Nanjie Deng

Insights into the Dynamics of HIV-1 Protease: a Kinetic Network Model Constructed from Atomistic Simulations

The conformational dynamics in the flaps of HIV-1 protease plays a crucial role in the mechanism of substrate binding. We develop a kinetic network model, constructed from detailed atomistic simulations, to determine the kinetic mechanisms of the conformational transitions in HIV-1 PR. To overcome the time scale limitation of conventional molecular dynamics (MD) simulations, our method combines replica exchange MD with transition path theory (TPT) to study the diversity and temperature dependence of the pathways connecting functionally important states of the protease. At low temperatures the large-scale flap opening is dominated by a small number of paths; at elevated temperatures the transition occurs through many structurally heterogeneous routes. The expanded conformation in the crystal structure 1TW7 is found to closely mimic a key intermediate in the flap-opening pathways at low temperature. We investigated the different transition mechanisms between the semi-open and closed forms. The calculated relaxation times reveal fast semi-open ↔ closed transitions, and infrequently the flaps fully open. The ligand binding rate predicted from this kinetic model increases by 38-fold from 285 to 309 K, which is in general agreement with experiments. To our knowledge, this is the first application of a network model constructed from atomistic simulations together with TPT to analyze conformational changes between different functional states of a natively folded protein.

Virtual screening of integrase inhibitors by large scale binding free energy calculations: the SAMPL4 challenge

AbstractAs part of the SAMPL4 blind challenge, filtered AutoDock Vina ligand docking predictions and large scale binding energy distribution analysis method binding free energy calculations have been applied to the virtual screening of a focused library of candidate binders to the LEDGF site of the HIV integrase protein. The computational protocol leveraged docking and high level atomistic models to improve enrichment. The enrichment factor of our blind predictions ranked best among all of the computational submissions, and second best overall. This work represents to our knowledge the first example of the application of an all-atom physics-based binding free energy model to large scale virtual screening. A total of 285 parallel Hamiltonian replica exchange molecular dynamics absolute protein-ligand binding free energy simulations were conducted starting from docked poses. The setup of the simulations was fully automated, calculations were distributed on multiple computing resources and were completed in a 6-weeks period. The accuracy of the docked poses and the inclusion of intramolecular strain and entropic losses in the binding free energy estimates were the major factors behind the success of the method. Lack of sufficient time and computing resources to investigate additional protonation states of the ligands was a major cause of mispredictions. The experiment demonstrated the applicability of binding free energy modeling to improve hit rates in challenging virtual screening of focused ligand libraries during lead optimization.

Distinguishing Binders from False Positives by Free Energy Calculations: Fragment Screening Against the Flap Site of HIV Protease

Molecular docking is a powerful tool used in drug discovery and structural biology for predicting the structures of ligand–receptor complexes. However, the accuracy of docking calculations can be limited by factors such as the neglect of protein reorganization in the scoring function; as a result, ligand screening can produce a high rate of false positive hits. Although absolute binding free energy methods still have difficulty in accurately rank-ordering binders, we believe that they can be fruitfully employed to distinguish binders from nonbinders and reduce the false positive rate. Here we study a set of ligands that dock favorably to a newly discovered, potentially allosteric site on the flap of HIV-1 protease. Fragment binding to this site stabilizes a closed form of protease, which could be exploited for the design of allosteric inhibitors. Twenty-three top-ranked protein–ligand complexes from AutoDock were subject to the free energy screening using two methods, the recently developed binding energy analysis method (BEDAM) and the standard double decoupling method (DDM). Free energy calculations correctly identified most of the false positives (≥83%) and recovered all the confirmed binders. The results show a gap averaging ≥3.7 kcal/mol, separating the binders and the false positives. We present a formula that decomposes the binding free energy into contributions from the receptor conformational macrostates, which provides insights into the roles of different binding modes. Our binding free energy component analysis further suggests that improving the treatment for the desolvation penalty associated with the unfulfilled polar groups could reduce the rate of false positive hits in docking. The current study demonstrates that the combination of docking with free energy methods can be very useful for more accurate ligand screening against valuable drug targets.

