Generalized simulated annealing applied to protein folding studies

Structure and dynamics of the E. coli chemotaxis core signaling complex by cryo-electron tomography and molecular simulations

To enable the processing of chemical gradients, chemotactic bacteria possess large arrays of transmembrane chemoreceptors, the histidine kinase CheA, and the adaptor protein CheW, organized as coupled core-signaling units (CSU). Despite decades of study, important questions surrounding the molecular mechanisms of sensory signal transduction remain unresolved, owing especially to the lack of a high-resolution CSU structure. Here, we use cryo-electron tomography and sub-tomogram averaging to determine a structure of the Escherichia coli CSU at sub-nanometer resolution. Based on our experimental data, we use molecular simulations to construct an atomistic model of the CSU, enabling a detailed characterization of CheA conformational dynamics in its native structural context. We identify multiple, distinct conformations of the critical P4 domain as well as asymmetries in the localization of the P3 bundle, offering several novel insights into the CheA signaling mechanism.

Enhanced sampling techniques in molecular dynamics simulations of biological systems

BACKGROUND

Molecular dynamics has emerged as an important research methodology covering systems to the level of millions of atoms. However, insufficient sampling often limits its application. The limitation is due to rough energy landscapes, with many local minima separated by high-energy barriers, which govern the biomolecular motion.

SCOPE OF REVIEW

In the past few decades methods have been developed that address the sampling problem, such as replica-exchange molecular dynamics, metadynamics and simulated annealing. Here we present an overview over theses sampling methods in an attempt to shed light on which should be selected depending on the type of system property studied.

MAJOR CONCLUSIONS

Enhanced sampling methods have been employed for a broad range of biological systems and the choice of a suitable method is connected to biological and physical characteristics of the system, in particular system size. While metadynamics and replica-exchange molecular dynamics are the most adopted sampling methods to study biomolecular dynamics, simulated annealing is well suited to characterize very flexible systems. The use of annealing methods for a long time was restricted to simulation of small proteins; however, a variant of the method, generalized simulated annealing, can be employed at a relatively low computational cost to large macromolecular complexes.

GENERAL SIGNIFICANCE

Molecular dynamics trajectories frequently do not reach all relevant conformational substates, for example those connected with biological function, a problem that can be addressed by employing enhanced sampling algorithms. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Chaotic multiquenching annealing applied to the protein folding problem

The Chaotic Multiquenching Annealing algorithm (CMQA) is proposed. CMQA is a new algorithm, which is applied to protein folding problem (PFP). This algorithm is divided into three phases: (i) multiquenching phase (MQP), (ii) annealing phase (AP), and (iii) dynamical equilibrium phase (DEP). MQP enforces several stages of quick quenching processes that include chaotic functions. The chaotic functions can increase the exploration potential of solutions space of PFP. AP phase implements a simulated annealing algorithm (SA) with an exponential cooling function. MQP and AP are delimited by different ranges of temperatures; MQP is applied for a range of temperatures which goes from extremely high values to very high values; AP searches for solutions in a range of temperatures from high values to extremely low values. DEP phase finds the equilibrium in a dynamic way by applying least squares method. CMQA is tested with several instances of PFP.

GSAFold: a new application of GSA to protein structure prediction

The folding process defines three-dimensional protein structures from their amino acid chains. A protein's structure determines its activity and properties; thus knowing such conformation on an atomic level is essential for both basic and applied studies of protein function and dynamics. However, the acquisition of such structures by experimental methods is slow and expensive, and current computational methods mostly depend on previously known structures to determine new ones. Here we present a new software called GSAFold that applies the generalized simulated annealing (GSA) algorithm on ab initio protein structure prediction. The GSA is a stochastic search algorithm employed in energy minimization and used in global optimization problems, especially those that depend on long-range interactions, such as gravity models and conformation optimization of small molecules. This new implementation applies, for the first time in ab initio protein structure prediction, an analytical inverse for the Visitation function of GSA. It also employs the broadly used NAMD Molecular Dynamics package to carry out energy calculations, allowing the user to select different force fields and parameterizations. Moreover, the software also allows the execution of several simulations simultaneously. Applications that depend on protein structures include rational drug design and structure-based protein function prediction. Applying GSAFold in a test peptide, it was possible to predict the structure of mastoparan-X to a root mean square deviation of 3.00 Å.

