Vibrational population relaxation of carbon monoxide in the heme pocket of photolyzed carbonmonoxy myoglobin: Comparison of time-resolved mid-IR absorbance experiments and molecular dynamics simulations

The vibrational energy relaxation of carbon monoxide in the heme pocket of sperm whale myoglobin was studied by using molecular dynamics simulation and normal mode analysis methods. Molecular dynamics trajectories of solvated myoglobin were run at 300 K for both the δ- and ɛ-tautomers of the distal His-64. Vibrational population relaxation times of 335 ± 115 ps for the δ-tautomer and 640 ± 185 ps for the ɛ-tautomer were estimated by using the Landau–Teller model. Normal mode analysis was used to identify those protein residues that act as the primary “doorway” modes in the vibrational relaxation of the oscillator. Although the CO relaxation rates in both the ɛ- and δ-tautomers are similar in magnitude, the simulations predict that the vibrational relaxation of the CO is faster in the δ-tautomer with the distal His playing an important role in the energy relaxation mechanism. Time-resolved mid-IR absorbance measurements were performed on photolyzed carbonmonoxy hemoglobin (Hb13CO). From these measurements, a T1 time of 600 ± 150 ps was determined. The simulation and experimental estimates are compared and discussed.

Induced fit DNA recognition by a minor groove binding analogue of Hoechst 33258: fluctuations in DNA A tract structure investigated by NMR and molecular dynamics simulations

NMR analysis and molecular dynamics simulations of d(GGTAATTACC)2 and its complex with a tetrahydropyrimidinium analogue of Hoechst 33258 suggest that DNA minor groove recognition in solution involves a combination of conformational selection and induced fit, rather than binding to a preorganised site. Analysis of structural fluctuations in the bound and unbound states suggests that the degree of induced fit observed is primarily a consequence of optimising van der Waals contacts with the walls of the minor groove resulting in groove narrowing through: (i) changes in base step parameters, including increased helical twist and propeller twist; (ii) changes to the sugar–phosphate backbone conformation to engulf the bound ligand; (iii) suppression of bending modes at the TpA steps. In contrast, the geometrical arrangement of hydrogen bond acceptors on the groove floor appears to be relatively insensitive to DNA conformation (helical twist and propeller twist). We suggest that effective recognition of DNA sequences (in this case an A tract structure) appears to depend to a significant extent on the sequence being flexible enough to be able to adopt the geometrically optimal conformation compatible with the various binding interactions, rather than involving ‘lock and key’ recognition.

Glass transition in DNA from molecular dynamics simulations.

Molecular dynamics simulations of the oligonucleotide duplex d(CGCGCG)2 in aqueous solution are used to investigate the glass transition phenomenon. The simulations were performed at temperatures in the 20 K to 340 K range. The mean square atomic fluctuations showed that the behavior of the oligonucleotide duplex was harmonic at low temperatures. A glass transition temperature at 223 K to 234 K was inferred for the oligonucleotide duplex, which is in agreement with experimental observations. The largest number of hydrogen bounds between the polar atoms of the oligonucleotide duplex and the water molecules was obtained at the glass transition temperature. With increasing temperature we observed a decrease in the average lifetime of the hydrogen bonds to water molecules.

A sampling problem in molecular dynamics simulations of macromolecules.

Correlations in low-frequency atomic displacements predicted by molecular dynamics simulations on the order of 1 ns are undersampled for the time scales currently accessible by the technique. This is shown with three different representations of the fluctuations in a macromolecule: the reciprocal space of crystallography using diffuse x-ray scattering data, real three-dimensional Cartesian space using covariance matrices of the atomic displacements, and the 3N-dimensional configuration space of the protein using dimensionally reduced projections to visualize the extent to which phase space is sampled.

