METHODS IN ENZYMOLOGY Editors-in-Chief ANNA MARIE PYLE Departments of Molecular, Cellular and Developmental Biology and Department of Chemistry Investigator, Howard Hughes Medical Institute Yale University DAVID W CHRISTIANSON Roy and Diana Vagelos Laboratories Department of Chemistry University of Pennsylvania Philadelphia, PA Founding Editors SIDNEY P COLOWICK and NATHAN O KAPLAN Academic Press is an imprint of Elsevier 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States 525 B Street, Suite 1800, San Diego, CA 92101–4495, United States The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 125 London Wall, London, EC2Y 5AS, United Kingdom First edition 2016 Copyright © 2016 Elsevier Inc All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein) Notices Knowledge and best practice in this field are constantly changing As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein ISBN: 978-0-12-811107-9 ISSN: 0076-6879 For information on all Academic Press publications visit our website at https://www.elsevier.com/ Publisher: Zoe Kruze Acquisition Editor: Zoe Kruze Editorial Project Manager: Helene Kabes Production Project Manager: Magesh Kumar Mahalingam Cover Designer: Greg Harris Typeset by SPi Global, India CONTRIBUTORS P.K Agarwal Computational Biology Institute, Oak Ridge National Laboratory, Oak Ridge; University of Tennessee, Knoxville, TN, United States N.A Baker Pacific Northwest National Laboratory, Richland, DC; Brown University, Providence, RI, United States J.L Baylon Center for Biophysics and Quantitative Biology; University of Illinois at UrbanaChampaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States D Bellinger Julius-Maximilians-Universit€at W€ urzburg, Institut f€ ur Physikalische und Theoretische Chemie, W€ urzburg, Germany R.B Best Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD, United States J Blumberger University College London, London, United Kingdom S Bowerman Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, Chicago, IL, United States G.R Bowman Washington University School of Medicine; Center for Biological Systems Engineering, Washington University School of Medicine, St Louis, MO, United States X Che College of Chemistry and Molecular Engineering, Beijing National Laboratory for Molecular Sciences; Biodynamic Optical Imaging Center (BIOPIC), Peking University, Beijing, PR China C Chennubhotla University of Pittsburgh, Pittsburgh, PA, United States P.P.-H Cheung The Hong Kong University of Science and Technology, Kowloon, Hong Kong J.-W Chu Institute of Bioinformatics and Systems Biology; Department of Biological Science and Technology; Institute of Molecular Medicine and Bioengineering, National Chiao Tung University, Hsinchu, Taiwan, ROC xi xii Contributors T.H Click Institute of Bioinformatics and Systems Biology, National Chiao Tung University, Hsinchu, Taiwan, ROC D De Sancho CIC NanoGUNE, Donostia-San Sebastia´n; Ikerbasque, Basque Foundation for Science, Bilbao, Spain N Doucet INRS—Institut Armand-Frappier, Universite du Quebec, Laval, QC, Canada M.W Dzierlenga University of Arizona, Tucson, AZ, United States B Engels Julius-Maximilians-Universit€at W€ urzburg, Institut f€ ur Physikalische und Theoretische Chemie, W€ urzburg, Germany Y.Q Gao College of Chemistry and Molecular Engineering, Beijing National Laboratory for Molecular Sciences; Biodynamic Optical Imaging Center (BIOPIC), Peking University, Beijing, PR China B Ginovska Pacific Northwest National Laboratory, Richland, WA, United States M.R Gunner City College of New York in the City University of New York, New York, United States X He School of Chemistry and Molecular Engineering, East China Normal University; NYUECNU Center for Computational Chemistry at NYU Shanghai, Shanghai, China X Huang The Hong Kong University of Science and Technology; State Key Laboratory of Molecular Neuroscience, Center for System Biology and Human Health, School of Science and Institute for Advance Study, The Hong Kong University of Science and Technology, Kowloon, Hong Kong P Imhof Institute of Theoretical Physics, Free University Berlin, Berlin, Germany H Jiang The Hong Kong University of Science and Technology, Kowloon, Hong Kong T Jiang Center for Biophysics and Quantitative Biology; University of Illinois at UrbanaChampaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States P Mahinthichaichan University of Illinois at Urbana-Champaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States Contributors xiii M.A Martı´ FCEN, UBA, Buenos Aires, Argentina C.G Mayne University of Illinois at Urbana-Champaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States M.P Muller Center for Biophysics and Quantitative Biology; University of Illinois at UrbanaChampaign; Beckman Institute for Advanced Science and Technology; College of Medicine, University of Illinois at Urbana-Champaign, Urbana, IL, United States C Narayanan INRS—Institut Armand-Frappier, Universite du Quebec, Laval, QC, Canada F Pardo-Avila The Hong Kong University of Science and Technology, Kowloon, Hong Kong J.M Parks Oak Ridge National Laboratory, Oak Ridge; University of Tennessee, Knoxville, TN, United States N Raj Institute of Bioinformatics and Systems Biology, National Chiao Tung University, Hsinchu, Taiwan, ROC A Ramanathan Oak Ridge National Laboratory, Oak Ridge, TN, United States C.L Ramı´rez FCEN, UBA, Buenos Aires, Argentina S Raugei Pacific Northwest National Laboratory, Richland, WA, United States A.E Roitberg University of Florida, Gainesville, FL, United States S Sacquin-Mora Laboratoire de Biochimie Theorique, CNRS UPR9080, Institut de Biologie PhysicoChimique, Paris, France S.D Schwartz University of Arizona, Tucson, AZ, United States W.J Shaw Pacific Northwest National Laboratory, Richland, WA, United States M Shekhar Center for Biophysics and Quantitative Biology; University of Illinois at UrbanaChampaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States F.K Sheong The Hong Kong University of Science and Technology, Kowloon, Hong