NMR Relaxation in Proteins with Fast Internal Motions and Slow Conformational Exchange: Model Free Framework and Markov State Simulations

Calculating NMR relaxation effects for proteins with dynamics on multiple time scales generally requires very long trajectories based on conventional molecular dynamics simulations. In this report, we have built Markov state models from multiple MD trajectories and used the resulting MSM to capture the very fast internal motions of the protein within a free energy basin on a time scale up to hundreds of picoseconds and the more than 3 orders of magnitude slower conformational exchange between macrostates. To interpret the relaxation data, we derive new equations using the model-free framework which includes two slowly exchanging macrostates, each of which also exhibits fast local motions. Using simulations of HIV-1 protease as an example, we show how the populations of slowly exchanging conformational states as well as order parameters for the different states can be determined from the NMR relaxation data.

The mechanism of H171T resistance reveals the importance of Nδ-protonated His171 for the binding of allosteric inhibitor BI-D to HIV-1 integrase.

BackgroundAllosteric HIV-1 integrase (IN) inhibitors (ALLINIs) are an important new class of anti-HIV-1 agents. ALLINIs bind at the IN catalytic core domain (CCD) dimer interface occupying the principal binding pocket of its cellular cofactor LEDGF/p75. Consequently, ALLINIs inhibit HIV-1 IN interaction with LEDGF/p75 as well as promote aberrant IN multimerization. Selection of viral strains emerging under the inhibitor pressure has revealed mutations at the IN dimer interface near the inhibitor binding site.ResultsWe have investigated the effects of one of the most prevalent substitutions, H171T IN, selected under increasing pressure of ALLINI BI-D. Virus containing the H171T IN substitution exhibited an ~68-fold resistance to BI-D treatment in infected cells. These results correlated with ~84-fold reduced affinity for BI-D binding to recombinant H171T IN CCD protein compared to its wild type (WT) counterpart. However, the H171T IN substitution only modestly affected IN-LEDGF/p75 binding and allowed HIV-1 containing this substitution to replicate at near WT levels. The x-ray crystal structures of BI-D binding to WT and H171T IN CCD dimers coupled with binding free energy calculations revealed the importance of the Nδ- protonated imidazole group of His171 for hydrogen bonding to the BI-D tert-butoxy ether oxygen and establishing electrostatic interactions with the inhibitor carboxylic acid, whereas these interactions were compromised upon substitution to Thr171.ConclusionsOur findings reveal a distinct mechanism of resistance for the H171T IN mutation to ALLINI BI-D and indicate a previously undescribed role of the His171 side chain for binding the inhibitor.

How long does it take to equilibrate the unfolded state of a protein

How long does it take to equilibrate the unfolded state of a protein? The answer to this question has important implications for our understanding of why many small proteins fold with two state kinetics. When the equilibration within the unfolded state U is much faster than the folding, the folding kinetics will be two state even if there are many folding pathways with different barriers. Yet the mean first passage times (MFPTs) between different regions of the unfolded state can be much longer than the folding time. This seems to imply that the equilibration within U is much slower than the folding. In this communication we resolve this paradox. We present a formula for estimating the time to equilibrate the unfolded state of a protein. We also present a formula for the MFPT to any state within U, which is proportional to the average lifetime of that state divided by the state population. This relation is valid when the equilibration within U is very fast as compared with folding as it often is for small proteins. To illustrate the concepts, we apply the formulas to estimate the time to equilibrate the unfolded state of Trp‐cage and MFPTs within the unfolded state based on a Markov State Model using an ultra‐long 208 microsecond trajectory of the miniprotein to parameterize the model. The time to equilibrate the unfolded state of Trp‐cage is ∼100 ns while the typical MFPTs within U are tens of microseconds or longer.

Parameterization of an effective potential for protein-ligand binding from host-guest affinity data.

Force field accuracy is still one of the “stalemates” in biomolecular modeling. Model systems with high quality experimental data are valuable instruments for the validation and improvement of effective potentials. With respect to protein–ligand binding, organic host–guest complexes have long served as models for both experimental and computational studies because of the abundance of binding affinity data available for such systems. Binding affinity data collected for cyclodextrin (CD) inclusion complexes, a popular model for molecular recognition, is potentially a more reliable resource for tuning energy parameters than hydration free energy measurements. Convergence of binding free energy calculations on CD host–guest systems can also be obtained rapidly, thus offering the opportunity to assess the robustness of these parameters. In this work, we demonstrate how implicit solvent parameters can be developed using binding affinity experimental data and the binding energy distribution analysis method (BEDAM) and validated using the Grid Inhomogeneous Solvation Theory analysis. These new solvation parameters were used to study protein–ligand binding in two drug targets against the HIV‐1 virus and improved the agreement between the calculated and the experimental binding affinities. This work illustrates how benchmark sets of high quality experimental binding affinity data and physics‐based binding free energy models can be used to evaluate and optimize force fields for protein–ligand systems. Copyright

Allosteric HIV-1 integrase inhibitors promote aberrant protein multimerization by directly mediating inter-subunit interactions: Structural and thermodynamic modeling studies.

