Holger Gohlke

The Amber biomolecular simulation programs.

We describe the development, current features, and some directions for future development of the Amber package of computer programs. This package evolved from a program that was constructed in the late 1970s to do Assisted Model Building with Energy Refinement, and now contains a group of programs embodying a number of powerful tools of modern computational chemistry, focused on molecular dynamics and free energy calculations of proteins, nucleic acids, and carbohydrates.

MMPBSA.py: An Efficient Program for End-State Free Energy Calculations

MM-PBSA is a post-processing end-state method to calculate free energies of molecules in solution. MMPBSA.py is a program written in Python for streamlining end-state free energy calculations using ensembles derived from molecular dynamics (MD) or Monte Carlo (MC) simulations. Several implicit solvation models are available with MMPBSA.py, including the Poisson-Boltzmann Model, the Generalized Born Model, and the Reference Interaction Site Model. Vibrational frequencies may be calculated using normal mode or quasi-harmonic analysis to approximate the solute entropy. Specific interactions can also be dissected using free energy decomposition or alanine scanning. A parallel implementation significantly speeds up the calculation by dividing frames evenly across available processors. MMPBSA.py is an efficient, user-friendly program with the flexibility to accommodate the needs of users performing end-state free energy calculations. The source code can be downloaded at http://ambermd.org/ with AmberTools, released under the GNU General Public License.

Converging free energy estimates: MM-PB(GB)SA studies on the protein-protein complex Ras-Raf.

Estimating protein–protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H‐Ras/C‐Raf1 using the MM‐PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas‐phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit‐solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent‐accessible surface area‐dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute–solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson–Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal‐mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper “one‐trajectory‐alternative” to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras–Raf obtained in this study of −8.3 kcal mol−1 is in good agreement with the experimental result of −9.6 kcal mol−1, however, further probing the transferability of the applied protocol that led to this result is necessary.

Free Energy Calculations by the Molecular Mechanics Poisson−Boltzmann Surface Area Method

Detailed knowledge of how molecules recognize interaction partners and of the conformational preferences of biomacromolecules is pivotal for understanding biochemical processes. Such knowledge also provides the foundation for the design of novel molecules, as undertaken in pharmaceutical research. Computer‐based free energy calculations enable a detailed investigation of the energetic factors that are responsible for molecular stability or binding affinity. The Molecular Mechanics Poisson–Boltzmann Surface Area (MM‐PBSA) approach is an efficient method for the calculation of free energies of diverse molecular systems. Here we describe the concepts of this approach and outline the practical proceeding. Furthermore we give an overview of the wide spectrum of problems that have been addressed with this method and of successful analyses carried out, thereby focussing on ambitious and recent studies. Limits of the approach in terms of accuracy and applicability are discussed. Despite these limitations MM‐PBSA is a method with great potential that allows comparative free energy analyses for various molecular systems at low computational cost.

Target Flexibility: An Emerging Consideration in Drug Discovery and Design†

Department of General and Inorganic Chemistry, UniVersity of Parma, Via G.P. Usberti 17/A 43100, Parma, Italy, National Institute for Biosystems and Biostructures, Rome, Italy, Department of Medicinal Chemistry and Institute for Structural Biology & Drug DiscoVery, Virginia Commonwealth UniVersity, Richmond, Virginia 23298-0540, Department of Pharmaceutics, UniVersity of Parma, Via GP Usberti 27/A, 43100 Parma, Italy, High Performance Systems, CINECA Supercomputing Centre, Casalecchio di Reno, Bologna, Italy, Dulbecco Telethon Institute, Department of Chemistry, UniVersity of Modena and Reggio Emilia, Via Campi 183, 41100 Modena, Italy, Department of Mathematics and Natural Sciences, Pharmaceutical Institute, Christian-Albrechts-UniVersity, Gutenbergstrasse 76, 24118 Kiel, Germany, Departments of Biochemistry & Molecular Biology, Computer Science & Engineering, and Physics & Astronomy, Michigan State UniVersity, East Lansing, Michigan 48824-1319, Department of Molecular Biology, MB-5, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037-1000, Molecular Modeling and Bioinformatics Unit, Institute of Biomedical Research, Scientific Park of Barcelona, Department of Biochemistry and Molecular Biology, UniVersity of Barcelona, Josep Samitier 1-5, Barcelona 08028, Spain, Department of Experimental Medicine, UniVersity of Parma, Via Volturno, 39, 43100, Parma, Italy, Department of Chemical, Food, Pharmaceutical and Pharmacological Sciences, UniVersity of Piemonte Orientale “Amedeo AVogadro”, Via BoVio 6, 28100 NoVara, Italy, Institute of Pharmacy and Food Chemistry, UniVersity of Wurzburg, Am Hubland, D-97074 Wurzburg, Germany

Statistical potentials and scoring functions applied to protein-ligand binding.

In virtual screening, small-molecule ligands are docked into protein binding sites and their binding affinity is predicted. Knowledge-based, regression-based and first-principle-based methods have been developed to rank computer-generated binding modes. As a result of still existing deficiencies, a best compromise might be the combination of several scoring schemes into a consensus scoring approach.