Kong xiv Contributors E Shinn Center for Biophysics and Quantitative Biology; University of Illinois at UrbanaChampaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States J.C Smith Oak Ridge National Laboratory, Oak Ridge; University of Tennessee, Knoxville, TN, United States E Tajkhorshid Center for Biophysics and Quantitative Biology; University of Illinois at UrbanaChampaign; Beckman Institute for Advanced Science and Technology; College of Medicine, University of Illinois at Urbana-Champaign, Urbana, IL, United States S Thangapandian University of Illinois at Urbana-Champaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States N Trebesch Center for Biophysics and Quantitative Biology; University of Illinois at UrbanaChampaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States M.J Varga University of Arizona, Tucson, AZ, United States J.V Vermaas Center for Biophysics and Quantitative Biology; University of Illinois at UrbanaChampaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States P.-H Wang RIKEN Theoretical Molecular Science Laboratory, Wako-shi, Saitama, Japan X Wang Center for Optics & Optoelectronics Research, College of Science, Zhejiang University of Technology, Hangzhou, Zhejiang; School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, China Y Wang Center for Biophysics and Quantitative Biology; University of Illinois at UrbanaChampaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States D Weber Julius-Maximilians-Universit€at W€ urzburg, Institut f€ ur Physikalische und Theoretische Chemie, W€ urzburg, Germany P.-C Wen University of Illinois at Urbana-Champaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States J Wereszczynski Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, Chicago, IL, United States Contributors xv L Yang College of Chemistry and Molecular Engineering, Beijing National Laboratory for Molecular Sciences; Biodynamic Optical Imaging Center (BIOPIC), Peking University, Beijing, PR China J Zhang College of Chemistry and Molecular Engineering, Beijing National Laboratory for Molecular Sciences; Biodynamic Optical Imaging Center (BIOPIC), Peking University, Beijing, PR China J.Z.H Zhang School of Chemistry and Molecular Engineering, East China Normal University; NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai, China; New York University, New York, NY, United States L Zhang The Hong Kong University of Science and Technology, Kowloon, Hong Kong Z Zhao Center for Biophysics and Quantitative Biology; University of Illinois at UrbanaChampaign; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States M.I Zimmerman Washington University School of Medicine, St Louis, MO, United States PREFACE The computational study of enzyme structure and function has reached exciting and unprecedented levels This state of affairs is due to a combination of powerful new computational methods, a critical evolution of ideas and insights, the ever-increasing power of computers, and important new experimental results for validation In these two volumes of Methods in Enzymology, many of the leading computational researchers present their latest work, representing a range of state-of-the-art topics in computational enzymology Generally speaking, the two volumes are divided into two general areas, the first being mostly devoted to the calculation of the free energy barriers and reaction pathways for enzymes—often using powerful quantum mechanics/molecular mechanics (QM/MM) methods—while the second volume contains a broader range of topics, including the role of enzyme dynamics and allostery, electrostatics, ligand binding, and several specific case studies The topic of computational enzymology—and the field of computational biophysics and biochemistry in general—has grown enormously since its inception in the early 1970s, with some of these original work being recognized by the 2013 Nobel Prize in Chemistry It is tempting to conclude that the field is now “mature” and all that remains is for researchers in it to carry out increasingly detailed and accurate set of applications of the powerful computational methods presented herein However, nothing could be further from the truth Real enzymes exist and function in highly complex, multiscale biological environments Often several enzymes function cooperatively, and they can be influenced by, or respond to, their local environment, whether be it a lipid membrane or the crowded cellular interior In the venerable theories of activated dynamics for condensed-phase chemical kinetics, such as transition state theory, it is tacitly assumed that the chemical reaction dictates the slowest dynamical timescale of the system, thus corresponding to the highest free energy barrier This basic assumption also allows one to apply these simpler theories to calculate quantities such as the free energy profile, ie, free energy barrier, for a reaction along a chemical pathway in an enzyme (the so-called “potential of mean force”) Yet, in complex biological systems, there are a wide range of timescales associated with numerous processes, some of which may be intrinsically coupled to the reactive process of the enzyme In that light a key question then arises for the xvii xviii Preface future Can we better understand enzyme kinetics in the larger biological context of the living cell through computation? This challenge awaits us There is also the important fact that real biological systems are not in a state of equilibrium Indeed, they can be rather far from it Much of the standard condensed-phase kinetic theory developed in the last century—and applied in present day computational enzymology—relies on the key notion of the famous fluctuation–dissipation theorem, ie, that the behavior of systems perturbed out of equilibrium can be understood from studies of ones that are actually in equilibrium This so-called “linear response” assumption leads us to powerful mathematical formulas for observables such as kinetic rate constants, as well as the algorithms one