hydrogen exchange (HX) provide de- tailed site resolved dynamic information on proteins, re- vealing the stability, extent, and time scale of motion of in- 1 dividual groups through HX protection factors, the gener- Grant sponsor: NIH; Grant number: GM48130; Grant sponsor: alized order parameter (S2), relaxation rates (s), chemical NSF; Grant number: MCB02-35440. shift averaging, and other quantities.2 Molecular dynam- *Correspondence to: Kim Sharp, Department of Biochemistry and Biophysics, University of Pennsylvania School of Medicine, Philadel- ics (MD) simulations also provide a detailed description of phia, PA 19104. E-mail: [email protected] protein motion and play an important role in the interpre- Received 7 February 2006; Revised 18 April 2006; Accepted 28 tation of experimental probes of protein dynamics. With June 2006 the routine ability to do all atom simulations on multi- Published online 24 August 2006 in Wiley InterScience (www. nanosecond time scales and longer, the amount of infor- interscience.wiley.com). DOI: 10.1002/prot.21146 VC 2006 WILEY-LISS, INC. 348 K. SHARP AND J. SKINNER Other methods take this a step further by actively manip- behavior on the ps to ns timescale from changes in NMR- ulating selected frequency components of the velocity derived backbone and side chain order parameters.41 A during MD simulations to probe, or drive conformational similar sequence/mutation analysis of coupling has been changes.23–26 Dynamics quantities such as amide and done on the large class of G-coupled protein receptors methyl NMR order parameters and relaxation rates can (GPCR). Significantly, these networks of interactions are be obtained directly from MD simulations, and are most quite sparse, i.e. relatively few of the residues mediate effectively obtained through the frequency domain via allostery, and not all close residues interact in way rele- fast Fourier transform (FFT).27–30 vant for allostery.42 More generally, recent NMR experi- The view of native protein motion as a superposition of ments show that mutations cause changes in dynamics oscillatory motions (harmonic or anharmonic) of different that propagate along nonhomogenous, long range, and frequencies around a minimum energy conformation has apparently specific paths.41,43,44 provided an attractive model for allosteric (literally ‘‘other Significantly, the specific residue–residue interactions site’’) interactions,7,19,31,32 which gives further impetus to that are mapped out by the experimental and genomic frequency-based methods of analysis. The logic is that al- analyses described above are far from obvious by retro- losteric effects require interaction between spatially sepa- spective analysis of these systems in purely structural rated sites. One such mechanism is via collective motion terms, i.e. in terms of distances between residues. It is of a large spatial array of atoms, which in turn is charac- hard to explain in purely structural terms why particular teristic of ‘‘low frequency modes’’ of protein motion. This residue interactions are important, while others of equal model (dubbed here the low frequency mode model) natu- or lesser distance are not. An extra dimension to the rally invokes analytical methods such as normal mode interactions must arise from the motions these groups analysis, essential dynamics, and quasi-harmonic analy- undergo, and the coupling between them, i.e. from pro- sis. A different but not necessarily mutually exclusive tein dynamics. However, in terms of the specific residue– view of allostery comes from many experiments, the spe- residue interaction model for allostery it is difficult with cific residue–residue interaction model. This model does existing MD techniques to frame and test simple hypoth- not derive from a low frequency mode view of protein eses about coupling such as the following: Does residue X motions, and different ways to analyze MD simulations influence Y, and by how much? Are they more strongly are required if they are to help interpret these types of coupled than an arbitrary pair X-Z. How does influence experiments. propagate as a function of direction and distance? Can The specific residue–residue interaction model for allos- one detect pathways of allosteric action analogous to those tery emerges from many studies on different proteins with found experimentally? Even experiments that probe sim- a variety of methods, of which we mention a few pertinent pler dynamic properties of proteins than allostery can be examples. Some classic examples involving oxygen carry- difficult to explain. An example is the NMR order parame- ing proteins and allosteric enzymes such as glycogen phos- ter, which is a measure of the mobility of a single back- phorylase and phosphofructokinase have been reviewed in bone or side chain group. CaM has anomalous order pa- detail by Perutz.33 For example, in hemoglobin, oxygen rameter data such as inverted temperature dependence binding to heme iron causes a flattening of the heme-por- for some residues (the order parameter increases with T), phyrin plane, which is transmitted to the distal histidine, and an unexpectedly large variation in methionine order then via a leucine and isoleucine on the F-helix, to move- parameters.45,46 These observations imply significant cor- ment of the end of the F-helix, and the CD loop in the co- relation between motions of specific residues, but these operative a1b2 and a2b1 interfaces.34 correlations are not evident in covariance fluctuation mat- Using a statistical mechanical ensemble model of pro- rices or standard frequency analysis.16,47