Molecular dynamics and free-energy calculations applied to affinity maturation in antibody 48G7

We investigated the relative free energies of hapten binding to the germ line and mature forms of the 48G7 antibody Fab fragments by applying a continuum model to structures sampled from molecular dynamics simulations in explicit solvent. Reasonable absolute and very good relative free energies were obtained. As a result of nine somatic mutations that do not contact the hapten, the affinity-matured antibody binds the hapten >104 tighter than the germ line antibody. Energetic analysis reveals that van der Waals interactions and nonpolar contributions to solvation are similar and drive the formations of both the germ line and mature antibody–hapten complexes. Affinity maturation of the 48G7 antibody therefore appears to occur through reorganization of the combining site geometry in a manner that optimizes the balance of gaining favorable electrostatic interactions with the hapten and losing those with solvent during the binding process. As reflected by lower rms fluctuations in the antibody–hapten complex, the mature complex undergoes more restricted fluctuations than the germ line complex. The dramatically increased affinity of the 48G7 antibody over its germ line precursor is thus made possible by electrostatic optimization.

Intrinsic compressibility and volume compression in solvated proteins by molecular dynamics simulation at high pressure.

Constant pressure and temperature molecular dynamics techniques have been employed to investigate the changes in structure and volumes of two globular proteins, superoxide dismutase and lysozyme, under pressure. Compression (the relative changes in the proteins' volumes), computed with the Voronoi technique, is closely related with the so-called protein intrinsic compressibility, estimated by sound velocity measurements. In particular, compression computed with Voronoi volumes predicts, in agreement with experimental estimates, a negative bound water contribution to the apparent protein compression. While the use of van der Waals and molecular volumes underestimates the intrinsic compressibilities of proteins, Voronoi volumes produce results closer to experimental estimates. Remarkably, for two globular proteins of very different secondary structures, we compute identical (within statistical error) protein intrinsic compressions, as predicted by recent experimental studies. Changes in the protein interatomic distances under compression are also investigated. It is found that, on average, short distances compress less than longer ones. This nonuniform contraction underlines the peculiar nature of the structural changes due to pressure in contrast with temperature effects, which instead produce spatially uniform changes in proteins. The structural effects observed in the simulations at high pressure can explain protein compressibility measurements carried out by fluorimetric and hole burning techniques. Finally, the calculation of the proteins static structure factor shows significant shifts in the peaks at short wavenumber as pressure changes. These effects might provide an alternative way to obtain information concerning compressibilities of selected protein regions.

Brownian dynamics simulations of protein folding: Access to milliseconds time scale and beyond

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion–collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion–collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

A molecular level picture of the stabilization of A-DNA in mixed ethanol–water solutions

Advances in computer power, methodology, and empirical force fields now allow routine “stable” nanosecond-length molecular dynamics simulations of DNA in water. The accurate representation of environmental influences on structure remains a major, unresolved issue. In contrast to simulations of A-DNA in water (where an A-DNA to B-DNA transition is observed) and in pure ethanol (where disruption of the structure is observed), A-DNA in ≈85% ethanol solution remains in a canonical A-DNA geometry as expected. The stabilization of A-DNA by ethanol is likely due to disruption of the spine of hydration in the minor groove and the presence of ion-mediated interhelical bonds and extensive hydration across the major groove.

Molecular dynamics of MHC genesis unraveled by sequence analysis of the 1,796,938-bp HLA class I region

The intensely studied MHC has become the paradigm for understanding the architectural evolution of vertebrate multigene families. The 4-Mb human MHC (also known as the HLA complex) encodes genes critically involved in the immune response, graft rejection, and disease susceptibility. Here we report the continuous 1,796,938-bp genomic sequence of the HLA class I region, linking genes between MICB and HLA-F. A total of 127 genes or potentially coding sequences were recognized within the analyzed sequence, establishing a high gene density of one per every 14.1 kb. The identification of 758 microsatellite provides tools for high-resolution mapping of HLA class I-associated disease genes. Most importantly, we establish that the repeated duplication and subsequent diversification of a minimal building block, MIC-HCGIX-3.8–1-P5-HCGIV-HLA class I-HCGII, engendered the present-day MHC. That the currently nonessential HLA-F and MICE genes have acted as progenitors to today’s immune-competent HLA-ABC and MICA/B genes provides experimental evidence for evolution by “birth and death,” which has general relevance to our understanding of the evolutionary forces driving vertebrate multigene families.