uses to compute them, which are based on equilibrium molecular dynamics simulation However, much work remains to be done to develop theories and computational algorithms for enzymes functioning in a nonequilibrium biological context, albeit some important work in that direction, motivated by experiments, has already been initiated The great degree of progress to date on the topic of computational enzymology in reflected in these two volumes of Methods in Enzymology Moreover, this field of research continues to evolve at an increasingly rapid pace The scope of the enzyme systems presently under study, and the elaboration of their complex behaviors, is remarkable As an example I can point to some of the research completed by talented young theorists as they passed through my own research group (see McCullagh, M., Saunders, M G., & Voth, G A (2014) Unraveling the mystery of ATP hydrolysis in actin filaments Journal of the American Chemical Society, 136, 13053–13058) In this work, QM/MM, molecular dynamics, advanced free energy sampling, and insights from coarse-grained modeling were all combined to explain the origins of the >104 acceleration of ATP hydrolysis in actin filaments (F-actin) over the free monomeric form (G-actin) This ATP hydrolysis by F-actin, which has been a mystery for years, is critical to the functioning of the actin-based eukaryotic cellular cytoskeleton and now computation has solved it Nevertheless, in light of the great remaining challenges described in the earlier paragraphs, it is abundantly clear that much remains to be done to further advance computational enzymology, in some cases even at a qualitative level of basic understanding It will certainly be both important and fascinating to survey future volume(s) of Methods in Enzymology devoted to this topic—perhaps 10 or even 20 years from now—and to celebrate what I am sure will the outcomes from an exciting and continual evolution of this important field of research G.A VOTH The University of Chicago CHAPTER ONE Continuum Electrostatics Approaches to Calculating pKas and Ems in Proteins M.R Gunner*,1, N.A Baker†,{ *City College of New York in the City University of New York, New York, United States † Pacific Northwest National Laboratory, Richland, DC, United States { Brown University, Providence, RI, United States Corresponding author: e-mail address: mgunner@ccny.cuny.edu Contents Introduction Biomolecular Structure and Flexibility Solvent Models or: How I Learned to Stop Worrying and Love the Dielectric Coefficient Modeling Ion–Solute Interactions Force Field and Parameter Choices Conclusions Acknowledgments References 11 12 14 14 15 Abstract Proteins change their charge state through protonation and redox reactions as well as through binding charged ligands The free energy of these reactions is dominated by solvation and electrostatic energies and modulated by protein conformational relaxation in response to the ionization state changes Although computational methods for calculating these interactions can provide very powerful tools for predicting protein charge states, they include several critical approximations of which users should be aware This chapter discusses the strengths, weaknesses, and approximations of popular computational methods for predicting charge states and understanding the underlying electrostatic interactions The goal of this chapter is to inform users about applications and potential caveats of these methods as well as outline directions for future theoretical and computational research Methods in Enzymology, Volume 578 ISSN 0076-6879 http://dx.doi.org/10.1016/bs.mie.2016.05.052 # 2016 Elsevier Inc All rights reserved 475 Author Index Ward, A., 393–394, 402–403 Warshel, A., 3–4, 7, 9, 27, 46, 60, 65–67, 110–111, 125, 249–250, 274 Wassenaar, T.A., 379, 382–383 Watanabe, A., 394–396 Waterhouse, A., 403 Waterman, M.R., 147 Wattal, C., 221–222 Webb, B., 380, 403 Webb, B.A., Webb, H., Webb, L.J., 46–48, 65, 67t Weber, D., 146–164 Weber, J., 374–375 Weber, J.K., 215 Wei, G.W., 12–13 Weikl, T.R., 345–346, 353 Weinan, E., 353–354 Weinstein, H., 394–396, 443 Weinzierl, R.O., 361 Weiss, C.J., 74–75, 91–94 Weiss, D.R., 345–348, 353–354, 359–361 Weiss, K.L., 286 Weiss, M., 412 Weiss, R.M., 249–250 Weiss, S., 344–345 Weiss, Y., 350 Weissig, H., 4, 380 Weixlbaumer, A., 361 Welford, R.W., 300–301 Wen, P.-C., 374–412 Weng, Y., 393–394 Wereszczynski, J., 430–443 Wertheim, H.F.L., 221–222 Wesenberg, G., 191, 193–194 Westbrook, J., 4, 380 Westover, K.D., 357–361 White, S.H., 394–395, 412 White, S.W., 392–393 Whittleston, C.S., 252 Wiame, J.M., 192–193 Wick, C.D., 35–36 Wickstrom, L., 435 Wickstrong, C., 75 Wiedenheft, B., 377 Wiegel, J., 2–3 Wieninger, S.A., 245–246 Wiesler, S., 361 Wiest, O., 128 Wiggins, P., 412 Wikstr€ om, M., 328 Wilke-Mounts, S., 374–375 Willett, P., 221–222 Williams, R.J., 2–3 Willkomm, S., 354 Wilmanns, M., 191 Wilmot, C.M., 300–301 Wilson, A.D., 94–95 Wilson, D., 400 Wilson, M.R., 431 Wilson, R.C., 354 Winger, M., 387 Winter, R., 301 Winther, A.-M.L., 395–396 Wise, M., Wisedchaisri, G., 380 Witham, S., 7, 13–14 Wojcik, M., 191 Wolf, M.G., 384–386, 385f Wolf, R.M., 60, 388–389, 435 Wollmer, A., 404–405 Wong, G.C., Woodcock, H.L., 128, 250 Woods, R.J., 51 Woodward, C.E., 387 Woolf, T.B., 333, 396, 401 Word, J.M., 4, 10–14 Wrabl, J.O., 430–431 Wraight, C.A., 75, 79, 379, 392 Wright, E.M., 394–396 Wright, P.E., 274–277, 289–291 Wu, C., 12–13, 60, 158–159 Wu, E., 382–386 Wu, H., 353, 409–410 Wu, J.X., 185 Wu, S., 139–140 Wu, X.W., 170–171 Wu, Z., 383 Wunderlich, B., 328 W€ uthrich, K., Wyckoff, H., 344–345 Wyman, J., 430 X Xia, C., 374–375 Xia, F., 35–36, 329–330 476 Xia, K., 13–14 Xia, T., 344–345 Xia, Z., 12–13, 158–159 Xiang, Y., 46, 274 Xiao, R., 360–361 Xie, D.X., 8–9 Xie, L., 79, 403–404 Xiong, G., 60 Xiong, H., 127–128 Xiong, Y., 74–75, 77–78, 96 Xu, D., 139–140, 267, 380–381 Xu, H., 213–214, 377 Xu, L., 46, 360–361 Xu, Q., 115 Xu, Y.C., 191–192 Y Yan, L., 79 Yang, C., 283–284 Yang, H., 75–76 Yang, H.Y., 191–192 