CHARMM is an academic research program used widely for macromolecular mechanics and dynamics with versatile analysis and manipulation tools of atomic coordinates and dynamics trajectories. CHARMM-GUI, http://www.charmm-gui.org, has been developed to provide a web-based graphical user interface to generate various input files and molecular systems to facilitate and standardize the usage of common and advanced simulation techniques in CHARMM. The web environment provides an ideal platform to build and validate a molecular model system in an interactive fashion such that, if a problem is found through visual inspection, one can go back to the previous setup and regenerate the whole system again. In this article, we describe the currently available functional modules of CHARMM-GUI Input Generator that form a basis for the advanced simulation techniques. Future directions of the CHARMM-GUI development project are also discussed briefly together with other features in the CHARMM-GUI website, such as Archive and Movie Gallery.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.20945

CHARMM-GUI: a web-based graphical user interface for CHARMM.

Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics.

A very fast empirical method is presented for structure-based protein pKa prediction and rationalization. The desolvation effects and intra-protein interactions, which cause variations in pKa values of protein ionizable groups, are empirically related to the positions and chemical nature of the groups proximate to the pKa sites. A computer program is written to automatically predict pKa values based on these empirical relationships within a couple of seconds. Unusual pKa values at buried active sites, which are among the most interesting protein pKa values, are predicted very well with the empirical method. A test on 233 carboxyl, 12 cysteine, 45 histidine, and 24 lysine pKa values in various proteins shows a root-mean-square deviation (RMSD) of 0.89 from experimental values. Removal of the 29 pKa values that are upper or lower limits results in an RMSD = 0.79 for the remaining 285 pKa values.

https://bioc.polytechnique.fr/biocomputing/papers/propka.pdf

Very fast empirical prediction and rationalization of protein pKa values

Calculation of hydrodynamic properties of globular proteins from their atomic-level structure.

The term molecular mechanics (MM) refers to the use of simple potential-energy functions (e.g., harmonic oscillator or Coulombic potentials) to model molecular systems. Molecular mechanics approaches are widely applied in molecular structure refinement, molecular dynamics (MD) simulations, Monte Carlo (MC) simulations, and ligand-docking simulations.

Typically, molecular mechanics models consist of spherical atoms connected by springs which represent bonds. Internal forces experienced in the model structure are described using simple mathematical functions. For example, Hooke’s law is commonly used to describe bonded interactions, and the nonbonded atoms might be treated as inelastic hard spheres or may interact according to a Lennard-Jones potential. Using these simple models, a molecular dynamics simulation numerically solves Newton’s equations of motion, thus allowing structural fluctuations to be observed with respect to time.

Dynamic simulation methods are widely used to obtain information on the time evolution of conformations of proteins and other biological macromolecules1–4 and also kinetic and thermodynamic information. Simulations can provide fine detail concerning the motions of individual particles as a function of time. They can be utilized to quantify the properties of a system at a precision and on a time scale that is otherwise inaccessible, and simulation is, therefore, a valuable tool in extending our understanding of model systems. Theoretical consideration of a system additionally allows one to investigate the specific contributions to a property through “computational alchemy”,5 that is, modifying the simulation in a way that is nonphysical but nonetheless allows a model’s characteristics to be probed. One particular example is the artificial conversion of the energy function from that representing one system to that of another during a simulation. This is an important technique in free-energy calculations.6 Thus, molecular dynamics simulations, along with a range of complementary computational approaches, have become valuable tools for investigating the basis of protein structure and function.

This review offers an outline of the origin of molecular dynamics simulation for protein systems and how it has developed into a robust and trusted tool. This review then covers more recent advances in theory and an illustrative selection of practical studies in which it played a central role. The range of studies in which MD has played a considerable or pivotal role is immense, and this review cannot do justice to them; MD simulations of biomedical importance were recently reviewed.4 Particular emphasis will be placed on the study of dynamic aspects of protein recognition, an area where molecular dynamics has scope to provide broad and far-ranging insights. This review concludes with a brief discussion of the future potential offered to advancement of the biological and biochemical sciences and the remaining issues that must be overcome to allow the full extent of this potential to be realized.

1.1. Historical Background
MD methods were originally conceived within the theoretical physics community during the 1950s. In 1957, Alder and Wainwright7 performed the earliest MD simulation using the so-called hard-sphere model, in which the atoms interacted only through perfect collisions. Rahman8 subsequently applied a smooth, continuous potential to mimic real atomic interactions. During the 1970s, as computers became more widespread, MD simulations were developed for more complex systems, culminating in 1976 with the first simulation of a protein9,10 using an empirical energy function constructed using physics-based first-principles assumptions. MD simulations are now widely and routinely applied and especially popular in the fields of materials science11,12 and biophysics.

As will be discussed later in this review, a variety of experimental conditions may be simulated with modern theories and algorithms. The initial simulations only considered single molecules in vacuo. Over time, more realistic or at least biologically relevant simulations could be performed. This trend is continuing today.

The initial protein MD simulation, of the small bovine pancreatic trypsin inhibitor (BPTI), covered only 9.2 ps of simulation time. Modern simulations routinely have so-called equilibration periods much longer than that, and production simulations of tens of nanoseconds are routine, with the first microsecond MD simulation being reported in 1998.13 In addition, the original BPTI simulation included only about 500 atoms rather than the 104-106 atoms that are common today. While much of this advancement results from an immense increase in availability of computing power, major theoretical and methodological developments also contribute significantly.