Yeast chorismate mutase in the R state: Simulations of the active site

The isomerization of chorismate to prephenate by chorismate mutase in the biosynthetic pathway that forms Tyr and Phe involves C5—O (ether) bond cleavage and C1—C9 bond formation in a Claisen rearrangement. Development of negative charge on the ether oxygen, stabilized by Lys-168 and Glu-246, is inferred from the structure of a complex with a transition state analogue (TSA) and from the pH-rate profile of the enzyme and the E246Q mutant. These studies imply a protonated Glu-246 well above pH 7. Here, several 500-ps molecular dynamics simulations test the stability of enzyme–TSA complexes by using a solvated system with stochastic boundary conditions. The simulated systems are (i) protonated Glu-246 (stable), (ii) deprotonated Glu-246 (unstable), (iii) deprotonated Glu-246 plus one H2O between Glu-246 and the ether oxygen (unstable), (iv) the E246Q mutant (stable), and (v) addition of OH− between protonated Glu-246 and the ether oxygen. In (v), a local conformational change of Lys-168 displaced the OH− into the solvent region, suggesting a possible rate-determining step that precedes the catalytic step. In a 500-ps simulation of the enzyme complexed with the reactant chorismate or the product prephenate, no water molecule remained near the oxygen of the ligand. Calculations using the linearized Poisson–Boltzmann equation show that the effective pKa of Glu-246 is shifted from 5.8 to 8.1 as the negative charge on the ether oxygen of the TSA is changed from −0.56 electron to −0.9 electron. Altogether, these results support retention of a proton on Glu-246 to high pH and the absence of a water molecule in the catalytic steps.

Molecular dynamics of a grid-mounted molecular dipolar rotor in a rotating electric field

Classical molecular dynamics is applied to the rotation of a dipolar molecular rotor mounted on a square grid and driven by rotating electric field E(ν) at T ≃ 150 K. The rotor is a complex of Re with two substituted o-phenanthrolines, one positively and one negatively charged, attached to an axial position of Rh\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{2}^{4+}}}\end{equation*}\end{document} in a [2]staffanedicarboxylate grid through 2-(3-cyanobicyclo[1.1.1]pent-1-yl)malonic dialdehyde. Four regimes are characterized by a, the average lag per turn: (i) synchronous (a < 1/e) at E(ν) = |E(ν)| > Ec(ν) [Ec(ν) is the critical field strength], (ii) asynchronous (1/e < a < 1) at Ec(ν) > E(ν) > Ebo(ν) > kT/μ, [Ebo(ν) is the break-off field strength], (iii) random driven (a ≃ 1) at Ebo(ν) > E(ν) > kT/μ, and (iv) random thermal (a ≃ 1) at kT/μ > E(ν). A fifth regime, (v) strongly hindered, W > kT, Eμ, (W is the rotational barrier), has not been examined. We find Ebo(ν)/kVcm−1 ≃ (kT/μ)/kVcm−1 + 0.13(ν/GHz)1.9 and Ec(ν)/kVcm−1 ≃ (2.3kT/μ)/kVcm−1 + 0.87(ν/GHz)1.6. For ν > 40 GHz, the rotor behaves as a macroscopic body with a friction constant proportional to frequency, η/eVps ≃ 1.14 ν/THz, and for ν < 20 GHz, it exhibits a uniquely molecular behavior.