Yang, J., 374–375 Yang, J.Y., 89–91 Yang, L., 170–207, 437–438 Yang, L.J., 170–172, 177–178, 192–193, 201, 205 Yang, L.W., 228–229, 237–238, 245 Yang, M., 390–392 Yang, M.J., 344–345 Yang, S., 4, 408 Yang, W., 25, 47–48, 126, 250 Yang, Y.I., 189–191, 206 Yang, Z., 139–140 Yao, Y., 345–346, 350 Ye, C.C., 360–361 Yee, N., 116–118 Yen, J.Y., 433–434 Yeo, J., 203 Yernool, D., 402–403 Yesselman, J.D., 389–390 Yin, D., 388–389 Yin, Y., 394–395 Yongye, A.B., 388–389 Yoon, Y., 127–128 York, D.M., 2–3, 7, 249–250 Yoshikawa, S., 75 Young, C., 379 Yu, B., 389–390 Author Index Yu, H., 328 Yu, J., 345–348, 361–363, 393–394, 402–403 Yuan, Z., 245 Yue, A., 345–346 Yue, W., 111–112 Z Zaccai, G., 238 Zacharias, M., 229 Zaidi, A.K.M., 221–222 Zaiss, M., 252 Zalkin, H., 191 Zamponi, M., 113–115 Zaraiskaya, T., 397 Zardecki, C., 228–229 Zasetsky, A.Y., 8–9 Zeitels, L.R., 354 Zeng, J., 51 Zhai, Y.L., 344–345 Zhang, C., 139–140, 345–348, 361 Zhang, D.W., 48–49, 51 Zhang, H.-X., 393 Zhang, I.L., 361 Zhang, J., 3, 12–13, 158–159, 170–207, 380–381, 392, 430 Zhang, J.Z.H., 46–69, 329–330 Zhang, L., 344–364 Zhang, L.Y., Zhang, Q.G., 51 Zhang, W., 60 Zhang, Y., 25 Zhang, Y.-W., 395–396, 403–404 Zhang, Y.X., 344–345 Zhang, Z., 7, 10, 13–14, 329 Zhao, B., 147 Zhao, J., 245 Zhao, W., 392–393 Zhao, Y., 348–351, 355, 394–395 Zhao, Z., 374–412 Zhen, X., 393 Zheng, H., 380 Zheng, L., 126, 250, 328 Zheng, W., 118–119 Zhong, S., 388–389, 392 Zhou, G., 215 Zhou, H., Zhou, H.X., 12–13 Zhou, J., 118 477 Author Index Zhou, X., 345–348, 361 Zhou, Y., 360–361 Zhu, G.Y., 360–361 Zhu, J., 344–345 Zhu, L., 345–346, 354–355 Zhu, T., 48–49, 54 Zhu, W., 375 Zhu, W.L., 191–192 Zhu, X., 13–14, 387–389 Zhuang, W., 345–346 Zhuo, R., 393–394 Zimmerman, M.I., 213–222 Zomot, E., 394–396 Zou, X., 393 Zou, X.W., 110 Zubarev, D.Y., 252 Zuo, L., 389–390 Zwanzig, R., 302–304 Zwanzig, R.W., 126, 401 Zwier, M.C., 213–214 SUBJECT INDEX Note: Page numbers followed by “f ” indicate figures, “t” indicate tables, and “s” indicate schemes A ab initio molecular dynamics (AIMD) simulations, 54 Active site charge transfer chemical structures, IDD743, 65, 66f EE–GMFCC method, 67–69, 67t LIG, 68–69 MD simulations, 65–67 electronic polarization on electrostatics chemical structures, IDD743, 58–59, 59f distribution, projected coordinates, 62–63, 64f electric fields, 62–63, 62f electrostatic potentials, 60, 61f K77M and V47D, 62–63 MD simulations, 60 Adaptive sampling schemes, 215 Alchembed method, 384–386, 385f Alchemical perturbation, 401–402 Allosteric mechanism Dijkstra’s algorithm, 433–434 domino effect, 433–434 functions, 430 graph theory approach, 433–434 induced fit mechanism, 430 mutations, 431 residue-pair correlations, 431 suboptimal pathways, 433–434 thrombin Exosite I, 440–442 Exosite II, 440–442 hirugen binding, 440–442 in isolated, 440, 441f suboptimal pathways, 440–442, 441f Alternating access mechanism cation coupled symporter, 375–376, 376f global conformational changes, 376–377 inward-facing (IF) state, 376 outward-facing (OF) state, 376 Anharmonic conformational analysis identification, conformational substates, 287f, 288–289 protein energy landscape, 286, 286f QAA extraction of, 282f, 288 property, 286–287 protein energy landscape, 286–287, 286f apo–RAT CG beads, 334t, 335–336 total coupling strength, 336–337, 338f Aqueous systems and global optimization DA–MCM, 148 hydrogen bonding, 147 Metropolis MCM approach, 148 nonburied water molecules, 149, 149f random water selection and movement, 150 solvation shell, 148 targets, 149 WM–MCM, 149 Arg-306 conformational change, 198–199, 199f free energy profiles, 198–199, 200f guanidinium carbon, 198–199 1-ns relaxation, 196 PMF, 196–198, 199–200f umbrella sampling, 198 Atomic and coarse-grained representations comparitive study, 379 vibrational modes, 378–379 Atom indices, 220 Automatic state partitioning for multibody (APM) systems escape probability, 351 k-centers algorithm, 350–351, 352–353f MSM, 350–352, 352–353f protocol, 351 B Bacterial Hg resistance, 109 Bacterial metalloregulator MerR, 110, 110f Bennett–Chandler theory, 34 479 480 Berezhkovskii–Hummer–Szabo (BHS) formalism, 311–312 Biased simulation less structured exploration methods, 400 REUS, 400 SMD, 398–399 umbrella sampling, 400 Bias-exchange umbrella sampling (BEUS), 409–412 BPTI–RAT BPTI-bound serine protease, 334–335, 335f CG beads, 334t, 335–336 total coupling strength, 336–337, 338f Brownian dynamics (BD) simulations, 232 See also Coarse-grain BD simulations C Carbamoyl phosphate synthetase (CPS) carbamate transport, 194 Escherichia coli, 192–193 x-ray crystal structure, 193–194, 193f Carbon monoxide dehydrogenase/acetylcoenzyme A synthase (CODH/ ACS) computed (comp.) and experimental (exp.) diffusion rates, 316–317, 318–319f, 319t dependence, ligand concentration, 317–320, 320f final transition, 316, 317f microstates and ligand diffusion paths, 314–316, 315f MSM validation, 320f, 321 Centroid molecular dynamics (CMD) LDH, 31–32 nuclear tunneling, 31–32 statistical method, 27–28 YADH, 31–32 CGenFF program, 390, 392 Chandler rate algorithm, 36 CHARMM software enzyme fluctuogram, 333 force field parameters, 390–392, 391f membrane transporters, 383–384 Cis/trans isomerization, Cyclophilin A, 291–294, 293f Coarse-grain BD simulations Subject Index BD, 232 carbonic anhydrase, 232–234, 233f enzymes, 229, 230–231t pseudo-atom, 229 rigidity profile, 232–234 Community analysis, 442–443, 442f Comprehensive transition networks conjugate peak refinement method, 258 Dijkstra’s algorithm, 262 edges, 261–262 enzymatic hydrolysis reaction carboxy peptidase (CPA), 262–263 conjugate peak refinement calculations, 263–264 Glu270 attack, 268 peptide hydrolysis, 263–264, 266–267f promoted-water mechanism, 267 protonation sites, 262–263, 264f QM/MM optimization, 262–263 geometry optimization, network nodes, 260 metal ion/water positions, 258 node state assignment, 260–261 protonation sampling, 259 rejection, nonmeaningful structures, 260 sampling bond lengths, 258 side chain rotation, 259, 259f