Bio

Bio


Ron Dror is an Associate Professor of Computer Science and, by courtesy, Molecular and Cellular Physiology and Structural Biology at Stanford University, where he is also affiliated with the Institute for Computational and Mathematical Engineering, the Stanford Artificial Intelligence Lab, Bio-X, ChEM-H, and the Biophysics and Biomedical Informatics Programs. Dr. Dror's research at Stanford addresses a broad set of computational biology problems related to the spatial organization and dynamics of biomolecules and cells.

Before joining Stanford in March 2014, Dr. Dror served as second-in-command of D. E. Shaw Research, a hundred-person company, having joined in 2002 as its first hire. At DESRES, he focused on high-performance computing and biomolecular simulation—in particular, developing technology that accelerates molecular dynamics simulations by orders of magnitude, and applying these simulations to the study of protein function, protein folding, and protein-drug interactions (part of a project highlighted by Science as one of the top 10 scientific breakthroughs of 2010).

Dr. Dror earned a PhD in Electrical Engineering and Computer Science at MIT, an MPhil in Biological Sciences as a Churchill Scholar at the University of Cambridge, and both a BA in Mathematics and a BS in Electrical and Computer Engineering at Rice University, summa cum laude. As a student, he worked in genomics, vision, image analysis, and neuroscience. He has been awarded a Fulbright Scholarship and fellowships from the National Science Foundation, the Department of Defense, and the Whitaker Foundation, as well as a Gordon Bell Prize and several Best Paper awards.

Academic Appointments


Honors & Awards


  • Gordon Bell Prize, (Performance) (2014)
  • Best Paper Award, International Parallel and Distributed Processing Symposium (2013)
  • Best Paper Award, ACM/IEEE Conference on Supercomputing (SC11) (2011)
  • Breakthrough of the Year runner-up, Science Magazine (2010)
  • Best Paper Award, ACM/IEEE Conference on Supercomputing (SC09) (2009)
  • Gordon Bell Prize, (Special Achievement) (2009)
  • Profiled by MIT EECS Dept., in feature on “EECS Alums: Major Players and Thinkers,” (2009)
  • Best Paper Award, ACM/IEEE Conference on Supercomputing (SC06) (2006)

Teaching

2017-18 Courses


Stanford Advisees


Publications

All Publications


  • Gi- and Gs-coupled GPCRs show different modes of G-protein binding Proceedings of the National Academy of Sciences of the United States of America Eps, N., Altenbach, C., Caro, L. N., Latorraca, N. R., Hollingsworth, S. A., Dror, R. O., Ernst, O. P., Hubbell, W. L. 2018
  • Structure-inspired design of β-arrestin-biased ligands for aminergic GPCRs Nature Chemical Biology McCorvy, J. D., Butler, K. V., Kelly, B., Rechsteiner, K., Karpiak, J., Betz, R. M., Kormos, B. L., Shoichet, B. K., Dror, R. O., Jin, J., Roth, B. L. 2018: 126-134
  • Molecular mechanism of GPCR-mediated arrestin activation Nature Latorraca, N. R., Wang, J. K., Bauer, B., Townshend, R. L., Hollingsworth, S. A., Olivieri, J. E., Xu, H. E., Sommer, M. E., Dror, R. O. 2018
  • Structural and Functional Analysis of a beta(2)-Adrenergic Receptor Complex with GRK5 CELL Komolov, K. E., Du, Y., Nguyen Minh Duc, N. M., Betz, R. M., Rodrigues, J. P., Leib, R. D., Patra, D., Skiniotis, G., Adams, C. M., Dror, R. O., Chung, K. Y., Kobilka, B. K., Benovic, J. L. 2017; 169 (3): 407-?
  • -Adrenergic Receptor Complex with GRK5. Cell Komolov, K. E., Du, Y., Duc, N. M., Betz, R. M., Rodrigues, J. P., Leib, R. D., Patra, D., Skiniotis, G., Adams, C. M., Dror, R. O., Chung, K. Y., Kobilka, B. K., Benovic, J. L. 2017; 169 (3): 407-421 e16

    Abstract

    The phosphorylation of agonist-occupied G-protein-coupled receptors (GPCRs) by GPCR kinases (GRKs) functions to turn off G-protein signaling and turn on arrestin-mediated signaling. While a structural understanding of GPCR/G-protein and GPCR/arrestin complexes has emerged in recent years, the molecular architecture of a GPCR/GRK complex remains poorly defined. We used a comprehensive integrated approach of cross-linking, hydrogen-deuterium exchange mass spectrometry (MS), electron microscopy, mutagenesis, molecular dynamics simulations, and computational docking to analyze GRK5 interaction with the β2-adrenergic receptor (β2AR). These studies revealed a dynamic mechanism of complex formation that involves large conformational changes in the GRK5 RH/catalytic domain interface upon receptor binding. These changes facilitate contacts between intracellular loops 2 and 3 and the C terminus of the β2AR with the GRK5 RH bundle subdomain, membrane-binding surface, and kinase catalytic cleft, respectively. These studies significantly contribute to our understanding of the mechanism by which GRKs regulate the function of activated GPCRs. PAPERCLIP.

    View details for DOI 10.1016/j.cell.2017.03.047

    View details for PubMedID 28431242

  • Mechanism of Substrate Translocation in an Alternating Access Transporter CELL Latorraca, N. R., Fastman, N. M., Venkatakrishnan, A. J., Frommer, W. B., Dror, R. O., Feng, L. 2017; 169 (1): 96-?

    Abstract

    Transporters shuttle molecules across cell membranes by alternating among distinct conformational states. Fundamental questions remain about how transporters transition between states and how such structural rearrangements regulate substrate translocation. Here, we capture the translocation process by crystallography and unguided molecular dynamics simulations, providing an atomic-level description of alternating access transport. Simulations of a SWEET-family transporter initiated from an outward-open, glucose-bound structure reported here spontaneously adopt occluded and inward-open conformations. Strikingly, these conformations match crystal structures, including our inward-open structure. Mutagenesis experiments further validate simulation predictions. Our results reveal that state transitions are driven by favorable interactions formed upon closure of extracellular and intracellular "gates" and by an unfavorable transmembrane helix configuration when both gates are closed. This mechanism leads to tight allosteric coupling between gates, preventing them from opening simultaneously. Interestingly, the substrate appears to take a "free ride" across the membrane without causing major structural rearrangements in the transporter.

    View details for DOI 10.1016/j.cell.2017.03.010

    View details for Web of Science ID 000397090000011

    View details for PubMedID 28340354

  • Crystal Structure of an LSD-Bound Human Serotonin Receptor. Cell Wacker, D., Wang, S., McCorvy, J. D., Betz, R. M., Venkatakrishnan, A. J., Levit, A., Lansu, K., Schools, Z. L., Che, T., Nichols, D. E., Shoichet, B. K., Dror, R. O., Roth, B. L. 2017; 168 (3): 377-389 e12

    Abstract

    The prototypical hallucinogen LSD acts via serotonin receptors, and here we describe the crystal structure of LSD in complex with the human serotonin receptor 5-HT2B. The complex reveals conformational rearrangements to accommodate LSD, providing a structural explanation for the conformational selectivity of LSD's key diethylamide moiety. LSD dissociates exceptionally slow from both 5-HT2BR and 5-HT2AR-a major target for its psychoactivity. Molecular dynamics (MD) simulations suggest that LSD's slow binding kinetics may be due to a "lid" formed by extracellular loop 2 (EL2) at the entrance to the binding pocket. A mutation predicted to increase the mobility of this lid greatly accelerates LSD's binding kinetics and selectively dampens LSD-mediated β-arrestin2 recruitment. This study thus reveals an unexpected binding mode of LSD; illuminates key features of its kinetics, stereochemistry, and signaling; and provides a molecular explanation for LSD's actions at human serotonin receptors. PAPERCLIP.

    View details for DOI 10.1016/j.cell.2016.12.033

    View details for PubMedID 28129538

    View details for PubMedCentralID PMC5289311

  • GPCR Dynamics: Structures in Motion CHEMICAL REVIEWS Latorraca, N. R., Venkatakrishnan, A. J., Dror, R. O. 2017; 117 (1): 139-155

    Abstract

    The function of G protein-coupled receptors (GPCRs)-which represent the largest class of both human membrane proteins and drug targets-depends critically on their ability to change shape, transitioning among distinct conformations. Determining the structural dynamics of GPCRs is thus essential both for understanding the physiology of these receptors and for the rational design of GPCR-targeted drugs. Here we review what is currently known about the flexibility and dynamics of GPCRs, as determined through crystallography, spectroscopy, and computer simulations. We first provide an overview of the types of motion exhibited by a GPCR and then discuss GPCR dynamics in the context of ligand binding, activation, allosteric modulation, and biased signaling. Finally, we discuss the implications of GPCR conformational plasticity for drug design.