Quantification of the hydrophobic interaction by simulations of the aggregation of small hydrophobic solutes in water

The hydrophobic interaction, the tendency for nonpolar molecules to aggregate in solution, is a major driving force in biology. In a direct approach to the physical basis of the hydrophobic effect, nanosecond molecular dynamics simulations were performed on increasing numbers of hydrocarbon solute molecules in water-filled boxes of different sizes. The intermittent formation of solute clusters gives a free energy that is proportional to the loss in exposed molecular surface area with a constant of proportionality of 45 ± 6 cal/mol⋅Å2. The molecular surface area is the envelope of the solute cluster that is impenetrable by solvent and is somewhat smaller than the more traditional solvent-accessible surface area, which is the area transcribed by the radius of a solvent molecule rolled over the surface of the cluster. When we apply a factor relating molecular surface area to solvent-accessible surface area, we obtain 24 cal/mol⋅Å2. Ours is the first direct calculation, to our knowledge, of the hydrophobic interaction from molecular dynamics simulations; the excellent qualitative and quantitative agreement with experiment proves that simple van der Waals interactions and atomic point-charge electrostatics account for the most important driving force in biology.

Ultrafast detection and control of molecular dynamics

Many elementary chemical and physical processes such as the breaking of a chemical bond or the vibrational motion of atoms within a molecule take place on a femtosecond (fs = 10−15 s) or picosecond (ps = 10−12 s) time scale. It is now possible to monitor these events as a function of time with temporal resolution well below 100 fs. This capability is based on the pump-probe technique where one optical pulse triggers a reaction and a second delayed optical pulse probes the changes that ensue. To illustrate this capability, the dynamics of ligand motion within a protein are presented. Moving beyond casual observation of a reaction to active control of its outcome requires additional experimental and theoretical effort. To illustrate the concept of control, the effect of optical pulse duration on the vibrational dynamics of a tri-atomic molecule are discussed. The experimental and theoretical resources currently available are poised to make the dream of reaction control a reality for certain molecular systems.

Thermodynamic parameters for the helix-coil transition of oligopeptides: molecular dynamics simulation with the peptide growth method.

The helix-coil transition equilibrium of polypeptides in aqueous solution was studied by molecular dynamics simulation. The peptide growth simulation method was introduced to generate dynamic models of polypeptide chains in a statistical (random) coil or an alpha-helical conformation. The key element of this method is to build up a polypeptide chain during the course of a molecular transformation simulation, successively adding whole amino acid residues to the chain in a predefined conformation state (e.g., alpha-helical or statistical coil). Thus, oligopeptides of the same length and composition, but having different conformations, can be incrementally grown from a common precursor, and their relative conformational free energies can be calculated as the difference between the free energies for growing the individual peptides. This affords a straightforward calculation of the Zimm-Bragg sigma and s parameters for helix initiation and helix growth. The calculated sigma and s parameters for the polyalanine alpha-helix are in reasonable agreement with the experimental measurements. The peptide growth simulation method is an effective way to study quantitatively the thermodynamics of local protein folding.

The role of enzyme distortion in the single displacement mechanism of family 19 chitinases

By using molecular dynamics simulations, we have examined the binding of a hexaNAG substrate and two potential hydrolysis intermediates (an oxazoline ion and an oxocarbenium ion) to a family 19 barley chitinase. We find the hexaNAG substrate binds with all sugars in a chair conformation, unlike the family 18 chitinase which causes substrate distortion. Glu 67 is in a position to protonate the anomeric oxygen linking sugar residues D and E whereas Asn 199 serves to hydrogen bond with the C2′ N-acetyl group of sugar D, thus preventing the formation of an oxazoline ion intermediate. In addition, Glu 89 is part of a flexible loop region allowing a conformational change to occur within the active site to bring the oxocarbenium ion intermediate and Glu 89 closer by 4–5 Å. A hydrolysis product with inversion of the anomeric configuration occurs because of nucleophilic attack by a water molecule that is coordinated by Glu 89 and Ser 120. Issues important for the design of inhibitors specific to family 19 chitinases over family 18 chitinases also are discussed.