Conformational Analysis and Search Tool (CAST), 154, 158–159 Conformational substates challenges, 277–278, 295 cis/trans isomerization, Cyclophilin A, 291–294, 293f elastic anisotropic network models, 285 enzyme landscape, 275–276, 276f extraction of, 280–283, 282f hiddeninvisible population, 278–279 higher-energy substates, 278–279, 278f HSQC, 279–280 hydride transfer, DHFR, 289–291, 290f identification, 287f, 288–289 NMA, 283 QHA, 284–285 rcCPMG, 279–280 sampling, 275 TANCA, 283–284 thermodynamic sampling, 276–277 TS, 278–279 481 Subject Index two-site conformational exchange, 280, 281f Conformation sampling bias potential methods, 171–172 characteristic motions, 170–171 complexity and roughness, 171–172 generalized ensemble methods, 171–172 ITS method ALA-PRO peptide, 175, 177t generalized non-Boltzmann distribution, 172 MD simulations, 175 SITS, 177–179 MTS method characteristics, 173–175 DOF, 173–175 pseudo-equilibrium, 173 vs SGMD, 170–171 SGMD, 170–171 slow and fast DOFs, 170–171 Continuum electrostatics biomolecular structure and flexibility charge state calculations, conformational sampling, DOF, interaction energies of O(m2), 6–7 MC simulations, 5–6 MD simulations, protein microstate, force field and parameter choices continuous-pH MD, 13–14 Garcia–Moreno lab, 13–14 ion-accessible regions, 12–13 RMSD, 13–14 standard molecular simulation force fields, 12–13 titration state prediction methods, 13 ionization states, 2–3 modeling ion–solute interactions, 11–12 nonideal titration curves, pKa values, polar and polarizable groups, protein function, solvent models dielectric coefficient value (εsolute), 9–10, 9f heuristics, high-dielectric treatment, 10–11 interior dielectric constant, 11 Lennard–Jones-like term, linear response, 8–9 local response, 8–9 MCCE, 11 Poisson equation, 8–9 supercharged proteins, titration curves, Correlated motion See Residue–residue correlations Covariance analysis, 86–88, 88f Cyclic di-nucleotides (CDNs) chemical structure, 185, 186f phase angle distribution and χ angle distribution, 185–187, 187f STING agonists, 185 structural deviation, 185–187, 188f thermodynamic properties, 185–187, 188t D Degrees of freedom (DOF) MTS method, 173–175 slow and fast, 170–171 Density functional theory (DFT) electric fields inside enzymes, 47–48 H2 oxidation, 92–94, 93f hydration free energies, 106–107 quantum chemistry, 105 Differential relaxation algorithm ratio (DRAr), 133–137, 133s Diffusion rate constants, small ligands applications, 301–302 assignment of states, 308–309 binding and, 312–313 classical master equations and Markovian dynamics, 302–304 cluster analysis, 306–307 computed (comp.) and experimental (exp.) diffusion rates, 316–317, 318–319f, 319t dependence, ligand concentration, 317–320, 320f DFT calculations, 323 diffusion–reaction model, 304, 305f energetic properties, 301 enhanced sampling, transitions, 309–311 final transition, 316, 317f 482 Diffusion rate constants, small ligands (Continued ) functions, 300 ligand concentration, 309 ligand locations, 306 limitation, 300 Markov states, 302 MD simulations, 301, 304–306 microstates and ligand diffusion paths, 314–316, 315f MSM validation, 320f, 321 mutation prediction, 313–314 phenomenological kinetic model, 311 rate matrix construction, 307–308 reactive flux, 311–312 sensitivity analysis, myoglobin, 321, 322f x-ray crystallography, 300–301 Dihedral angle MCM (DA–MCM), 148 Dihydrofolate reductase (DHFR), 289–291, 290f Dijkstra’s algorithm allosteric mechanism, 433–434 comprehensive transition networks, 262 graph construction and calculations, 436 Dudko–Hummer–Szabo (DHS) model, 310–311 Dynamic cross-correlation, 431–432 E EcoRV enzyme phosphodiester hydrolysis reaction, 253–255, 254–255f reactant and product state, 253, 253f Elastic anisotropic network models, 285 Elastic network model (ENM) Cα and Cα–SC model, 334 CG beads, 330, 333 fluctuation matching, 330 harmonic bonds, 329–330 Electric fields inside enzymes active site charge transfer, 65–69, 66f, 67t electronic polarization on electrostatics, 58–64, 59f, 61–62f, 64–65f catalytic rate, 46 DFT, 47–48 EE–GMFCC method, 51–54, 52f, 55f Subject Index frequency shift and, 46–47 Hartree–Fock (HF) method, 47–48 MFCC method, 48–49, 49–50f quantum calculation AIMD simulations, 54 EE–GMFCC, 56–57, 58f fragment, 49–51, 50f globular proteins, 56–57 molecular electrostatic potential (MEP), 56–57, 57f protein–ligand interaction, 48–49, 49–50f Stark tuning rate, 46 vibrational Stark effect (VSE), 46–47 Electrostatically embedded generalized molecular fractionation with conjugate caps (EE–GMFCC) method charge transfer, 67–69, 67t enzyme energy calculation, 51–54, 52f, 55f quantum calculation, 56–57, 58f End-point catastrophes, 401 Enhanced sampling of reactive trajectories (ESoRT) in-water Claisen rearrangement, 206 reactive trajectories, 205 traditional TPS, 205–206 Ensemble docking AutoDock, 393–394 definition, 393 molecular docking, 393 P-glycoprotein (P-gp), 393–394, 394f Enzymatic hydrolysis reaction carboxy peptidase (CPA), 262–263 conjugate peak refinement calculations, 263–264 Glu270 attack, 268 peptide hydrolysis, 263–264, 266–267f promoted-water mechanism, 267 protonation sites, 262–263, 264f QM/MM optimization, 262–263 Enzymatic quantum particle transfer reactions enzymatic free energy barriers and rates blue moon sampling, 25 FEP, 25 Grote–Hynes theory, 25 Subject Index MD simulation, 23–24 PMF, 23–24 TST, 25–26 umbrella sampling, 24–25 KIE calculation of, 25–26 competitive method, 22 definition, 22 equilibrium perturbation method, 22 free energy differences, 23 MD simulations, 23 noncompetitive methods, 22 Swain–Schaad equation, 22–23 nuclear tunneling advantages, 31 CMD method, 31–32 disadvantages, 30–31 distribution, transfer barriers, 33, 34f isotopic substitution, 33 LDH, 33 microscopic free energy changes, 30 Swain–Schaad exponents, 31–32 TPS properties, 32–33, 32–33t YADH, 31 quantum particle transfer, KIE modified algorithm and YADH, 36–39, 37f, 38t, 39f rate calculation algorithm, 34–36 