    View details for DOI 10.1021/acs.chemrev.6b00177

    View details for Web of Science ID 000392036100007

    View details for PubMedID 27622975

  • Identification of phosphorylation codes for arrestin recruitment by G protein-coupled receptors Cell Zhou, X. E., He, Y., de Waal, P. W., Gao, X., Kang, Y., Van Eps, N., Yin, Y., Pal, K., Goswami, D., White, T. A., Barty, A., Latorraca, N. R., Chapman, H. N., Hubbell, W. L., Dror, R. O., Stevens, R. C., Cherezov, V., Gurevich, V. V., Griffin, P. R., Ernst, O. P., Melcher, K., Xu, H. E. 2017: 457-469
  • Mechanism of intracellular allosteric β2AR antagonist revealed by X-ray crystal structure Nature Liu, X., Ahn, S., Kahsai, A. W., Meng, K. C., Latorraca, N. R., Pani, B., Venkatakrishnan, A., Masoudi, A., Weis, W. I., Dror, R. O., Chen, X., Lefkowitz, R. J., Kobilka, B. W. 2017: 480-484
  • D4 dopamine receptor high-resolution structures enable the discovery of selective agonists Science Wang, S., Wacker, D., Levit, A., Che, T., Betz, R. M., McCorvy, J. D., Venkatakrishnan, A., Huang, X. P., Dror, R. O., Shoichet, B. K., Roth, B. L. 2017: 381-386
  • Structural and functional analysis of a β2-adrenergic receptor complex with GRK5 Cell Komolov, K. E., Du, Y., Duc, N. M., Betz, R. M., Rodrigues, J. M., Leib, R. D., Patra, D., Skiniotis, G., Adams, C. M., Dror, R. O., Chung, K. Y., Kobilka, B. K., Benovic, J. L. 2017: 407-421
  • Crystal Structure of a Full-Length Human Tetraspanin Reveals a Cholesterol-Binding Pocket CELL Zimmerman, B., Kelly, B., McMillan, B. J., Seegar, T. C., Dror, R. O., Kruse, A. C., Blacklow, S. C. 2016; 167 (4): 1041-?

    Abstract

    Tetraspanins comprise a diverse family of four-pass transmembrane proteins that play critical roles in the immune, reproductive, genitourinary, and auditory systems. Despite their pervasive roles in human physiology, little is known about the structure of tetraspanins or the molecular mechanisms underlying their various functions. Here, we report the crystal structure of human CD81, a full-length tetraspanin. The transmembrane segments of CD81 pack as two largely separated pairs of helices, capped by the large extracellular loop (EC2) at the outer membrane leaflet. The two pairs of helices converge at the inner leaflet to create an intramembrane pocket with additional electron density corresponding to a bound cholesterol molecule within the cavity. Molecular dynamics simulations identify an additional conformation in which EC2 separates substantially from the transmembrane domain. Cholesterol binding appears to modulate CD81 activity in cells, suggesting a potential mechanism for regulation of tetraspanin function.

    View details for DOI 10.1016/j.cell.2016.09.056

    View details for Web of Science ID 000389469000020

    View details for PubMedID 27881302

    View details for PubMedCentralID PMC5127602

  • Revealing Atomic-Level Mechanisms of Protein Allostery with Molecular Dynamics Simulations PLOS COMPUTATIONAL BIOLOGY Hertig, S., Latorraca, N. R., Dror, R. O. 2016; 12 (6)

    Abstract

    Molecular dynamics (MD) simulations have become a powerful and popular method for the study of protein allostery, the widespread phenomenon in which a stimulus at one site on a protein influences the properties of another site on the protein. By capturing the motions of a protein's constituent atoms, simulations can enable the discovery of allosteric binding sites and the determination of the mechanistic basis for allostery. These results can provide a foundation for applications including rational drug design and protein engineering. Here, we provide an introduction to the investigation of protein allostery using molecular dynamics simulation. We emphasize the importance of designing simulations that include appropriate perturbations to the molecular system, such as the addition or removal of ligands or the application of mechanical force. We also demonstrate how the bidirectional nature of allostery-the fact that the two sites involved influence one another in a symmetrical manner-can facilitate such investigations. Through a series of case studies, we illustrate how these concepts have been used to reveal the structural basis for allostery in several proteins and protein complexes of biological and pharmaceutical interest.

    View details for DOI 10.1371/journal.pcbi.1004746

    View details for Web of Science ID 000379349700002

    View details for PubMedID 27285999

    View details for PubMedCentralID PMC4902200

  • Molecular Basis of Ligand Dissociation from the Adenosine A(2A) Receptor MOLECULAR PHARMACOLOGY Guo, D., Pan, A. C., Dror, R. O., Mocking, T., Liu, R., Heitman, L. H., Shaw, D. E., IJzerman, A. P. 2016; 89 (5): 485-491

    Abstract

    How drugs dissociate from their targets is largely unknown. We investigated the molecular basis of this process in the adenosine A2Areceptor (A2AR), a prototypical G protein-coupled receptor (GPCR). Through kinetic radioligand binding experiments, we characterized mutant receptors selected based on molecular dynamic simulations of the antagonist ZM241385 dissociating from the A2AR. We discovered mutations that dramatically altered the ligand's dissociation rate despite only marginally influencing its binding affinity, demonstrating that even receptor features with little contribution to affinity may prove critical to the dissociation process. Our results also suggest that ZM241385 follows a multistep dissociation pathway, consecutively interacting with distinct receptor regions, a mechanism that may also be common to many other GPCRs.

    View details for DOI 10.1124/mol.115.102657

    View details for Web of Science ID 000374963400001

    View details for PubMedID 26873858

  • Molecular basis of ligand dissociation from the adenosine A2A receptor Molecular Pharmacology Guo, D., Pan, A. C., Dror, R. O., Mocking, T., Liu, R., Heitman, L., Shaw, D. E., IJzerman, A. P. 2016: 485-491
  • Structural insights into mu-opioid receptor activation NATURE Huang, W., Manglik, A., Venkatakrishnan, A. J., Laeremans, T., Feinberg, E. N., Sanborn, A. L., Kato, H. E., Livingston, K. E., Thorsen, T. S., Kling, R. C., Granier, S., Gmeiner, P., Husbands, S. M., Traynor, J. R., Weis, W. I., Steyaert, J., Dror, R. O., Kobilka, B. K. 2015; 524 (7565): 315-?
  • Structural insights into µ-opioid receptor activation. Nature Huang, W., Manglik, A., Venkatakrishnan, A. J., Laeremans, T., Feinberg, E. N., Sanborn, A. L., Kato, H. E., Livingston, K. E., Thorsen, T. S., Kling, R. C., Granier, S., Gmeiner, P., Husbands, S. M., Traynor, J. R., Weis, W. I., Steyaert, J., Dror, R. O., Kobilka, B. K. 2015; 524 (7565): 315-321

    Abstract

    Activation of the μ-opioid receptor (μOR) is responsible for the efficacy of the most effective analgesics. To shed light on the structural basis for μOR activation, here we report a 2.1 Å X-ray crystal structure of the murine μOR bound to the morphinan agonist BU72 and a G protein mimetic camelid antibody fragment. The BU72-stabilized changes in the μOR binding pocket are subtle and differ from those observed for agonist-bound structures of the β2-adrenergic receptor (β2AR) and the M2 muscarinic receptor. Comparison with active β2AR reveals a common rearrangement in the packing of three conserved amino acids in the core of the μOR, and molecular dynamics simulations illustrate how the ligand-binding pocket is conformationally linked to this conserved triad. Additionally, an extensive polar network between the ligand-binding pocket and the cytoplasmic domains appears to play a similar role in signal propagation for all three G-protein-coupled receptors.

    View details for DOI 10.1038/nature14886

    View details for PubMedID 26245379

  • Structural basis for nucleotide exchange in heterotrimeric G proteins SCIENCE Dror, R. O., Mildorf, T. J., Hilger, D., Manglik, A., Borhani, D. W., Arlow, D. H., Philippsen, A., Villanueva, N., Yang, Z., Lerch, M. T., Hubbell, W. L., Kobilka, B. K., Sunahara, R. K., Shaw, D. E. 2015; 348 (6241): 1361-1365
  • SIGNAL TRANSDUCTION. Structural basis for nucleotide exchange in heterotrimeric G proteins. Science Dror, R. O., Mildorf, T. J., Hilger, D., Manglik, A., Borhani, D. W., Arlow, D. H., Philippsen, A., Villanueva, N., Yang, Z., Lerch, M. T., Hubbell, W. L., Kobilka, B. K., Sunahara, R. K., Shaw, D. E. 2015; 348 (6241): 1361-1365

    Abstract

    G protein-coupled receptors (GPCRs) relay diverse extracellular signals into cells by catalyzing nucleotide release from heterotrimeric G proteins, but the mechanism underlying this quintessential molecular signaling event has remained unclear. Here we use atomic-level simulations to elucidate the nucleotide-release mechanism. We find that the G protein α subunit Ras and helical domains-previously observed to separate widely upon receptor binding to expose the nucleotide-binding site-separate spontaneously and frequently even in the absence of a receptor. Domain separation is necessary but not sufficient for rapid nucleotide release. Rather, receptors catalyze nucleotide release by favoring an internal structural rearrangement of the Ras domain that weakens its nucleotide affinity. We use double electron-electron resonance spectroscopy and protein engineering to confirm predictions of our computationally determined mechanism.

    View details for DOI 10.1126/science.aaa5264

    View details for PubMedID 26089515

  • Identifying localized changes in large systems: Change-point detection for biomolecular simulations PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Fan, Z., Dror, R. O., Mildorf, T. J., Piana, S., Shaw, D. E. 2015; 112 (24): 7454-7459

    Abstract

    Research on change-point detection, the classical problem of detecting abrupt changes in sequential data, has focused predominantly on datasets with a single observable. A growing number of time series datasets, however, involve many observables, often with the property that a given change typically affects only a few of the observables. We introduce a general statistical method that, given many noisy observables, detects points in time at which various subsets of the observables exhibit simultaneous changes in data distribution and explicitly identifies those subsets. Our work is motivated by the problem of identifying the nature and timing of biologically interesting conformational changes that occur during atomic-level simulations of biomolecules such as proteins. This problem has proved challenging both because each such conformational change might involve only a small region of the molecule and because these changes are often subtle relative to the ever-present background of faster structural fluctuations. We show that our method is effective in detecting biologically interesting conformational changes in molecular dynamics simulations of both folded and unfolded proteins, even in cases where these changes are difficult to detect using alternative techniques. This method may also facilitate the detection of change points in other types of sequential data involving large numbers of observables-a problem likely to become increasingly important as such data continue to proliferate in a variety of application domains.