Distinctions in early stage unwinding mechanisms of zwitterionic, capped, and neutral forms of different α-helical homopolymeric peptides

Molecular dynamics simulations of α-helical polyalanine, polyleucine, polylysine, and poly(glutamic acid) with different forms of terminal groups in water at 300 K showed sharp distinctions in their unwinding mechanisms. Zwitterionic, capped, and neutral forms of polyalanine, polyleucine, and polylysine have been explored to elucidate their unwinding mechanism at very early stage, e.g., initial time window. Role of water in the unwinding mechanisms of the various helices has been envisaged. Also, it is evident from our calculations that the short- and long-range nonbonded interactions among the side chains is an important factor determining the unwinding mechanisms of the various homopolymeric α-helices. These findings can be helpful in constructing predictive models for understanding of the unwinding of α-helical proteins and peptides.

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

In this work we present a thorough analysis of the phase transitions that occur in a ferromagnetic two-dimensional Ising model, with only nearest-neighbors interactions, in the framework of the Tsallis nonextensive statistics. We performed Monte Carlo simulations on square lattices with linear sizes L ranging from 32 up to 512. The statistical weight of the Metropolis algorithm was changed according to the nonextensive statistics. Discontinuities in the m(T) curve are observed for q< or =0.5 . However, we have verified only one peak on the energy histograms at the critical temperatures, indicating the occurrence of continuous phase transitions. For the 0.5<q< or =1.0 regime, we have found continuous phase transitions between the ordered and the disordered phases, and determined the critical exponents via finite-size scaling. We verified that the critical exponents alpha , beta , and gamma depend on the entropic index q in the range 0.5<q< or =1.0 in the form alpha(q)=(10q2-33q+23)/20 , beta(q)=(2q-1)/8 , and gamma(q)=(q2-q+7)/4 . On the other hand, the critical exponent nu does not depend on q . This suggests a violation of the scaling relations 2beta+gamma=dnu and alpha+2beta+gamma=2 and a nonuniversality of the critical exponents along the ferro-paramagnetic frontier.

Self-similarity and protein compactness

The hydrophobic effect is the major factor that drives a protein toward collapse and folding. As a consequence of the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We analyze the solvent-accessible surface area of 1825 nonhomolog protein chains deposited in the Brookhaven Protein Data Bank. This solvent-accessible surface area presents an intrinsic self-similarity behavior. The comparison between the accessible surface area as function of the number of amino acids and the accessible surface area as function of gyration radius supplies a measure of the scaling exponent close to the one observed by volume as function of radius of gyration or by mass-size exponent. The present finding indicates that the fractal analysis describes the protein compactness as an object packing between random spheres in percolation threshold and crumpled wires.

e-Science: relieving bottlenecks in large-scale genome analyses

The development of affordable, high-throughput sequencing technology has led to a flood of publicly available bacterial genome-sequence data. The availability of multiple genome sequences presents both an opportunity and a challenge for microbiologists, and new computational approaches are needed to extract the knowledge that is required to address specific biological problems and to analyse genomic data. The field of e-Science is maturing, and Grid-based technologies can help address this challenge.

Helix forming tendency of valine substituted poly-alanine: a molecular dynamics investigation

In this study, classical molecular dynamics simulations have been carried out on the valine (guest) substituted poly alanine (host) using the host-guest peptide approach to understand the role of valine in the formation and stabilization of helix. Valine has been substituted in the host peptide starting from N terminal to C terminal. Various structural parameters have been obtained from the molecular dynamics simulation to understand the tolerance of helical motif to valine. Depending on the position of valine in the host peptide, it stabilizes (or destabilizes) the formation of the helical structure. The substitution of valine in the poly alanine at some positions has no effect on the helix formation (deformation). It is interesting to observe the coexistence of 3 10 and alpha-helix in the peptides due to the dynamical nature of the hydrogen bonding interaction and sterical interactions.