TPS ensemble analysis, 28–30 statistical method, 26–28 Enzymatic structure function active site residues identification, 235f, 237–238 coarse-grain BD simulations BD, 232 carbonic anhydrase, 232–234, 233f enzymes, 229, 230–231t pseudo-atom, 229 rigidity profile, 232–234 force constant spectra, 233f, 234–239 ligand binding flexibility, 241–242, 243f no mechanical impact, 242–244, 244f rigidity, 241 mechanical variations Cα atoms, 240 ligand binding, 241 483 RMSD, 240, 240f mixed mechanical responses, 242 multidomain proteins EPSP synthase, 234–236, 235f ProPHet approach, 234–236 PDB, 228–229 protein folds analysis, conserved mechanical properties, 238 chitinase, 237f, 238 glucoamylase, 236f, 238 heme oxygenase, 238, 239f Enzyme catalysis anharmonic conformational analysis identification, conformational substates, 287f, 288–289 protein energy landscape, 286, 286f QAA, 286–288 catalytic efficiency, 275–276 conformational fluctuations, 294–295 conformational substates challenge, 277–278, 295 cis/trans isomerization, Cyclophilin A, 291–294, 293f elastic anisotropic network models, 285 enzyme landscape, 275–276, 276f extraction of, 280–283, 282f hiddeninvisible population, 278–279 higher-energy substates, 278–279, 278f HSQC, 279–280 hydride transfer, DHFR, 289–291, 290f identification, 287f, 288–289 NMA, 283 QHA, 284–285 rcCPMG, 279–280 sampling, 275 TANCA, 283–284 thermodynamic sampling, 276–277 transition state (TS), 278–279 two-site conformational exchange, 280, 281f protein motions, 274–275 structural role, 274 transition state (TS), 274 Enzyme fluctuogram alanine, coarse grained configuration, 331, 331f 484 Enzyme fluctuogram (Continued ) CG model, 328–329 definition, 330 dynamics, 328 ENM Cα and Cα–SC model, 334 CG beads, 330, 333 fluctuation matching, 330 harmonic bonds, 329–330 fluctuation matching, 330 implementation considerations all-atom-to-CG mapping, 334, 334t apo-RAT, 335–336 BPTI-bound serine protease, 334–335, 335f Cα model, 334–335 Cα–SC model, 334–335 CG beads, 333 CHARMM software, 333 intermolecular couplings, 335–336 mechanical coupling strangths, 336–337, 338f Python 2.7 code, 333 RAT, 334 resolutions, 334 total coupling strengths, 335–336, 336–337f normal mode analysis (NMA), 329–330 principle, 332 properties, 337–339 structural transitions, 328 Essential dynamics (ED), 29–30 Exosite I catalytic core, 443 H57 community, 442–443 S195 community, 442–443 thrombin, 440–442 F Fluctuation amplification of specific traits (FAST) algorithm ANTON supercomputer, 214 directed and undirected components, 217 FAST-Φ reward function, 216–217 folding and allostery, 214 MSMs adaptive sampling schemes, 215 construction, 214–215 Subject Index simulation length, 220 sampling parameters atom indices, 220 FRET study, 223 number of runs, 218 number of simulations per run, 219 resolution, 220–221 SASA, 221–222 scaling parameter, α, 218–219 simulation length, 220 softwares, 217–218 Fluctuation matching, 330 Force field parameters biopolymer force fields, 388–389 CGenFF program, 390, 392 CHARMM-compatible parameters, 390–392, 391f ffTK, 392 molecular mechanics (MM), 388–389 parametrization, 389–390 Force field toolkit (ffTK), 392 Free energy perturbation (FEP), 25, 401–402 Free energy profile advantages, 139 chorismate to prephenate, 136t, 137–138 MSMD, 128–132, 130f quasi reversible, 129 G Girvan–Newman algorithm, 436 Global optimization algorithms aqueous systems DA–MCM, 148 hydrogen bonding, 147 Metropolis MCM approach, 148 nonburied water molecules, 149, 149f random water selection and movement, 150 solvation shell, 148 targets, 149 WM–MCM, 149 GOTS, 146–147 MCM, 146–147 PES, 146–147 PO Ar38 and (H2O)20 cluster calculations, 158–159 Subject Index Ar38 results, 159–162 (H2O)20 cluster results, 163, 164f connection strategy, 155–158 reaction pathways, 154–155 RP, 147 transition state (TS), 146 water clusters (H2O)20, (H2O)30, and (H2O)40 algorithm assessment criteria, 150–151 calculations and methodology, 151 computational results, 151, 152f quality appraisement, 151–154, 154f, 154t, 156f Goal-oriented sampling algorithm See Fluctuation amplification of specific traits (FAST) algorithm Gradient Only Tabu-Search (GOTS), 146–147 H H-15N heteronuclear single quantum coherence (HSQC), 279–280 H2 oxidation, hydrogenase mimics DFT calculations, 92–94, 93f Fe-based, 91–92, 92f H2 production, hydrogenase mimics outer coordination sphere, 94–95, 94f REMD, 95–96, 95f Human argonaute-2 (hAgo2) and miRNA, molecular recognition APM algorithm, 355 macrostates, 355 MD simulations, 355, 356–357f MSMs, 355, 356–357f role of, 354 selective binding, 355–357 selective binding and structural rearrangement, 355, 356–357f Hybrid differential relaxation algorithm (HyDRA) AMBER computer simulation package, 134–135 BsCM, 136 chorismate to prephenate reaction, 135, 135f DRAr, 133–137, 133s FEP advantages, 139 485 chorismate to prephenate, 136t, 137–138 MSMD, 137–138 multiple time step scheme, 132–133 QM/MM Hamiltonian, 134 Zn hydrolases, 139–140 Hydration free energies, 106–107 Hydride transfer isotopic substitution, 33 LDH CMD method, 31–32 distribution, transfer barriers, 33, 34f TPS properties, 33, 33t YADH CMD method, 31–32 distribution, transfer barriers, 33, 34f Swain–Schaad exponents, 31–32 TPS properties, 32–33, 32t Hydride transfer, DHFR, 289–291, 290f Hydrogenase computational strategy ab initio/semiempirical approaches, 78 metadynamics, 78 MSEVB method, 77–78 REMD, 77–78 [FeFe]-hydrogenases, 74 functions, 74 [NiFe]-hydrogenases, 74 proton transport classical MD simulations, 79, 80f Clostridium pastuerianum [FeFe]hydrogenase, 75–76, 76f dynamics, enzymatic activity, 86–88, 87–88f evaluation, protein dynamics, 82–83, 82–83f force field parameters, 79–82, 81f functions, 75 glutamic residue, 77 hydrogen bond analysis, 84–86, 84f, 86–87f mimics, 89–96, 90f, 92–95f Hydrogenase mimics endergonic process, 91 H2 oxidation DFT calculations, 92–94, 93f Fe-based, 91–92, 92f H2 production 486 Hydrogenase mimics (Continued ) outer coordination sphere, 94–95, 94f