    View details for DOI 10.1073/pnas.1415846112

    View details for Web of Science ID 000356251800044

    View details for PubMedID 26025225

    View details for PubMedCentralID PMC4475967

  • Structural biology. Structural basis for chemokine recognition and activation of a viral G protein-coupled receptor. Science Burg, J. S., Ingram, J. R., Venkatakrishnan, A. J., Jude, K. M., Dukkipati, A., Feinberg, E. N., Angelini, A., Waghray, D., Dror, R. O., Ploegh, H. L., Garcia, K. C. 2015; 347 (6226): 1113-1117

    Abstract

    Chemokines are small proteins that function as immune modulators through activation of chemokine G protein-coupled receptors (GPCRs). Several viruses also encode chemokines and chemokine receptors to subvert the host immune response. How protein ligands activate GPCRs remains unknown. We report the crystal structure at 2.9 angstrom resolution of the human cytomegalovirus GPCR US28 in complex with the chemokine domain of human CX3CL1 (fractalkine). The globular body of CX3CL1 is perched on top of the US28 extracellular vestibule, whereas its amino terminus projects into the central core of US28. The transmembrane helices of US28 adopt an active-state-like conformation. Atomic-level simulations suggest that the agonist-independent activity of US28 may be due to an amino acid network evolved in the viral GPCR to destabilize the receptor's inactive state.

    View details for DOI 10.1126/science.aaa5026

    View details for PubMedID 25745166

    View details for PubMedCentralID PMC4445376

  • Structural basis for chemokine recognition and activation of a viral G protein-coupled receptor SCIENCE Burg, J. S., Ingram, J. R., Venkatakrishnan, A. J., Jude, K. M., Dukkipati, A., Feinberg, E. N., Angelini, A., Waghray, D., Dror, R. O., Ploegh, H. L., Garcia, K. C. 2015; 347 (6226): 1113-1117
  • Structural insights into µ-opioid receptor activation Nature Huang, W., Manglik, A., Venkatakrishnan, A., Laeremans, T., Feinberg, E. N., Sanborn, A. L., Kato, H., Livingston, K. E., Thorsen, T. S., Kling, R., Granier, S., Gmeiner, P., Husbands, S. M., Traynor, J. R., Weis, W. I., Steyaert, J., Dror, R. O., Kobilka, B. K. 2015: 315-321
  • Insights into the Role of Asp79(2.50) in beta(2) Adrenergic Receptor Activation from Molecular Dynamics Simulations BIOCHEMISTRY Ranganathan, A., Dror, R. O., Carlsson, J. 2014; 53 (46): 7283-7296

    Abstract

    Achieving a molecular-level understanding of G-protein-coupled receptor (GPCR) activation has been a long-standing goal in biology and could be important for the development of novel drugs. Recent breakthroughs in structural biology have led to the determination of high-resolution crystal structures for the β2 adrenergic receptor (β2AR) in inactive and active states, which provided an unprecedented opportunity to understand receptor signaling at the atomic level. We used molecular dynamics (MD) simulations to explore the potential roles of ionizable residues in β2AR activation. One such residue is the strongly conserved Asp79(2.50), which is buried in a transmembrane cavity and becomes dehydrated upon β2AR activation. MD free energy calculations based on β2AR crystal structures suggested an increase in the population of the protonated state of Asp79(2.50) upon activation, which may contribute to the experimentally observed pH-dependent activation of this receptor. Analysis of MD simulations (in total > 100 μs) with two different protonation states further supported the conclusion that the protonated Asp79(2.50) shifts the conformation of the β2AR toward more active-like states. On the basis of our calculations and analysis of other GPCR crystal structures, we suggest that the protonation state of Asp(2.50) may act as a functionally important microswitch in the activation of the β2AR and other class A receptors.

    View details for DOI 10.1021/bi5008723

    View details for Web of Science ID 000345551800013

    View details for PubMedID 25347607

  • Insights into the role of Asp792.50 in β2 adrenergic receptor activation from molecular dynamics simulations Biochemistry Ranganathan, A., Dror, R. O., Carlsson, J. 2014: 7283-7296
  • Anton 2: Raising the bar for performance and programmability in a special-purpose molecular dynamics supercomputer SC14: INTERNATIONAL CONFERENCE FOR HIGH PERFORMANCE COMPUTING, NETWORKING, STORAGE AND ANALYSIS Shaw, D. E., Grossman, J. P., Bank, J. A., Batson, B., Butts, J. A., Chao, J. C., Deneroff, M. M., Dror, R. O., Even, A., Fenton, C. H., Forte, A., Gagliardo, J., Gill, G., Greskamp, B., Ho, C. R., Ierardi, D. J., Iserovich, L., Kuskin, J. S., Larson, R. H., Layman, T., Lee, L., Lerer, A. K., Li, C., Killebrew, D., Mackenzie, K. M., Mok, S. Y., Moraes, M. A., Mueller, R., Nociolo, L. J., Peticolas, J. L., Quan, T., Ramot, D., Salmon, J. K., Scarpazza, D. P., Ben Schafer, U., Siddique, N., Snyder, C. W., Spengler, J., Tang, P. T., Theobald, M., Toma, H., Towles, B., Vitale, B., Wang, S. C., Young, C. 2014: 41-53

    View details for DOI 10.1109/SC.2014.9

    View details for Web of Science ID 000393484400004

  • The role of ligands on the equilibria between functional States of a g protein-coupled receptor. Journal of the American Chemical Society Kim, T. H., Chung, K. Y., Manglik, A., Hansen, A. L., Dror, R. O., Mildorf, T. J., Shaw, D. E., Kobilka, B. K., Prosser, R. S. 2013; 135 (25): 9465-9474

    Abstract

    G protein-coupled receptors exhibit a wide variety of signaling behaviors in response to different ligands. When a small label was incorporated on the cytosolic interface of transmembrane helix 6 (Cys-265), (19)F NMR spectra of the β2 adrenergic receptor (β2AR) reconstituted in maltose/neopentyl glycol detergent micelles revealed two distinct inactive states, an activation intermediate state en route to activation, and, in the presence of a G protein mimic, a predominant active state. Analysis of the spectra as a function of temperature revealed that for all ligands, the activation intermediate is entropically favored and enthalpically disfavored. β2AR enthalpy changes toward activation are notably lower than those observed with rhodopsin, a likely consequence of basal activity and the fact that the ionic lock and other interactions stabilizing the inactive state of β2AR are weaker. Positive entropy changes toward activation likely reflect greater mobility (configurational entropy) in the cytoplasmic domain, as confirmed through an order parameter analysis. Ligands greatly influence the overall changes in enthalpy and entropy of the system and the corresponding changes in population and amplitude of motion of given states, suggesting a complex landscape of states and substates.

    View details for DOI 10.1021/ja404305k

    View details for PubMedID 23721409

  • Hardware Support for Fine-Grained Event-Driven Computation in Anton 2 ACM SIGPLAN NOTICES Grossman, J. P., Kuskin, J. S., Bank, J. A., Theobald, M., Dror, R. O., Ierardi, D. J., Larson, R. H., Ben Schafer, U., Towles, B., Young, C., Shaw, D. E. 2013; 48 (4): 549-560
  • The Dynamic Process of beta(2)-Adrenergic Receptor Activation CELL Nygaard, R., Zou, Y., Dror, R. O., Mildorf, T. J., Arlow, D. H., Manglik, A., Pan, A. C., Liu, C. W., Fung, J. J., Bokoch, M. P., Thian, F. S., Kobilka, T. S., Shaw, D. E., Mueller, L., Prosser, R. S., Kobilka, B. K. 2013; 152 (3): 532-542

    Abstract

    G-protein-coupled receptors (GPCRs) can modulate diverse signaling pathways, often in a ligand-specific manner. The full range of functionally relevant GPCR conformations is poorly understood. Here, we use NMR spectroscopy to characterize the conformational dynamics of the transmembrane core of the β(2)-adrenergic receptor (β(2)AR), a prototypical GPCR. We labeled β(2)AR with (13)CH(3)ε-methionine and obtained HSQC spectra of unliganded receptor as well as receptor bound to an inverse agonist, an agonist, and a G-protein-mimetic nanobody. These studies provide evidence for conformational states not observed in crystal structures, as well as substantial conformational heterogeneity in agonist- and inverse-agonist-bound preparations. They also show that for β(2)AR, unlike rhodopsin, an agonist alone does not stabilize a fully active conformation, suggesting that the conformational link between the agonist-binding pocket and the G-protein-coupling surface is not rigid. The observed heterogeneity may be important for β(2)AR's ability to engage multiple signaling and regulatory proteins.

    View details for DOI 10.1016/j.cell.2013.01.008

    View details for Web of Science ID 000314362800022

    View details for PubMedID 23374348

    View details for PubMedCentralID PMC3586676

  • The dynamic process of β2-adrenergic receptor activation Cell Nygaard, R., Zou, Y., Dror, R. O., Mildorf, T. J., Arlow, D. H., Manglik, A., Pan, A. C., Liu, C. W., Fung, J. J., Bokoch, M. P., Thian, F. S., Kobilka, T. S., Shaw, D. E., Mueller, L., Prosser, R. S., Kobilka, B. K. 2013: 532-542
  • Extending the generality of molecular dynamics simulations on a special-purpose machine IEEE 27TH INTERNATIONAL PARALLEL AND DISTRIBUTED PROCESSING SYMPOSIUM (IPDPS 2013) Scarpazza, D. P., Ierardi, D. J., Lerer, A. K., Mackenzie, K. M., Pan, A. C., Bank, J. A., Chow, E., Dror, R. O., Grossman, J. P., Killebrew, D., Moraes, M. A., Predescu, C., Salmon, J. K., Shaw, D. E. 2013: 933-945
  • Structural basis for modulation of a GPCR by allosteric drugs Nature Dror, R. O., Green, H. F., Valant, C., Borhani, D. W., Valcourt, J. R., Pan, A. C., Arlow, D. H., Canals, M., Lane, J. R., Rahmani, R., Baell, J. B., Sexton, P. M., Christopoulos, A., Shaw, D. E. 2013: 295-299
  • High-resolution crystal structure of human protease-activated receptor 1 NATURE Zhang, C., Srinivasan, Y., Arlow, D. H., Fung, J. J., Palmer, D., Zheng, Y., Green, H. F., Pandey, A., Dror, R. O., Shaw, D. E., Weis, W. I., Coughlin, S. R., Kobilka, B. K. 2012; 492 (7429): 387-?