The number of publications regarding MD theory and application of MD to biological systems is growing at an extraordinary pace. A single review cannot do justice to the recent applications of MD. Using data from ISI Web of Science, the authors estimate that during 2005 at least 800 articles will be published that discuss molecular dynamics and proteins. The historical counts are shown in Figure 1.






Open in a separate window


Figure 1


Articles matching ISI Web of Science query “TS=(protein) AND TS=(molecular dynamics)”.

/pdf/molecular-dynamics-survey-of-methods-for-simulating-the-45fcz5gua9.pdf

Molecular dynamics: survey of methods for simulating the activity of proteins.

Relationships between protein structure and ionization of carboxyl groups were investigated in 24 proteins of known structure and for which 115 aspartate and 97 glutamate pK a values are known. Mean pK a values for aspartates and glutamates are ≤ 3.4 (′1.0) and 4.1 (′0.8), respectively. For aspartates, mean pK a values are 3.9 (′1.0) and 3.1 (′0.9) in acidic (pI 8) proteins, respectively, while mean pK a values for glutamates are approximately 4.2 for acidic and basic proteins. Burial of carboxyl groups leads to dispersion in pK a values: pK a values for solvent-exposed groups show narrow distributions while values for buried groups range from 5.5 and most are found in active sites or ligand-binding sites. These carboxyl groups are buried and usually accept no more than one hydrogen bond. Aspartates and glutamates at the N-termini of helices have mean pK a values of 2.8 (′0.5) and 3.4 (′0.6), respectively, about 0.6 units less than the overall mean values.

Empirical relationships between protein structure and carboxyl pKa values in proteins

In Part 2 we discuss application of several different types of UV–Vis spectroscopy, such as normal, difference, and second-derivative UV absorption spectroscopy, fluorescence spectroscopy, linear and circular dichroism spectroscopy, and Raman spectroscopy, of the side-chain of tyrosine residues in different molecular environments. We review the ways these spectroscopies can be used to probe complex protein structures.

/pdf/uv-vis-spectroscopy-of-tyrosine-side-groups-in-studies-of-fx5eaj52h4.pdf

UV–Vis spectroscopy of tyrosine side-groups in studies of protein structure. Part 2: selected applications

Charge-charge interactions are key determinants of the pK values of ionizable groups in ribonuclease Sa (pI=3.5) and a basic variant (pI=10.2).

A method for performing constant-pH molecular dynamics (MD) simulations, with an implicit solvent and explicit treatment of protonation/deprotonation phenomena, is applied to a succinic acid molecule. The protonation state of each ionizable group in the molecule is allowed to change during the MD trajectory at predefined time intervals, dividing the whole simulation into a set of sub-trajectories. Each change in the protonation state of the molecule at the beginning of a new sub-trajectory is made with a probability determined by the electrostatic free energies of the available states, based on the last structure of the preceding sub-trajectory. Our simulations resulted in the distribution of conformational states of the molecule, and in its molecular p K a s, in good agreement with available experimental data. Moreover, dependence of the distribution of the trans /gauche conformers on the time interval selected for the sub-trajectories between making decisions regarding protonation states of the residues, indicates that this equilibrium is sensitive to the dynamics of proton exchange.

Constant-pH molecular dynamics simulations: a test case of succinic acid

The aspartyl dyad of free HIV-1 protease has apparent pK(a)s of approximately 3 and approximately 6, but recent NMR studies indicate that the aspartyl dyad is fixed in the doubly protonated form over a wide pH range when cyclic urea inhibitors are bound, and in the monoprotonated form when the inhibitor KNI-272 is bound. We present computations and measurements related to these changes in protonation and to the thermodynamic linkage between protonation and inhibition. The Poisson-Boltzmann model of electrostatics is used to compute the apparent pK(a)s of the aspartyl dyad in the free enzyme and in complexes with four different inhibitors. The calculations are done with two parameter sets. One assigns epsilon = 4 to the solute interior and uses a detailed model of ionization; the other uses epsilon = 20 for the solute interior and a simplified representation of ionization. For the free enzyme, both parameter sets agree well with previously measured apparent pK(a)s of approximately 3 and approximately 6. However, the calculations with an internal dielectric constant of 4 reproduce the large pKa shifts upon binding of inhibitors, but the calculations with an internal dielectric constant of 20 do not. This observation has implications for the accurate calculation of pK(a)s in complex protein environments. Because binding of a cyclic urea inhibitor shifts the pK(a)s of the aspartyl dyad, changing the pH is expected to change its apparent binding affinity. However, we find experimentally that the affinity is independent of pH from 5.5 to 7.0. Possible explanations for this discrepancy are discussed.

Jan M. Antosiewicz

Papers

Empirical relationships between protein structure and carboxyl pKa values in proteins

UV–Vis spectroscopy of tyrosine side-groups in studies of protein structure. Part 2: selected applications

Charge-charge interactions are key determinants of the pK values of ionizable groups in ribonuclease Sa (pI=3.5) and a basic variant (pI=10.2).

Constant-pH molecular dynamics simulations: a test case of succinic acid

Thermodynamic linkage between the binding of protons and inhibitors to HIV-1 protease.