REMD, 95–96, 95f Ni-based catalysts, 91 protonation (deprotonation), 89–91, 90f I Implicit ligand sampling (ILS), 397, 398f Integrated tempering enhanced sampling (ITS) method ALA–PRO peptide, 175, 177t generalized non-Boltzmann distribution, 172 MD simulations, 175 SITS, 177–179 Intramolecular Hg2+ transfer, 115, 116f Isolated thrombin allosteric mechanism, 440, 441f system construction and simulation details, 435 vs.thrombin–hirugen, 438, 438f J Jarzynski’s relationship (JR) definition, 126–127 MSMD, 127–128 SMD simulations, 127 Javanainen’s method, 384–386, 385f K Kinetic isotope effect (KIE) modified algorithm and YADH Chandler rate algorithm, 36 cumulative histograms, 36, 37f deuteride system, 36, 38t Hermite interpolation, 36, 39f hydride system, 36, 38t rate calculation algorithm applications, 35–36 Bennett–Chandler theory, 34 rare event system, 35 Kinetic network models (KNMs) functional study, enzymes, 344–345 k-centers, 348 k-medoids, 348 MD simulation Newton’s equations of motion, 345 timescale gap, 345, 345f Subject Index modified Climber algorithm, 347–348 molecular recognition, hAgo2 and miRNA APM algorithm, 355 macrostates, 355 MD simulations, 355, 356–357f MSMs, 355, 356–357f role of, 354 selective binding, 355–357 selective binding and structural rearrangement, 355, 356–357f MSM APM systems, 350–352, 352–353f applications, 345–346 construction work flow, 346–347, 347f splitting-and-lumping protocol, 347f, 348–350 thermodynamic and kinetic quantities, 353–354 validation of, 353 nucleoside triphosphate (NTP), 347–348 RNA polymerase II translocation, 357–361, 358–359f whole NAC, 361–364, 362–363f Kramers theory, 310–311 L Lactate dehydrogenase (LDH) CMD method, 31–32 distribution, transfer barriers, 33, 34f TPS properties, 33, 33t Lennard–Jones (LJ) clusters, 159–160 Ligand binding flexibility, 241–242, 243f free energies experimental and theoretical differences, 107, 108f Hg(SH)2, 108f, 109 solvation, 107, 108f KNMs, 350–351, 352–353f mechanical variations, 241 no mechanical impact, 242–244, 244f rigidity, 241 M Markov state model (MSM) adaptive sampling schemes, 215 Subject Index APM systems escape probability, 351 k-centers algorithm, 350–351, 352–353f protocol, 351 applications, 345–346 construction work flow, 214–215, 346–347, 347f molecular recognition, hAgo2 and miRNA, 355, 356–357f simulation length, 220 splitting-and-lumping protocol clustering, 348–350 density peaks, 349–350 MD conformations, 349–350 microstate-MSM, 350 thermodynamic and kinetic quantities, 353–354 translocation, RNA polymerase II, 358–359f, 359–360 validation of, 353 MCCE software, 11 MD simulation continuum electrostatics, KNMs Newton’s equations of motion, 345 timescale gap, 345, 345f membrane transporters, 377 molecular recognition, hAgo2 and miRNA, 355, 356–357f protein and small molecule interaction CVs, 203–205 ESoRT, 205–206 metadynamics and umbrella sampling, 203 NEIL1 protein, 203, 204f RCs, 202–203 translocation, RNA polymerase II, 360 MD simulations ANTON supercomputer, 214 charge transfer, 65–67 diffusion, small ligands, 301 electronic polarization on electrostatics, 60 MSM, 301–302 Mean first passage times, 310 Membrane Builder, 384–386 487 Membrane-embedded transporter system assembly Alchembed method, 384–386, 385f CHARMM, 384 Javanainen’s method, 384–386, 385f Membrane Builder, 384–386 MemProtMD method, 384–386, 385f noncylindrical transporters, 384–386 positioning of proteins in membrane (PPM), 383 Membrane transporters alternating access mechanism cation coupled symporter, 375–376, 376f global conformational changes, 376–377 inward-facing (IF) state, 376 outward-facing (OF) state, 376 atomic and coarse-grained representations comparitive study, 379 vibrational modes, 378–379 augmenting mechanistic studies, 377 complete system construction, 378 initial structural model construction and refinement PROPKA, 381 protein databank (PDB), 380 protein structure, 380–381 protonation states, 381 large-scale structural transitions biasing protocol generation, 404–407, 406f defining target end states, 402–404, 403f free energy profile, 409–412, 410f refinement, transition pathway, 408–409, 408f Maxwellian “demon”, 374–375 membrane composition and construction considerations apoptosis, 382–383 CHARMM-GUI membrane, 383 location, 382 phosphatidylcholine (PC) and phosphatidylethanolamine (PE) lipids, 381–382 signaling lipids, 382 sterols, 382 488 Membrane transporters (Continued ) membrane-embedded transporter system assembly Alchembed method, 384–386, 385f CHARMM, 384 Javanainen’s method, 384–386, 385f Membrane Builder, 384–386 MemProtMD method, 384–386, 385f noncylindrical transporters, 384–386 positioning of proteins in membrane (PPM), 383 membrane protein field, 412 simulation condition considerations barostats, 386 vs solution simulations, 387 thermostat, 386–387 structure, 375 substrate binding and unbinding processes alchemical perturbation, 401–402 ensemble docking, 392–394, 394f force field parameters, 388–392, 391f pathway and mechanism, biased simulation, 398–400 substrate association and dissociation, 387–388, 388f unbiased simulation, 394–397, 395f, 398f transporter-driven processes, 374–375 MemProtMD method, 384–386, 385f MerA See Mercuric reductase MerA MerB See Organomercurial lyase MerB Mercuric reductase MerA MD simulation, 113 neutron spin-echo (NSE) spectroscopy, 113–115, 114f N-terminal metallochaperone-like domain (NmerA), 112–113 Mercury (Hg) hydration free energies, 106–107 inorganic chemistry, 105 ligand binding free energies experimental and theoretical differences, 107, 108f Hg(SH)2, 108f, 109 solvation, 107, 108f microbial interactions bacterial resistance, 109 intramolecular transfer, 115, 116f Subject Index MerA, 112–115 MerB, 110–112 MerR, 110 methylation, 116–119, 117f quantum chemistry, 105–106 toxicity, 104 mer operon, 109 MerR See Bacterial metalloregulator MerR Methylation corrinoid iron–sulfur protein (CFeSP), 116–118 Cys ligand, 118 Cys-on cobalt binding configuration, 116–118, 117f Herculean