    Abstract

    Protease-activated receptor 1 (PAR1) is the prototypical member of a family of G-protein-coupled receptors that mediate cellular responses to thrombin and related proteases. Thrombin irreversibly activates PAR1 by cleaving the amino-terminal exodomain of the receptor, which exposes a tethered peptide ligand that binds the heptahelical bundle of the receptor to affect G-protein activation. Here we report the 2.2 Å resolution crystal structure of human PAR1 bound to vorapaxar, a PAR1 antagonist. The structure reveals an unusual mode of drug binding that explains how a small molecule binds virtually irreversibly to inhibit receptor activation by the tethered ligand of PAR1. In contrast to deep, solvent-exposed binding pockets observed in other peptide-activated G-protein-coupled receptors, the vorapaxar-binding pocket is superficial but has little surface exposed to the aqueous solvent. Protease-activated receptors are important targets for drug development. The structure reported here will aid the development of improved PAR1 antagonists and the discovery of antagonists to other members of this receptor family.

    View details for DOI 10.1038/nature11701

    View details for Web of Science ID 000312488200047

    View details for PubMedID 23222541

    View details for PubMedCentralID PMC3531875

  • Refinement of protein structure homology models via long, all-atom molecular dynamics simulations PROTEINS-STRUCTURE FUNCTION AND BIOINFORMATICS Raval, A., Piana, S., Eastwood, M. P., Dror, R. O., Shaw, D. E. 2012; 80 (8): 2071-2079

    Abstract

    Accurate computational prediction of protein structure represents a longstanding challenge in molecular biology and structure-based drug design. Although homology modeling techniques are widely used to produce low-resolution models, refining these models to high resolution has proven difficult. With long enough simulations and sufficiently accurate force fields, molecular dynamics (MD) simulations should in principle allow such refinement, but efforts to refine homology models using MD have for the most part yielded disappointing results. It has thus far been unclear whether MD-based refinement is limited primarily by accessible simulation timescales, force field accuracy, or both. Here, we examine MD as a technique for homology model refinement using all-atom simulations, each at least 100 μs long-more than 100 times longer than previous refinement simulations-and a physics-based force field that was recently shown to successfully fold a structurally diverse set of fast-folding proteins. In MD simulations of 24 proteins chosen from the refinement category of recent Critical Assessment of Structure Prediction (CASP) experiments, we find that in most cases, simulations initiated from homology models drift away from the native structure. Comparison with simulations initiated from the native structure suggests that force field accuracy is the primary factor limiting MD-based refinement. This problem can be mitigated to some extent by restricting sampling to the neighborhood of the initial model, leading to structural improvement that, while limited, is roughly comparable to the leading alternative methods.

    View details for DOI 10.1002/prot.24098

    View details for Web of Science ID 000306132400014

    View details for PubMedID 22513870

  • Evaluating the Effects of Cutoffs and Treatment of Long-range Electrostatics in Protein Folding Simulations PLOS ONE Piana, S., Lindorff-Larsen, K., Dirks, R. M., Salmon, J. K., Dror, R. O., Shaw, D. E. 2012; 7 (6)

    Abstract

    The use of molecular dynamics simulations to provide atomic-level descriptions of biological processes tends to be computationally demanding, and a number of approximations are thus commonly employed to improve computational efficiency. In the past, the effect of these approximations on macromolecular structure and stability has been evaluated mostly through quantitative studies of small-molecule systems or qualitative observations of short-timescale simulations of biological macromolecules. Here we present a quantitative evaluation of two commonly employed approximations, using a test system that has been the subject of a number of previous protein folding studies--the villin headpiece. In particular, we examined the effect of (i) the use of a cutoff-based force-shifting technique rather than an Ewald summation for the treatment of electrostatic interactions, and (ii) the length of the cutoff used to determine how many pairwise interactions are included in the calculation of both electrostatic and van der Waals forces. Our results show that the free energy of folding is relatively insensitive to the choice of cutoff beyond 9 Å, and to whether an Ewald method is used to account for long-range electrostatic interactions. In contrast, we find that the structural properties of the unfolded state depend more strongly on the two approximations examined here.

    View details for DOI 10.1371/journal.pone.0039918

    View details for Web of Science ID 000305892100138

    View details for PubMedID 22768169

    View details for PubMedCentralID PMC3386949

  • Oncogenic Mutations Counteract Intrinsic Disorder in the EGFR Kinase and Promote Receptor Dimerization CELL Shan, Y., Eastwood, M. P., Zhang, X., Kim, E. T., Arkhipov, A., Dror, R. O., Jumper, J., Kuriyan, J., Shaw, D. E. 2012; 149 (4): 860-870

    Abstract

    The mutation and overexpression of the epidermal growth factor receptor (EGFR) are associated with the development of a variety of cancers, making this prototypical dimerization-activated receptor tyrosine kinase a prominent target of cancer drugs. Using long-timescale molecular dynamics simulations, we find that the N lobe dimerization interface of the wild-type EGFR kinase domain is intrinsically disordered and that it becomes ordered only upon dimerization. Our simulations suggest, moreover, that some cancer-linked mutations distal to the dimerization interface, particularly the widespread L834R mutation (also referred to as L858R), facilitate EGFR dimerization by suppressing this local disorder. Corroborating these findings, our biophysical experiments and kinase enzymatic assays indicate that the L834R mutation causes abnormally high activity primarily by promoting EGFR dimerization rather than by allowing activation without dimerization. We also find that phosphorylation of EGFR kinase domain at Tyr845 may suppress the intrinsic disorder, suggesting a molecular mechanism for autonomous EGFR signaling.

    View details for DOI 10.1016/j.cell.2012.02.063

    View details for Web of Science ID 000303934700018

    View details for PubMedID 22579287

  • Structure and dynamics of the M3 muscarinic acetylcholine receptor NATURE Kruse, A. C., Hu, J., Pan, A. C., Arlow, D. H., Rosenbaum, D. M., Rosemond, E., Green, H. F., Liu, T., Chae, P. S., Dror, R. O., Shaw, D. E., Weis, W. I., Wess, J., Kobilka, B. K. 2012; 482 (7386): 552-556

    Abstract

    Acetylcholine, the first neurotransmitter to be identified, exerts many of its physiological actions via activation of a family of G-protein-coupled receptors (GPCRs) known as muscarinic acetylcholine receptors (mAChRs). Although the five mAChR subtypes (M1-M5) share a high degree of sequence homology, they show pronounced differences in G-protein coupling preference and the physiological responses they mediate. Unfortunately, despite decades of effort, no therapeutic agents endowed with clear mAChR subtype selectivity have been developed to exploit these differences. We describe here the structure of the G(q/11)-coupled M3 mAChR ('M3 receptor', from rat) bound to the bronchodilator drug tiotropium and identify the binding mode for this clinically important drug. This structure, together with that of the G(i/o)-coupled M2 receptor, offers possibilities for the design of mAChR subtype-selective ligands. Importantly, the M3 receptor structure allows a structural comparison between two members of a mammalian GPCR subfamily displaying different G-protein coupling selectivities. Furthermore, molecular dynamics simulations suggest that tiotropium binds transiently to an allosteric site en route to the binding pocket of both receptors. These simulations offer a structural view of an allosteric binding mode for an orthosteric GPCR ligand and provide additional opportunities for the design of ligands with different affinities or binding kinetics for different mAChR subtypes. Our findings not only offer insights into the structure and function of one of the most important GPCR families, but may also facilitate the design of improved therapeutics targeting these critical receptors.

    View details for DOI 10.1038/nature10867

    View details for Web of Science ID 000300770500056

    View details for PubMedID 22358844

    View details for PubMedCentralID PMC3529910

  • Systematic Validation of Protein Force Fields against Experimental Data PLOS ONE Lindorff-Larsen, K., Maragakis, P., Piana, S., Eastwood, M. P., Dror, R. O., Shaw, D. E. 2012; 7 (2)

    Abstract

    Molecular dynamics simulations provide a vehicle for capturing the structures, motions, and interactions of biological macromolecules in full atomic detail. The accuracy of such simulations, however, is critically dependent on the force field--the mathematical model used to approximate the atomic-level forces acting on the simulated molecular system. Here we present a systematic and extensive evaluation of eight different protein force fields based on comparisons of experimental data with molecular dynamics simulations that reach a previously inaccessible timescale. First, through extensive comparisons with experimental NMR data, we examined the force fields' abilities to describe the structure and fluctuations of folded proteins. Second, we quantified potential biases towards different secondary structure types by comparing experimental and simulation data for small peptides that preferentially populate either helical or sheet-like structures. Third, we tested the force fields' abilities to fold two small proteins--one α-helical, the other with β-sheet structure. The results suggest that force fields have improved over time, and that the most recent versions, while not perfect, provide an accurate description of many structural and dynamical properties of proteins.