Change in protein flexibility upon complex formation: Analysis of Ras-Raf using molecular dynamics and a molecular framework approach

Changes in flexibility upon protein–protein complex formation of H‐Ras and the Ras‐binding domain of C‐Raf1 have been investigated using the molecular framework approach FIRST (Floppy Inclusion and Rigid Substructure Topology) and molecular dynamics simulations (MD) of in total ∼35 ns length. In a computational time of about one second, FIRST identifies flexible and rigid regions in a single, static three‐dimensional molecular framework, whose vertices represent protein atoms and whose edges represent covalent and non‐covalent (hydrogen bond and hydrophobic) constraints and fixed bond angles within the protein. The two methods show a very good agreement with respect to the identification of changes in flexibility in both binding partners on a local scale. This implies that flexibility can be successfully predicted by identifying which bonds limit motion within a molecule and how they are coupled. In particular, as identified by MD, the β‐sheet in Raf shows considerably more pronounced orientational correlations in the bound state compared to the unbound state. Similarly, FIRST assigns the β‐sheet to the largest rigid cluster of the complex. Interestingly, FIRST allows us to identify that interactions across the interface (but not conformational changes upon complex formation) result in the observed rigidification. Since regions of the β‐sheet of Raf that do not interact directly with Ras become rigidified, this also demonstrates the long‐range aspect to rigidity percolation. Possible implications of the change of flexibility of the Ras‐binding domain of Raf on the activation of Raf upon complex formation are discussed. Finally, the sensitivity of FIRST results with respect to the representation of non‐covalent interactions used as constraints is probed. Proteins 2004.

Hot spots and transient pockets: predicting the determinants of small-molecule binding to a protein-protein interface.

Protein-protein interfaces are considered difficult targets for small-molecule protein-protein interaction modulators (PPIMs ). Here, we present for the first time a computational strategy that simultaneously considers aspects of energetics and plasticity in the context of PPIM binding to a protein interface. The strategy aims at identifying the determinants of small-molecule binding, hot spots, and transient pockets, in a protein-protein interface in order to make use of this knowledge for predicting binding modes of and ranking PPIMs with respect to their affinity. When applied to interleukin-2 (IL-2), the computationally inexpensive constrained geometric simulation method FRODA outperforms molecular dynamics simulations in sampling hydrophobic transient pockets. We introduce the PPIAnalyzer approach for identifying transient pockets on the basis of geometrical criteria only. A sequence of docking to identified transient pockets, starting structure selection based on hot spot information, RMSD clustering and intermolecular docking energies, and MM-PBSA calculations allows one to enrich IL-2 PPIMs from a set of decoys and to discriminate between subgroups of IL-2 PPIMs with low and high affinity. Our strategy will be applicable in a prospective manner where nothing else than a protein-protein complex structure is known; hence, it can well be the first step in a structure-based endeavor to identify PPIMs.

Protein rigidity and thermophilic adaptation

We probe the hypothesis of corresponding states, according to which homologues from mesophilic and thermophilic organisms are in corresponding states of similar rigidity and flexibility at their respective optimal temperatures. For this, the local distribution of flexible and rigid regions in 19 pairs of homologous proteins from meso‐ and thermophilic organisms is analyzed and related to activity characteristics of the enzymes by constraint network analysis (CNA). Two pairs of enzymes are considered in more detail: 3‐isopropylmalate dehydrogenase and thermolysin‐like protease. By comparing microscopic stability features of homologues with the help of stability maps, introduced for the first time, we show that adaptive mutations in enzymes from thermophilic organisms maintain the balance between overall rigidity, important for thermostability, and local flexibility, important for activity, at the appropriate working temperature. Thermophilic adaptation in general leads to an increase of structural rigidity but conserves the distribution of functionally important flexible regions between homologues. This finding provides direct evidence for the hypothesis of corresponding states. CNA thereby implicitly captures and unifies many different mechanisms that contribute to increased thermostability and to activity at high temperatures. This allows to qualitatively relate changes in the flexibility of active site regions, induced either by a temperature change or by the introduction of mutations, to experimentally observed losses of the enzyme function. As for applications, the results demonstrate that exploiting the principle of corresponding states not only allows for successful thermostability optimization but also for guiding experiments in order to improve enzyme activity in protein engineering. Proteins 2011.

Multiscale modeling of macromolecular conformational changes combining concepts from rigidity and elastic network theory

The development of a two‐step approach for multiscale modeling of macromolecular conformational changes is based on recent developments in rigidity and elastic network theory. In the first step, static properties of the macromolecule are determined by decomposing the molecule into rigid clusters by using the graph‐theoretical approach FIRST and an all‐atom representation of the protein. In this way, rigid clusters are not limited to consist of residues adjacent in sequence or secondary structure elements as in previous studies. Furthermore, flexible links between rigid clusters are identified and can be modeled as such subsequently. In the second step, dynamical properties of the molecule are revealed by the rotations‐translations of blocks approach (RTB) using an elastic network model representation of the coarse‐grained protein. In this step, only rigid body motions are allowed for rigid clusters, whereas links between them are treated as fully flexible. The approach was tested on a data set of 10 proteins that showed conformational changes on ligand binding. For efficiency, coarse‐graining the protein results in a remarkable reduction of memory requirements and computational times by factors of 9 and 27 on average and up to 25 and 125, respectively. For accuracy, directions and magnitudes of motions predicted by our approach agree well with experimentally determined ones, despite embracing in extreme cases >50% of the protein into one rigid cluster. In fact, the results of our method are in general comparable with when no or a uniform coarse‐graining is applied; and the results are superior if the movement is dominated by loop or fragment motions. This finding indicates that explicitly distinguishing between flexible and rigid regions is advantageous when using a simplified protein representation in the second step. Finally, motions of atoms in rigid clusters are also well predicted by our approach, which points to the need to consider mobile protein regions in addition to flexible ones when modeling correlated motions. Proteins 2006.