Allosteric HIV‐1 integrase (IN) inhibitors (ALLINIs) bind at the dimer interface of the IN catalytic core domain (CCD), and potently inhibit HIV‐1 by promoting aberrant, higher‐order IN multimerization. Little is known about the structural organization of the inhibitor‐induced IN multimers and important questions regarding how ALLINIs promote aberrant IN multimerization remain to be answered. On the basis of physical chemistry principles and from our analysis of experimental information, we propose that inhibitor‐induced multimerization is mediated by ALLINIs directly promoting inter‐subunit interactions between the CCD dimer and a C‐terminal domain (CTD) of another IN dimer. Guided by this hypothesis, we have built atomic models of inter‐subunit interfaces in IN multimers by incorporating information from hydrogen‐deuterium exchange (HDX) measurements to drive protein‐protein docking. We have also developed a novel free energy simulation method to estimate the effects of ALLINI binding on the association of the CCD and CTD. Using this structural and thermodynamic modeling approach, we show that multimer inter‐subunit interface models can account for several experimental observations about ALLINI‐induced multimerization, including large differences in the potencies of various ALLINIs, the mechanisms of resistance mutations, and the crucial role of solvent exposed R‐groups in the high potency of certain ALLINIs. Our study predicts that CTD residues Tyr226, Trp235 and Lys266 are involved in the aberrant multimer interfaces. The key finding of the study is that it suggests the possibility of ALLINIs facilitating inter‐subunit interactions between an external CTD and the CCD‐CCD dimer interface.

A framework for flexible and scalable replica-exchange on production distributed CI

Replica exchange represents a powerful class of algorithms used for enhanced configurational and energetic sampling in a range of physical systems. Computationally it represents a type of application with multiple scales of communication. At a fine-grained level there is often communication with a replica, typically an MPI process. At a coarse-grained level, the replicas communicate with other replicas -- both temporally as well as in amount of data exchanged. This paper outlines a novel framework developed to support the flexible execution of large-scale replica exchange. The framework is flexible in the sense that it supports different coupling schemes between replicas and is agnostic to the specific underlying simulation -- classical or quantum, serial or parallel simulation. The scalability of the framework is assessed using standard simulation benchmarks. In spite of the increasing communication and coordination requirements as a function of the number of replicas, our framework supports the execution of hundreds replicas without significant overhead. Although there are several specific aspects that will benefit from further optimization, a first working prototype has the ability to fundamentally change the scale of replica exchange simulations possible on production distributed cyberinfrastructure such as XSEDE, as well as support novel usage modes. This paper also represents the release of the framework to the broader biophysical simulation community and provides details on its usage.

Computing conformational free energy differences in explicit solvent: An efficient thermodynamic cycle using an auxiliary potential and a free energy functional constructed from the end points

Many biomolecules undergo conformational changes associated with allostery or ligand binding. Observing these changes in computer simulations is difficult if their timescales are long. These calculations can be accelerated by observing the transition on an auxiliary free energy surface with a simpler Hamiltonian and connecting this free energy surface to the target free energy surface with free energy calculations. Here, we show that the free energy legs of the cycle can be replaced with energy representation (ER) density functional approximations. We compute: (1) The conformational free energy changes for alanine dipeptide transitioning from the right‐handed free energy basin to the left‐handed basin and (2) the free energy difference between the open and closed conformations of β‐cyclodextrin, a “host” molecule that serves as a model for molecular recognition in host‐guest binding. β‐cyclodextrin contains 147 atoms compared to 22 atoms for alanine dipeptide, making β‐cyclodextrin a large molecule for which to compute solvation free energies by free energy perturbation or integration methods and the largest system for which the ER method has been compared to exact free energy methods. The ER method replaced the 28 simulations to compute each coupling free energy with two endpoint simulations, reducing the computational time for the alanine dipeptide calculation by about 70% and for the β‐cyclodextrin by > 95%. The method works even when the distribution of conformations on the auxiliary free energy surface differs substantially from that on the target free energy surface, although some degree of overlap between the two surfaces is required.