    View details for DOI 10.1371/journal.pone.0032131

    View details for Web of Science ID 000302875500077

    View details for PubMedID 22384157

    View details for PubMedCentralID PMC3285199

  • Biomolecular Simulation: A Computational Microscope for Molecular Biology ANNUAL REVIEW OF BIOPHYSICS, VOL 41 Dror, R. O., Dirks, R. M., Grossman, J. P., Xu, H., Shaw, D. E. 2012; 41: 429-452

    Abstract

    Molecular dynamics simulations capture the behavior of biological macromolecules in full atomic detail, but their computational demands, combined with the challenge of appropriately modeling the relevant physics, have historically restricted their length and accuracy. Dramatic recent improvements in achievable simulation speed and the underlying physical models have enabled atomic-level simulations on timescales as long as milliseconds that capture key biochemical processes such as protein folding, drug binding, membrane transport, and the conformational changes critical to protein function. Such simulation may serve as a computational microscope, revealing biomolecular mechanisms at spatial and temporal scales that are difficult to observe experimentally. We describe the rapidly evolving state of the art for atomic-level biomolecular simulation, illustrate the types of biological discoveries that can now be made through simulation, and discuss challenges motivating continued innovation in this field.

    View details for DOI 10.1146/annurev-biophys-042910-155245

    View details for Web of Science ID 000307955100020

    View details for PubMedID 22577825

  • Computationally efficient molecular dynamics integrators with improved sampling accuracy MOLECULAR PHYSICS Predescu, C., Lippert, R. A., Eastwood, M. P., Ierardi, D., Xu, H., Jensen, M. O., Bowers, K. J., Gullingsrud, J., Rendleman, C. A., Dror, R. O., Shaw, D. E. 2012; 110 (9-10): 967-983
  • Mechanism of voltage gating in K+ channels Science Jensen, M. O., Jogini, V., Borhani, D. W., Lefler, A. E., Dror, R. O., Shaw, D. E. 2012: 229-233
  • How Fast-Folding Proteins Fold SCIENCE Lindorff-Larsen, K., Piana, S., Dror, R. O., Shaw, D. E. 2011; 334 (6055): 517-520

    Abstract

    An outstanding challenge in the field of molecular biology has been to understand the process by which proteins fold into their characteristic three-dimensional structures. Here, we report the results of atomic-level molecular dynamics simulations, over periods ranging between 100 μs and 1 ms, that reveal a set of common principles underlying the folding of 12 structurally diverse proteins. In simulations conducted with a single physics-based energy function, the proteins, representing all three major structural classes, spontaneously and repeatedly fold to their experimentally determined native structures. Early in the folding process, the protein backbone adopts a nativelike topology while certain secondary structure elements and a small number of nonlocal contacts form. In most cases, folding follows a single dominant route in which elements of the native structure appear in an order highly correlated with their propensity to form in the unfolded state.

    View details for DOI 10.1126/science.1208351

    View details for Web of Science ID 000296230500048

    View details for PubMedID 22034434

  • Pathway and mechanism of drug binding to G-protein-coupled receptors PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Dror, R. O., Pan, A. C., Arlow, D. H., Borhani, D. W., Maragakis, P., Shan, Y., Xu, H., Shaw, D. E. 2011; 108 (32): 13118-13123

    Abstract

    How drugs bind to their receptors--from initial association, through drug entry into the binding pocket, to adoption of the final bound conformation, or "pose"--has remained unknown, even for G-protein-coupled receptor modulators, which constitute one-third of all marketed drugs. We captured this pharmaceutically critical process in atomic detail using the first unbiased molecular dynamics simulations in which drug molecules spontaneously associate with G-protein-coupled receptors to achieve final poses matching those determined crystallographically. We found that several beta blockers and a beta agonist all traverse the same well-defined, dominant pathway as they bind to the β(1)- and β(2)-adrenergic receptors, initially making contact with a vestibule on each receptor's extracellular surface. Surprisingly, association with this vestibule, at a distance of 15 Å from the binding pocket, often presents the largest energetic barrier to binding, despite the fact that subsequent entry into the binding pocket requires the receptor to deform and the drug to squeeze through a narrow passage. The early barrier appears to reflect the substantial dehydration that takes place as the drug associates with the vestibule. Our atomic-level description of the binding process suggests opportunities for allosteric modulation and provides a structural foundation for future optimization of drug-receptor binding and unbinding rates.

    View details for DOI 10.1073/pnas.1104614108

    View details for Web of Science ID 000293691400036

    View details for PubMedID 21778406

    View details for PubMedCentralID PMC3156183

  • How Does a Drug Molecule Find Its Target Binding Site? JOURNAL OF THE AMERICAN CHEMICAL SOCIETY Shan, Y., Kim, E. T., Eastwood, M. P., Dror, R. O., Seeliger, M. A., Shaw, D. E. 2011; 133 (24): 9181-9183

    Abstract

    Although the thermodynamic principles that control the binding of drug molecules to their protein targets are well understood, detailed experimental characterization of the process by which such binding occurs has proven challenging. We conducted relatively long, unguided molecular dynamics simulations in which a ligand (the cancer drug dasatinib or the kinase inhibitor PP1) was initially placed at a random location within a box that also contained a protein (Src kinase) to which that ligand was known to bind. In several of these simulations, the ligand correctly identified its target binding site, forming a complex virtually identical to the crystallographically determined bound structure. The simulated trajectories provide a continuous, atomic-level view of the entire binding process, revealing persistent and noteworthy intermediate conformations and shedding light on the role of water molecules. The technique we employed, which does not assume any prior knowledge of the binding site's location, may prove particularly useful in the development of allosteric inhibitors that target previously undiscovered binding sites.

    View details for DOI 10.1021/ja202726y

    View details for Web of Science ID 000291915100013

    View details for PubMedID 21545110

    View details for PubMedCentralID PMC3221467

  • OVERCOMING COMMUNICATION LATENCY BARRIERS IN MASSIVELY PARALLEL SCIENTIFIC COMPUTATION IEEE MICRO Dror, R. O., Grossman, J. P., Mackenzie, K. M., Towles, B., Chow, E., Salmon, J. K., Young, C., Bank, J. A., Batson, B., Deneroff, M. M., Kuskin, J. S., Larson, R. H., Moraes, M. A., Shaw, D. E. 2011; 31 (3): 8-19
  • Structure and function of an irreversible agonist-beta(2) adrenoceptor complex NATURE Rosenbaum, D. M., Zhang, C., Lyons, J. A., Holl, R., Aragao, D., Arlow, D. H., Rasmussen, S. G., Choi, H., DeVree, B. T., Sunahara, R. K., Chae, P. S., Gellman, S. H., Dror, R. O., Shaw, D. E., Weis, W. I., Caffrey, M., Gmeiner, P., Kobilka, B. K. 2011; 469 (7329): 236-240

    Abstract

    G-protein-coupled receptors (GPCRs) are eukaryotic integral membrane proteins that modulate biological function by initiating cellular signalling in response to chemically diverse agonists. Despite recent progress in the structural biology of GPCRs, the molecular basis for agonist binding and allosteric modulation of these proteins is poorly understood. Structural knowledge of agonist-bound states is essential for deciphering the mechanism of receptor activation, and for structure-guided design and optimization of ligands. However, the crystallization of agonist-bound GPCRs has been hampered by modest affinities and rapid off-rates of available agonists. Using the inactive structure of the human β(2) adrenergic receptor (β(2)AR) as a guide, we designed a β(2)AR agonist that can be covalently tethered to a specific site on the receptor through a disulphide bond. The covalent β(2)AR-agonist complex forms efficiently, and is capable of activating a heterotrimeric G protein. We crystallized a covalent agonist-bound β(2)AR-T4L fusion protein in lipid bilayers through the use of the lipidic mesophase method, and determined its structure at 3.5 Å resolution. A comparison to the inactive structure and an antibody-stabilized active structure (companion paper) shows how binding events at both the extracellular and intracellular surfaces are required to stabilize an active conformation of the receptor. The structures are in agreement with long-timescale (up to 30 μs) molecular dynamics simulations showing that an agonist-bound active conformation spontaneously relaxes to an inactive-like conformation in the absence of a G protein or stabilizing antibody.

    View details for DOI 10.1038/nature09665

    View details for Web of Science ID 000286143400043

    View details for PubMedID 21228876

    View details for PubMedCentralID PMC3074335

  • Activation mechanism of the β2-adrenergic receptor Proceedings of the National Academy of Sciences of the United States of America Dror, R. O., Arlow, D. H., Maragakis, P., Mildorf, T. J., Pan, A. C., Xu, H., Borhani, D. W., Shaw, D. E. 2011: 18684-18689
  • Radix-8 Digit-by-Rounding: Achieving High-Performance Reciprocals, Square Roots, and Reciprocal Square Roots 2011 20TH IEEE SYMPOSIUM ON COMPUTER ARITHMETIC (ARITH-20) Butts, J. A., Tang, P. T., Dror, R. O., Shaw, D. E. 2011: 149-158
  • Structure and function of an irreversible agonist–β2 adrenoceptor complex Nature Rosenbaum, D. M., Zhang, C., Lyons, J. A., Holl, R., Aragao, D., Arlow, D. H., Rasmussen, S. F., Choi, H. J., DeVree, B. T., Sunahara, R. K., Chae, P. S., Gellman, S. H., Dror, R. O., Shaw, D. E., Weis, W. I., Caffrey, M., Gmeiner, P., Kobilka, B. K. 2011: 236-240
  • Atomic-Level Characterization of the Structural Dynamics of Proteins SCIENCE Shaw, D. E., Maragakis, P., Lindorff-Larsen, K., Piana, S., Dror, R. O., Eastwood, M. P., Bank, J. A., Jumper, J. M., Salmon, J. K., Shan, Y., Wriggers, W. 2010; 330 (6002): 341-346

    Abstract

    Molecular dynamics (MD) simulations are widely used to study protein motions at an atomic level of detail, but they have been limited to time scales shorter than those of many biologically critical conformational changes. We examined two fundamental processes in protein dynamics--protein folding and conformational change within the folded state--by means of extremely long all-atom MD simulations conducted on a special-purpose machine. Equilibrium simulations of a WW protein domain captured multiple folding and unfolding events that consistently follow a well-defined folding pathway; separate simulations of the protein's constituent substructures shed light on possible determinants of this pathway. A 1-millisecond simulation of the folded protein BPTI reveals a small number of structurally distinct conformational states whose reversible interconversion is slower than local relaxations within those states by a factor of more than 1000.