Efficient and reliable calculation of Rice-Ramsperger-Kassel-Marcus unimolecular reaction rate constants for biopolymers: modification of Beyer-Swinehart algorithm for degenerate vibrations

The Beyer-Swinehart (BS) algorithm, which calculates vibrational state density and sum, was modified for simultaneous treatment of degenerate vibrations. The modified algorithm was used in the grouped-frequency mode of the Rice-Ramsperger-Kassel-Marcus (RRKM) unimolecular reaction rate constant calculation for proteins with relative molecular mass as large as 100,000. Compared to the original BS method, reduction in computation time by a factor of around 3000 was achieved. Even though large systematic errors arising from frequency grouping were observed for state densities and sums, they more or less canceled each other, thus enabling reliable rate constant calculation. The present method is thought to be adequate for efficient and reliable RRKM calculations for any macromolecule in the gas phase such as the molecular ions of proteins, nucleic acids, and carbohydrates generated inside a mass spectrometer. The algorithm can also be used to calculate the internal energy distribution of a macromolecule at thermal equilibrium.

UV Raman spatially resolved melting dynamics of isotopically labeled polyalanyl peptide: slow alpha-helix melting follows 3(10)-helices and pi-bulges premelting

We used UV resonance Raman (UVRR) to examine the spatial dependence of the T-jump secondary structure relaxation of an isotopically labeled 21-residue mainly Ala peptide, AdP. The AdP penultimate Ala residues were perdeuterated, leaving the central residues hydrogenated, to allow separate monitoring of melting of the middle versus the end peptide bonds. For 5 to 30 degrees C T-jumps, the central peptide bonds show a approximately 2-fold slower relaxation time (189 +/- 31 ns) than do the exterior peptide bonds (97 +/- 15 ns). In contrast, for a 20 to 40 degrees C T-jump, the central peptide bond relaxation appears to be faster (56 +/- 6 ns) than that of the penultimate peptide bonds (131 +/- 46 ns). We show that, if the data are modeled as a two-state transition, we find that only exterior peptide bonds show anti-Arrhenius folding behavior; the middle peptide bonds show both normal Arrhenius-like folding and unfolding. This anti-Arrhenius behavior results from the involvement of pi-bulges/helices and 3(10)-helix states in the melting. The unusual temperature dependence of the (un)folding rates of the interior and exterior peptide bonds is due to the different relative (un)folding rates of 3(10)-helices, alpha-helices, and pi-bulges/helices. Pure alpha-helix unfolding rates are approximately 12-fold slower (approximately 1 micros) than that of pi-bulges and 3(10)-helices. In addition, we also find that the alpha-helix is most stable at the AdP N-terminus where eight consecutive Ala occur, whereas the three hydrophilic Arg located in the middle and at the C-terminus destabilize the alpha-helix in these regions and induce defects such as pi-bulges and 3(10)-helices.

Amino acid hydrophobicity and accessible surface area

It is well known that the hydrophobic effect is the major factor that drives a protein toward collapse and folding. We analyze the variation of the solvent-accessible surface area of amino acids in small fragments of protein (3N45) . In this way, we look into 5526 protein chains deposited in the Brookhaven Protein Data Bank. The accessible surface area behaves as a power law for N9 . The comparison between the loss of accessible area and the self-similar behavior gives us a measure of the possibility of an amino acid to have apolar or polar side chain. It is therefore possible to infer about amino acid hydrophobicity, i.e., if one amino acid has a hydrophobic side chain or if it has a hydrophilic one. Furthermore, the present findings indicate that the variation of the accessible surface area describes an alternative hydrophobicity scale.