experimental effort, 118 transporters, 118–119 Wood–Ljungdahl (WL) pathway, 116–118 Methylmercury, 104 Metropolis MCM approach, 148 Microbial interactions, Hg bacterial resistance, 109 intramolecular transfer, 115, 116f MerA MD simulation, 113 neutron spin-echo (NSE) spectroscopy, 113–115, 114f N-terminal metallochaperone-like domain (NmerA), 112–113 MerB active site, 110, 111f Cartesian coordinates, 111–112 QM/MM, 110–111 reaction mechanism, 112, 112f MerR, 110, 110f methylation corrinoid iron–sulfur protein (CFeSP), 116–118 Cys ligand, 118 Cys-on cobalt binding configuration, 116–118, 117f Herculean experimental effort, 118 transporters, 118–119 Wood–Ljungdahl (WL) pathway, 116–118 Mixed discrete-continuum method, 105–106 Subject Index Modeling enzymatic reactions applications, 252 comprehensive transition networks Dijkstra’s algorithm, 262 edges, 261–262 edge weights, 258 enzymatic hydrolysis reaction, 262–268, 264–267f geometry optimization, network nodes, 260 metal ion/water positions, 258 node state assignment, 260–261 protonation sampling, 259 rejection, nonmeaningful structures, 260 sampling bond lengths, 258 side chain rotation, 259, 259f direct mechanism, 255–257, 257f EcoRV enzyme phosphodiester hydrolysis reaction, 253–255, 254–255f reactant and product state, 253, 253f energy landscape with valleys, 250–251, 251f enhanced sampling techniques, 249–250 histidine mechanism, 255–257, 257f optimization-based methods, 250 proton transfers, 250–251 thymine DNA glycosylase (TDG), 255, 256f transition networks approach, 252 Molecular dynamics (MD) simulation allosteric mechanisms Dijkstra’s algorithm, 433–434 domino effect, 433–434 functions, 430 graph theory approach, 433–434 induced fit mechanism, 430 mutations, 431 residue-pair correlations, 431 suboptimal pathways, 433–434 thrombin, 440–442, 441f community structure analysis, 434 contact definition analysis, 438–439, 439f, 440t correlation calculations, 436 cross-correlation vs linear mutual information, 437–438, 437f 489 enzymatic free energy barriers and rates, 23–24 Exosite I catalytic core, 443 H57 community, 442–443 S195 community, 442–443 graph construction and calculations, 436 isolated thrombin vs thrombin–hirugen, 438, 438f KIE, 23 residue–residue correlations dynamic cross-correlation, 431–432 limitations, 431–432 mutual information based correlations, 433 Pearson-like correlation, 432 system construction and simulation, 435 Molecular fractionation with conjugate caps (MFCC) method EE-GMFCC, 56–57, 58f electric fields inside enzymes, 48–49, 49–50f PB protocol, 49–51 Monte Carlo (MC) simulations, 5–6 Monte Carlo with minimization (MCM) DA–MCM, 148 global optimization algorithms, 146–147 Metropolis MCM approach, 148 WM–MCM, 149 Multidomain proteins EPSP synthase, 234–236, 235f ProPHet approach, 234–236 Multiple steered molecular dynamics (MSMD) FEP, 128–132, 130f HyDRA, 137–138 JR, 127–128 Multistate empirical valence bond (MSEVB) method, 77–78 Multitime scale molecular dynamics (MTS) method characteristics, 173–175 DOF, 173–175 pseudo-equilibrium, 173 vs SGMD, 170–171 Mutual information based correlations, 433 490 Myoglobin computed (comp.) and experimental (exp.) diffusion rates, 316–317, 318–319f, 319t dependence, ligand concentration, 317–320, 320f final transition, 316, 317f microstates and ligand diffusion paths, 314–316, 315f MSM validation, 320f, 321 sensitivity analysis, 321, 322f N NetworkX Python module, 436 [NiFe]-hydrogenase computed (comp.) and experimental (exp.) diffusion rates, 316–317, 318–319f, 319t dependence, ligand concentration, 317–320, 320f final transition, 316, 317f microstates and ligand diffusion paths, 314–316, 315f MSM validation, 320f, 321 Nodes geometry optimization, 260 state assignment, 260–261 Normal mode analysis (NMA), 283 Nuclear tunneling advantages, 31 disadvantages, 30–31 isotopic substitution, 33 LDH CMD method, 31–32 distribution, transfer barriers, 33, 34f TPS properties, 33, 33t microscopic free energy changes, 30 YADH CMD method, 31–32 distribution, transfer barriers, 33, 34f Swain–Schaad exponents, 31–32 TPS properties, 32–33, 32t O Organomercurial lyase MerB active site, 110, 111f Cartesian coordinates, 111–112 QM/MM, 110–111 reaction mechanism, 112, 112f Subject Index P Pearson-like correlation, 432 pKa values, Poisson–Boltzmann (PB) methods, 12–13 Polarizable continuum model (PCM), 105–106 Polarized protein-specific charge (PPC), 49–51, 50f Positioning of proteins in membrane (PPM), 383 Potential energy surface (PES), 146–147 Potential of mean force (PMF) Arg-306, 196–198, 199–200f carbamate formation, 196–197, 197f enzymatic free energy barriers and rates, 23–24 RC, 198 Thr-37, 201, 201f WHAM, 196 Principal component analysis (PCA) ensemble analysis, 29–30 free energy profile, 410–411 Probing Protein Heterogeneity (ProPHet) program coarse-grain BD simulations, 229 hemoproteins and globins, 228–229 multidomain proteins, 234–236 Protein and small molecule interaction conformation sampling bias potential methods, 171–172 characteristic motions, 170–171 complexity and roughness, 171–172 generalized ensemble methods, 171–172 ITS, 175–179, 177t MTS method, 173–174 SGMD, 170–171 slow and fast DOFs, 170–171 free ligand/substrate, solution conformation chemical structure, CDNs, 185, 186f chorismate mutase (EcCM and BsCM), 188–189 Claisen rearrangement, 188–189, 189s phase angle distribution and χ angle distribution, CDNs, 185–187, 187f SITS–QM/MM method, 189–191, 190f STING, 185 ... resulting ion cloud interacts with the protein in several ways, including saltspecific protein binding, electrostatic screening, and changing the thermodynamic activity of the protein in solution (Grochowski... experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein In using such information or methods they should be mindful of their own safety... changes in flexibility and conformation that occur upon introduction of new charges into a protein Calculating Ems and pKas in Proteins One of the key choices in charge state modeling involves