    View details for DOI 10.1126/science.1187409

    View details for Web of Science ID 000282986700033

    View details for PubMedID 20947758

  • Equipartition and the Calculation of Temperature in Biomolecular Simulations JOURNAL OF CHEMICAL THEORY AND COMPUTATION Eastwood, M. P., Stafford, K. A., Lippert, R. A., Jensen, M. O., Maragakis, P., Predescu, C., Dror, R. O., Shaw, D. E. 2010; 6 (7): 2045-2058

    Abstract

    Since the behavior of biomolecules can be sensitive to temperature, the ability to accurately calculate and control the temperature in molecular dynamics (MD) simulations is important. Standard analysis of equilibrium MD simulations-even constant-energy simulations with negligible long-term energy drift-often yields different calculated temperatures for different motions, however, in apparent violation of the statistical mechanical principle of equipartition of energy. Although such analysis provides a valuable warning that other simulation artifacts may exist, it leaves the actual value of the temperature uncertain. We observe that Tolman's generalized equipartition theorem should hold for long stable simulations performed using velocity-Verlet or other symplectic integrators, because the simulated trajectory is thought to sample almost exactly from a continuous trajectory generated by a shadow Hamiltonian. From this we conclude that all motions should share a single simulation temperature, and we provide a new temperature estimator that we test numerically in simulations of a diatomic fluid and of a solvated protein. Apparent temperature variations between different motions observed using standard estimators do indeed disappear when using the new estimator. We use our estimator to better understand how thermostats and barostats can exacerbate integration errors. In particular, we find that with large (albeit widely used) time steps, the common practice of using two thermostats to remedy so-called hot solvent-cold solute problems can have the counterintuitive effect of causing temperature imbalances. Our results, moreover, highlight the utility of multiple-time step integrators for accurate and efficient simulation.

    View details for DOI 10.1021/ct9002916

    View details for Web of Science ID 000279751500014

    View details for PubMedID 26615934

  • Exploring atomic resolution physiology on a femtosecond to millisecond timescale using molecular dynamics simulations JOURNAL OF GENERAL PHYSIOLOGY Dror, R. O., Jensen, M. O., Borhani, D. W., Shaw, D. E. 2010; 135 (6): 555-562

    View details for DOI 10.1085/jgp.200910373

    View details for Web of Science ID 000278186500003

    View details for PubMedID 20513757

    View details for PubMedCentralID PMC2888062

  • Improved side-chain torsion potentials for the Amber ff99SB protein force field PROTEINS-STRUCTURE FUNCTION AND BIOINFORMATICS Lindorff-Larsen, K., Piana, S., Palmo, K., Maragakis, P., Klepeis, J. L., Dror, R. O., Shaw, D. E. 2010; 78 (8): 1950-1958

    Abstract

    Recent advances in hardware and software have enabled increasingly long molecular dynamics (MD) simulations of biomolecules, exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, we further advance simulation accuracy by improving the amino acid side-chain torsion potentials of the Amber ff99SB force field. First, we used simulations of model alpha-helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, we optimized the side-chain torsion potentials of these residues to match new, high-level quantum-mechanical calculations. Finally, we used microsecond-timescale MD simulations in explicit solvent to validate the resulting force field against a large set of experimental NMR measurements that directly probe side-chain conformations. The new force field, which we have termed Amber ff99SB-ILDN, exhibits considerably better agreement with the NMR data.

    View details for DOI 10.1002/prot.22711

    View details for Web of Science ID 000277767700012

    View details for PubMedID 20408171

    View details for PubMedCentralID PMC2970904

  • Principles of conduction and hydrophobic gating in K+ channels PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Jensen, M. O., Borhani, D. W., Lindorff-Larsen, K., Maragakis, P., Jogini, V., Eastwood, M. P., Dror, R. O., Shaw, D. E. 2010; 107 (13): 5833-5838

    Abstract

    We present the first atomic-resolution observations of permeation and gating in a K(+) channel, based on molecular dynamics simulations of the Kv1.2 pore domain. Analysis of hundreds of simulated permeation events revealed a detailed conduction mechanism, resembling the Hodgkin-Keynes "knock-on" model, in which translocation of two selectivity filter-bound ions is driven by a third ion; formation of this knock-on intermediate is rate determining. In addition, at reverse or zero voltages, we observed pore closure by a novel "hydrophobic gating" mechanism: A dewetting transition of the hydrophobic pore cavity-fastest when K(+) was not bound in selectivity filter sites nearest the cavity-caused the open, conducting pore to collapse into a closed, nonconducting conformation. Such pore closure corroborates the idea that voltage sensors can act to prevent pore collapse into the intrinsically more stable, closed conformation, and it further suggests that molecular-scale dewetting facilitates a specific biological function: K(+) channel gating. Existing experimental data support our hypothesis that hydrophobic gating may be a fundamental principle underlying the gating of voltage-sensitive K(+) channels. We suggest that hydrophobic gating explains, in part, why diverse ion channels conserve hydrophobic pore cavities, and we speculate that modulation of cavity hydration could enable structural determination of both open and closed channels.

    View details for DOI 10.1073/pnas.0911691107

    View details for Web of Science ID 000276159500027

    View details for PubMedID 20231479

    View details for PubMedCentralID PMC2851896

  • Improved Twiddle Access for Fast Fourier Transforms IEEE TRANSACTIONS ON SIGNAL PROCESSING Bowers, K. J., Lippert, R. A., Dror, R. O., Shaw, D. E. 2010; 58 (3): 1122-1130
  • Automated Event Detection and Activity Monitoring in Long Molecular Dynamics Simulations JOURNAL OF CHEMICAL THEORY AND COMPUTATION Wriggers, W., Stafford, K. A., Shan, Y., Piana, S., Maragakis, P., Lindorff-Larsen, K., Miller, P. J., Gullingsrud, J., Rendleman, C. A., Eastwood, M. P., Dror, R. O., Shaw, D. E. 2009; 5 (10): 2595-2605

    Abstract

    Events of scientific interest in molecular dynamics (MD) simulations, including conformational changes, folding transitions, and translocations of ligands and reaction products, often correspond to high-level structural rearrangements that alter contacts between molecules or among different parts of a molecule. Due to advances in computer architecture and software, MD trajectories representing such structure-changing events have become easier to generate, but the length of these trajectories poses a challenge to scientific interpretation and analysis. In this paper, we present automated methods for the detection of potentially important structure-changing events in long MD trajectories. In contrast with traditional tools for the analysis of such trajectories, our methods provide a detailed report of broken and formed contacts that aids in the identification of specific time-dependent side-chain interactions. Our approach employs a coarse-grained representation of amino acid side chains, a contact metric based on higher order generalizations of Delaunay tetrahedralization, techniques for detecting significant shifts in the resulting contact time series, and a new kernel-based measure of contact alteration activity. The analysis methods we describe are incorporated in a newly developed package, called TimeScapes, which is freely available and compatible with trajectories generated by a variety of popular MD programs. Tests based on actual microsecond time scale simulations demonstrate that the package can be used to efficiently detect and characterize important conformational changes in realistic protein systems.

    View details for DOI 10.1021/ct900229u

    View details for Web of Science ID 000270595800003

    View details for PubMedID 26631775

  • Minimizing thermodynamic length to select intermediate states for free-energy calculations and replica-exchange simulations (vol 80, 046705, 2009) PHYSICAL REVIEW E Shenfeld, D. K., Xu, H., Eastwood, M. P., Dror, R. O., Shaw, D. E. 2009; 80 (4)
  • Long-timescale molecular dynamics simulations of protein structure and function CURRENT OPINION IN STRUCTURAL BIOLOGY Klepeis, J. L., Lindorff-Larsen, K., Dror, R. O., Shaw, D. E. 2009; 19 (2): 120-127

    Abstract

    Molecular dynamics simulations allow for atomic-level characterization of biomolecular processes such as the conformational transitions associated with protein function. The computational demands of such simulations, however, have historically prevented them from reaching the microsecond and greater timescales on which these events often occur. Recent advances in algorithms, software, and computer hardware have made microsecond-timescale simulations with tens of thousands of atoms practical, with millisecond-timescale simulations on the horizon. This review outlines these advances in high-performance molecular dynamics simulation and discusses recent applications to studies of protein dynamics and function as well as experimental validation of the underlying computational models.

    View details for DOI 10.1016/j.sbi.2009.03.004

    View details for Web of Science ID 000266114000002

    View details for PubMedID 19361980

  • A conserved protonation-dependent switch controls drug binding in the Abl kinase PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Shan, Y., Seeliger, M. A., Eastwood, M. P., Frank, F., Xu, H., Jensen, M. O., Dror, R. O., Kuriyan, J., Shaw, D. E. 2009; 106 (1): 139-144

    Abstract

    In many protein kinases, a characteristic conformational change (the "DFG flip") connects catalytically active and inactive conformations. Many kinase inhibitors--including the cancer drug imatinib--selectively target a specific DFG conformation, but the function and mechanism of the flip remain unclear. Using long molecular dynamics simulations of the Abl kinase, we visualized the DFG flip in atomic-level detail and formulated an energetic model predicting that protonation of the DFG aspartate controls the flip. Consistent with our model's predictions, we demonstrated experimentally that the kinetics of imatinib binding to Abl kinase have a pH dependence that disappears when the DFG aspartate is mutated. Our model suggests a possible explanation for the high degree of conservation of the DFG motif: that the flip, modulated by electrostatic changes inherent to the catalytic cycle, allows the kinase to access flexible conformations facilitating nucleotide binding and release.

    View details for DOI 10.1073/pnas.0811223106

    View details for Web of Science ID 000262263900028

    View details for PubMedID 19109437

    View details for PubMedCentralID PMC2610013

  • . Identification of two distinct inactive conformations of the β2-adrenergic receptor reconciles structural and biochemical observations Proceedings of the National Academy of Sciences of the United States of America Dror, R. O., Arlow, D. H., Borhani, D. W., Jensen, M. O., Piana, S., Shaw, D. E. 2009: 4689-4694
  • Elucidating membrane protein function through long-timescale molecular dynamics simulation 2009 ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY, VOLS 1-20 Dror, R. O., Jensen, M. O., Shaw, D. E. 2009: 2340-2342

    Abstract

    Recent advances in algorithms, software, and hardware for molecular dynamics (MD) simulations have brought previously inaccessible simulation timescales within reach, allowing the use of MD simulation to address a substantially broader set of questions regarding protein function. MD has proved particularly useful in elucidating the functional mechanisms of membrane proteins, whose dynamics are especially difficult to characterize experimentally. Here, we illustrate the utility of state-of-the-art high-performance MD simulations in the study of membrane proteins, using as examples a G-protein-coupled receptor, an aquaporin, and an antiporter. In each case, we used MD either to deduce an atomic-level mechanism for protein function or to reconcile apparent discrepancies among recent experimental observations.

    View details for Web of Science ID 000280543601319

    View details for PubMedID 19965181

  • Dynamic control of slow water transport by aquaporin 0: Implications for hydration and junction stability in the eye lens PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Jensen, M. O., Dror, R. O., Xu, H., Borhani, D. W., Arkin, I. T., Eastwood, M. P., Shaw, D. E. 2008; 105 (38): 14430-14435

    Abstract

    Aquaporin 0 (AQP0), the most abundant membrane protein in mammalian lens fiber cells, not only serves as the primary water channel in this tissue but also appears to mediate the formation of thin junctions between fiber cells. AQP0 is remarkably less water permeable than other aquaporins, but the structural basis and biological significance of this low permeability remain uncertain, as does the permeability of the protein in a reported junctional form. To address these issues, we performed molecular dynamics (MD) simulations of water transport through membrane-embedded AQP0 in both its (octameric) junctional and (tetrameric) nonjunctional forms. From our simulations, we measured an osmotic permeability for the nonjunctional form that agrees with experiment and found that the distinct dynamics of the conserved, lumen-protruding side chains of Tyr-23 and Tyr-149 modulate water passage, accounting for the slow permeation. The junctional and nonjunctional forms conducted water equivalently, in contrast to a previous suggestion based on static crystal structures that water conduction is lost on junction formation. Our analysis suggests that the low water permeability of AQP0 may help maintain the mechanical stability of the junction. We hypothesize that the structural features leading to low permeability may have evolved in part to allow AQP0 to form junctions that both conduct water and contribute to the organizational structure of the fiber cell tissue and microcirculation within it, as required to maintain transparency of the lens.

    View details for DOI 10.1073/pnas.0802401105

    View details for Web of Science ID 000259592400038

    View details for PubMedID 18787121

    View details for PubMedCentralID PMC2533686

  • Anton, a special-purpose machine for molecular dynamics simulation COMMUNICATIONS OF THE ACM Shaw, D. E., Deneroff, M. M., Dror, R. O., Kuskin, J. S., Larson, R. H., Salmon, J. K., Young, C., Batson, B., Bowers, K. J., Chao, J. C., Eastwood, M. P., Gagliardo, J., Grossman, J. P., Ho, C. R., Ierardi, D. J., Kolossvary, I., Klepeis, J. L., Layman, T., Mcleavey, C., Moraes, M. A., Mueller, R., Priest, E. C., Shan, Y., Spengler, J., Theobald, M., Towles, B., Wang, S. C. 2008; 51 (7): 91-97
  • Microsecond molecular dynamics simulation shows effect of slow loop dynamics on backbone amide order parameters of proteins JOURNAL OF PHYSICAL CHEMISTRY B Maragakis, P., Lindorff-Larsen, K., Eastwood, M. P., Dror, R. O., Klepeis, J. L., Arkin, I. T., Jensen, M. O., Xu, H., Trbovic, N., Friesner, R. A., Palmer, A. G., Shaw, D. E. 2008; 112 (19): 6155-6158

    Abstract

    A molecular-level understanding of the function of a protein requires knowledge of both its structural and dynamic properties. NMR spectroscopy allows the measurement of generalized order parameters that provide an atomistic description of picosecond and nanosecond fluctuations in protein structure. Molecular dynamics (MD) simulation provides a complementary approach to the study of protein dynamics on similar time scales. Comparisons between NMR spectroscopy and MD simulations can be used to interpret experimental results and to improve the quality of simulation-related force fields and integration methods. However, apparent systematic discrepancies between order parameters extracted from simulations and experiments are common, particularly for elements of noncanonical secondary structure. In this paper, results from a 1.2 micros explicit solvent MD simulation of the protein ubiquitin are compared with previously determined backbone order parameters derived from NMR relaxation experiments [Tjandra, N.; Feller, S. E.; Pastor, R. W.; Bax, A. J. Am. Chem. Soc. 1995, 117, 12562-12566]. The simulation reveals fluctuations in three loop regions that occur on time scales comparable to or longer than that of the overall rotational diffusion of ubiquitin and whose effects would not be apparent in experimentally derived order parameters. A coupled analysis of internal and overall motion yields simulated order parameters substantially closer to the experimentally determined values than is the case for a conventional analysis of internal motion alone. Improved agreement between simulation and experiment also is encouraging from the viewpoint of assessing the accuracy of long MD simulations.

    View details for DOI 10.1021/jp077018h

    View details for Web of Science ID 000255649600033

    View details for PubMedID 18311962

    View details for PubMedCentralID PMC2805408

  • Hierarchical Simulation-Based Verification of Anton, a Special-Purpose Parallel Machine 2008 IEEE INTERNATIONAL CONFERENCE ON COMPUTER DESIGN Grossman, J. P., Salmon, J. K., Ho, C. R., Ierardi, D. J., Towles, B., Batson, B., Spengler, J., Wang, S. C., Mueller, R., Theobald, M., Young, C., Gagliardo, J., Deneroff, M. M., Dror, R. O., Shaw, D. E. 2008: 340-347
  • Incorporating Flexibility in Anton, a Specialized Machine for Molecular Dynamics Simulation 2008 IEEE 14TH INTERNATIONAL SYMPOSIUM ON HIGH PEFORMANCE COMPUTER ARCHITECTURE Kuskin, J. S., Young, C., Grossman, J. P., Batson, B., Deneroff, M. M., Dror, R. O., Shaw, D. E. 2008: 315-326
  • High-Throughput Pairwise Point Interactions in Anton, a Specialized Machine for Molecular Dynamics Simulation 2008 IEEE 14TH INTERNATIONAL SYMPOSIUM ON HIGH PEFORMANCE COMPUTER ARCHITECTURE Larson, R. H., Salmon, J. K., Dror, R. O., Deneroff, M. M., Young, C., Grossman, J. P., Shan, Y., Klepeis, J. L., Shaw, D. E. 2008: 303-314
  • Mechanism of Na+/H+ antiporting SCIENCE Arkin, I. T., Xu, H., Jensen, M. O., Arbely, E., Bennett, E. R., Bowers, K. J., Chow, E., Dror, R. O., Eastwood, M. P., Flitman-Tene, R., Gregersen, B. A., Klepeis, J. L., Kolossvary, I., Shan, Y., Shaw, D. E. 2007; 317 (5839): 799-803

    Abstract

    Na+/H+ antiporters are central to cellular salt and pH homeostasis. The structure of Escherichia coli NhaA was recently determined, but its mechanisms of transport and pH regulation remain elusive. We performed molecular dynamics simulations of NhaA that, with existing experimental data, enabled us to propose an atomically detailed model of antiporter function. Three conserved aspartates are key to our proposed mechanism: Asp164 (D164) is the Na+-binding site, D163 controls the alternating accessibility of this binding site to the cytoplasm or periplasm, and D133 is crucial for pH regulation. Consistent with experimental stoichiometry, two protons are required to transport a single Na+ ion: D163 protonates to reveal the Na+-binding site to the periplasm, and subsequent protonation of D164 releases Na+. Additional mutagenesis experiments further validated the model.

    View details for DOI 10.1126/science.1142824

    View details for Web of Science ID 000248624500039

    View details for PubMedID 17690293

  • A common, avoidable source of error in molecular dynamics integrators JOURNAL OF CHEMICAL PHYSICS Lippert, R. A., Bowers, K. J., Dror, R. O., Eastwood, M. P., Gregersen, B. A., Klepeis, J. L., Kolossvary, I., Shaw, D. E. 2007; 126 (4)

    View details for DOI 10.1063/1.2431176

    View details for Web of Science ID 000243891100069

    View details for PubMedID 17286520

  • Zonal methods for the parallel execution of range-limited N-body simulations JOURNAL OF COMPUTATIONAL PHYSICS Bowers, K. J., Dror, R. O., Shaw, D. E. 2007; 221 (1): 303-329
  • The midpoint method for parallelization of particle simulations JOURNAL OF CHEMICAL PHYSICS Bowers, K. J., Dror, R. O., Shaw, D. E. 2006; 124 (18)

    Abstract

    The evaluation of interactions between nearby particles constitutes the majority of the computational workload involved in classical molecular dynamics (MD) simulations. In this paper, we introduce a new method for the parallelization of range-limited particle interactions that proves particularly suitable to MD applications. Because it applies not only to pairwise interactions but also to interactions involving three or more particles, the method can be used for evaluation of both nonbonded and bonded forces in a MD simulation. It requires less interprocessor data transfer than traditional spatial decomposition methods at all but the lowest levels of parallelism. It gains an additional practical advantage in certain commonly used interprocessor communication networks by distributing the communication burden more evenly across network links and by decreasing the associated latency. When used to parallelize MD, it further reduces communication requirements by allowing the computations associated with short-range nonbonded interactions, long-range electrostatics, bonded interactions, and particle migration to use much of the same communicated data. We also introduce certain variants of this method that can significantly improve the balance of computational load across processors.

    View details for DOI 10.1063/1.2191489

    View details for Web of Science ID 000237477800011

    View details for PubMedID 16709099

  • Gaussian split Ewald: A fast Ewald mesh method for molecular simulation JOURNAL OF CHEMICAL PHYSICS Shan, Y. B., Klepeis, J. L., Eastwood, M. P., Dror, R. O., Shaw, D. E. 2005; 122 (5)

    Abstract

    Gaussian split Ewald (GSE) is a versatile Ewald mesh method that is fast and accurate when used with both real-space and k-space Poisson solvers. While real-space methods are known to be asymptotically superior to k-space methods in terms of both computational cost and parallelization efficiency, k-space methods such as smooth particle-mesh Ewald (SPME) have thus far remained dominant because they have been more efficient than existing real-space methods for simulations of typical systems in the size range of current practical interest. Real-space GSE, however, is approximately a factor of 2 faster than previously described real-space Ewald methods for the level of force accuracy typically required in biomolecular simulations, and is competitive with leading k-space methods even for systems of moderate size. Alternatively, GSE may be combined with a k-space Poisson solver, providing a conveniently tunable k-space method that performs comparably to SPME. The GSE method follows naturally from a uniform framework that we introduce to concisely describe the differences between existing Ewald mesh methods.

    View details for DOI 10.1063/1.1839571

    View details for Web of Science ID 000226880100002

    View details for PubMedID 15740304

  • Statistical characterization of real-world illumination JOURNAL OF VISION Dror, R., WILLSKY, A. S., Adelson, E. H. 2004; 4 (9): 821-837

    Abstract

    Although studies of vision and graphics often assume simple illumination models, real-world illumination is highly complex, with reflected light incident on a surface from almost every direction. One can capture the illumination from every direction at one point photographically using a spherical illumination map. This work illustrates, through analysis of photographically acquired, high dynamic range illumination maps, that real-world illumination possesses a high degree of statistical regularity. The marginal and joint wavelet coefficient distributions and harmonic spectra of illumination maps resemble those documented in the natural image statistics literature. However, illumination maps differ from typical photographs in that illumination maps are statistically nonstationary and may contain localized light sources that dominate their power spectra. Our work provides a foundation for statistical models of real-world illumination, thereby facilitating the understanding of human material perception, the design of robust computer vision systems, and the rendering of realistic computer graphics imagery.

    View details for DOI 10.1167/4.9.11

    View details for Web of Science ID 000224835300012

    View details for PubMedID 15493972

  • Bayesian estimation of transcript levels using a general model of array measurement noise JOURNAL OF COMPUTATIONAL BIOLOGY Dror, R. O., Murnick, J. G., Rinaldi, N. J., Marinescu, V. D., Rifkin, R. M., Young, R. A. 2003; 10 (3-4): 433-452

    Abstract

    Gene arrays demonstrate a promising ability to characterize expression levels across the entire genome but suffer from significant levels of measurement noise. We present a rigorous new approach to estimate transcript levels and ratios from one or more gene array experiments, given a model of measurement noise and available prior information. The Bayesian estimation of array measurements (BEAM) technique provides a principled method to identify changes in expression level, combine repeated measurements, or deal with negative expression level measurements. BEAM is more flexible than existing techniques, because it does not assume a specific functional form for noise and prior models. Instead, it relies on computational techniques that apply to a broad range of models. We use Affymetrix yeast chip data to illustrate the process of developing accurate noise and prior models from existing experimental data. The resulting noise model includes novel features such as heavy-tailed additive noise and a gene-specific bias term. We also verify that the resulting noise and prior models fit data from an Affymetrix human chip set.

    View details for Web of Science ID 000184535800013

    View details for PubMedID 12935337

  • Real-world illumination and the perception of surface reflectance properties JOURNAL OF VISION Fleming, R. W., Dror, R. O., Adelson, E. H. 2003; 3 (5): 347-368

    Abstract

    Under typical viewing conditions, we find it easy to distinguish between different materials, such as metal, plastic, and paper. Recognizing materials from their surface reflectance properties (such as lightness and gloss) is a nontrivial accomplishment because of confounding effects of illumination. However, if subjects have tacit knowledge of the statistics of illumination encountered in the real world, then it is possible to reject unlikely image interpretations, and thus to estimate surface reflectance even when the precise illumination is unknown. A surface reflectance matching task was used to measure the accuracy of human surface reflectance estimation. The results of the matching task demonstrate that subjects can match surface reflectance properties reliably and accurately in the absence of context, as long as the illumination is realistic. Matching performance declines when the illumination statistics are not representative of the real world. Together these findings suggest that subjects do use stored assumptions about the statistics of real-world illumination to estimate surface reflectance. Systematic manipulations of pixel and wavelet properties of illuminations reveal that the visual system's assumptions about illumination are of intermediate complexity (e.g., presence of edges and bright light sources), rather than of high complexity (e.g., presence of recognizable objects in the environment).

    View details for DOI 10.1167/3.5.3

    View details for Web of Science ID 000223081500003

    View details for PubMedID 12875632

  • Accuracy of velocity estimation by Reichardt corr¬elators Journal of the Optical Society of America A Dror, R. O., O'Carroll, D. C., Laughlin, S. B. 2001: 241-252
  • A mathematical criterion based on phase response curves for stability in a ring of coupled oscillators BIOLOGICAL CYBERNETICS Dror, R., Canavier, C. C., Butera, R. J., Clark, J. W., Byrne, J. H. 1999; 80 (1): 11-23

    Abstract

    Canavier et al. (1997) used phase response curves (PRCs) of individual oscillators to characterize the possible modes of phase-locked entrainment of an N-oscillator ring network. We extend this work by developing a mathematical criterion to determine the local stability of such a mode based on the PRCs. Our method does not assume symmetry; neither the oscillators nor their connections need be identical. To use these techniques for predicting modes and determining their stability, one need only determine the PRC of each oscillator in the ring either experimentally or from a computational model. We show that network stability cannot be determined by simply testing the ability of each oscillator to entrain the next. Stability depends on the number of neurons in the ring, the type of mode, and the slope of each PRC at the point of entrainment of the respective neuron. We also describe simple criteria which are either necessary or sufficient for stability and examine the implications of these results.

    View details for Web of Science ID 000078109300002

    View details for PubMedID 20809292

  • Phase response characteristics of model neurons determine which patterns are expressed in a ring circuit model of gait generation BIOLOGICAL CYBERNETICS Canavier, C. C., Butera, R. J., Dror, R. O., Baxter, D. A., Clark, J. W., Byrne, J. H. 1997; 77 (6): 367-380

    Abstract

    In order to assess the relative contributions to pattern-generation of the intrinsic properties of individual neurons and of their connectivity, we examined a ring circuit composed of four complex physiologically based oscillators. This circuit produced patterns that correspond to several quadrupedal gaits, including the walk, the bound, and the gallop. An analysis using the phase response curve (PRC) of an uncoupled oscillator accurately predicted all modes exhibited by this circuit and their phasic relationships--with the caveat that in certain parameter ranges, bistability in the individual oscillators added nongait patterns that were not amenable to PRC analysis, but further enriched the pattern-generating repertoire of the circuit. The key insights in the PRC analysis were that in a gait pattern, since all oscillators are entrained at the same frequency, the phase advance or delay caused by the action of each oscillator on its postsynaptic oscillator must be the same, and the sum of the normalized phase differences around the ring must equal to an integer. As suggested by several previous studies, our analysis showed that the capacity to exhibit a large number of patterns is inherent in the ring circuit configuration. In addition, our analysis revealed that the shape of the PRC for the individual oscillators determines which of the theoretically possible modes can be generated using these oscillators as circuit elements. PRCs that have a complex shape enable a circuit to produce a wider variety of patterns, and since complex neurons tend to have complex PRCs, enriching the repertoire of patterns exhibited by a circuit may be the function of some intrinsic neuronal complexity. Our analysis showed that gait transitions, or more generally, pattern transitions, in a ring circuit do not require rewiring the circuit or any changes in the strength of the connections. Instead, transitions can be achieved by using a control parameter, such as stimulus intensity, to sculpt the PRC so that it has the appropriate shape for the desired pattern(s). A transition can then be achieved simply by changing the value of the control parameter so that the first pattern either ceases to exist or loses stability, while a second pattern either comes into existence or gains stability. Our analysis illustrates the predictive value of PRCs in circuit analysis and can be extended to provide a design method for pattern-generating circuits.

    View details for Web of Science ID 000071002200001

    View details for PubMedID 9433752

  • A search for best constants in the Hardy-Littlewood maximal theorem Journal of Fourier Analysis and Applications Dror, R. O., Ganguli, S., Strichartz, R. S. 1996: 473-486