Toy amphiphiles on the computer: What can we learn from generic models?

Generic coarse-grained models are designed such that they are (i) simple and (ii) computationally efficient. They do not aim at representing particular materials, but classes of materials, hence they can offer insight into universal properties of these classes. Here we review generic models for amphiphilic molecules and discuss applications in studies of self-assembling nanostructures and the local structure of bilayer membranes, i.e. their phases and their interactions with nanosized inclusions. Special attention is given to the comparison of simulations with elastic continuum models, which are, in some sense, generic models on a higher coarse-graining level. In many cases, it is possible to bridge quantitatively between generic particle models and continuum models, hence multiscale modeling works on principle. On the other side, generic simulations can help to interpret experiments by providing information that is not accessible otherwise.Comment: Invited feature article, to appear in Macromolecular Rapid Communication

Comparative analysis of rigidity across protein families

We present a comparative study in which 'pebble game' rigidity analysis is applied to multiple protein crystal structures, for each of six different protein families. We find that the main-chain rigidity of a protein structure at a given hydrogen bond energy cutoff is quite sensitive to small structural variations, and conclude that the hydrogen bond constraints in rigidity analysis should be chosen so as to form and test specific hypotheses about the rigidity of a particular protein. Our comparative approach highlights two different characteristic patterns ('sudden' or 'gradual') for protein rigidity loss as constraints are removed, in line with recent results on the rigidity transitions of glassy networks

Mechanical models of proteins

textIn general, this dissertation is concerned with modeling of mechanical behavior of protein molecules. In particular, we focus on coarse-grained models, which bridge the gap in time and length scale between the atomistic simulation and biological processes. The dissertation presents three independent studies involving such models. The first study is concerned with a rigorous coarse-graining method for dynamics of linear systems. In this method, as usual, the conformational space of the original atomistic system is divided into master and slave degrees of freedom. Under the assumption that the characteristic timescales of the masters are slower than those of the slaves, the method results in Langevin-type equations of motion governed by an effective potential of mean force. In addition, coarse-graining introduces hydrodynamic-like coupling among the masters as well as non-trivial inertial effects. Application of our method to the long-timescale part of the relaxation spectra of proteins shows that such dynamic coupling is essential for reproducing their relaxation rates and modes. The second study is concerned with calibration of elastic network models based on the so-called B-factors, obtained from x-ray crystallographic measurements. We show that a proper calibration procedure must account for rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used elastic network models, leading to potentially erroneous network parameters. We develop an elastic network model that properly takes rigid-body motion and crystalline constraints into account. This model reveals that B-factors are dominated by rigid-body motion rather than deformation, and therefore B-factors are poorly suited for identifying elastic properties of protein molecules. Furthermore, it turns out that B-factors for a benchmark set of three hundred and thirty protein molecules can be well approximated by assuming that the protein molecules are rigid. The third study is concerned with the polymer mediated interaction between two planar surfaces. In particular, we consider the case where a thin polymer layer bridges two parallel plates. We consider two models of monodisperse and polydisperse for the polymer layer and obtain an analytical expression for the force-distance relationship of the two plates.Engineering Mechanic

DNA nano-mechanics: how proteins deform the double helix

It is a standard exercise in mechanical engineering to infer the external forces and torques on a body from its static shape and known elastic properties. Here we apply this kind of analysis to distorted double-helical DNA in complexes with proteins. We extract the local mean forces and torques acting on each base-pair of bound DNA from high-resolution complex structures. Our method relies on known elastic potentials and a careful choice of coordinates of the well-established rigid base-pair model of DNA. The results are robust with respect to parameter and conformation uncertainty. They reveal the complex nano-mechanical patterns of interaction between proteins and DNA. Being non-trivially and non-locally related to observed DNA conformations, base-pair forces and torques provide a new view on DNA-protein binding that complements structural analysis.Comment: accepted for publication in JCP; some minor changes in response to review 18 pages, 5 figure + supplement: 4 pages, 3 figure

Structural Dynamics of Free Proteins in Diffraction

Among the macromolecular patterns of biological significance, right-handed α-helices are perhaps the most abundant structural motifs. Here, guided by experimental findings, we discuss both ultrafast initial steps and longer-time-scale structural dynamics of helix-coil transitions induced by a range of temperature jumps in large, isolated macromolecular ensembles of an α-helical protein segment thymosin β_9 (Tβ_9), and elucidate the comprehensive picture of (un)folding. In continuation of an earlier theoretical work from this laboratory that utilized a simplistic structure-scrambling algorithm combined with a variety of self-avoidance thresholds to approximately model helix-coil transitions in Tβ_9, in the present contribution we focus on the actual dynamics of unfolding as obtained from massively distributed ensemble-convergent MD simulations which provide an unprecedented scope of information on the nature of transient macromolecular structures, and with atomic-scale spatiotemporal resolution. In addition to the use of radial distribution functions of ultrafast electron diffraction (UED) simulations in gaining an insight into the elementary steps of conformational interconversions, we also investigate the structural dynamics of the protein via the native (α-helical) hydrogen bonding contact metric which is an intuitive coarse graining approach. Importantly, the decay of α-helical motifs and the (globular) conformational annealing in Tβ_9 occur consecutively or competitively, depending on the magnitude of temperature jump

MAVENs: Motion analysis and visualization of elastic networks and structural ensembles

<p>Abstract</p> <p>Background</p> <p>The ability to generate, visualize, and analyze motions of biomolecules has made a significant impact upon modern biology. Molecular Dynamics has gained substantial use, but remains computationally demanding and difficult to setup for many biologists. Elastic network models (ENMs) are an alternative and have been shown to generate the dominant equilibrium motions of biomolecules quickly and efficiently. These dominant motions have been shown to be functionally relevant and also to indicate the likely direction of conformational changes. Most structures have a small number of dominant motions. Comparing computed motions to the structure's conformational ensemble derived from a collection of static structures or frames from an MD trajectory is an important way to understand functional motions as well as evaluate the models. Modes of motion computed from ENMs can be visualized to gain functional and mechanistic understanding and to compute useful quantities such as average positional fluctuations, internal distance changes, collectiveness of motions, and directional correlations within the structure.</p> <p>Results</p> <p>Our new software, MAVEN, aims to bring ENMs and their analysis to a broader audience by integrating methods for their generation and analysis into a user friendly environment that automates many of the steps. Models can be constructed from raw PDB files or density maps, using all available atomic coordinates or by employing various coarse-graining procedures. Visualization can be performed either with our software or exported to molecular viewers. Mixed resolution models allow one to study atomic effects on the system while retaining much of the computational speed of the coarse-grained ENMs. Analysis options are available to further aid the user in understanding the computed motions and their importance for its function.</p> <p>Conclusion</p> <p>MAVEN has been developed to simplify ENM generation, allow for diverse models to be used, and facilitate useful analyses, all on the same platform. This represents an integrated approach that incorporates all four levels of the modeling process - generation, evaluation, analysis, visualization - and also brings to bear multiple ENM types. The intension is to provide a versatile modular suite of programs to a broader audience. MAVEN is available for download at <url>http://maven.sourceforge.net</url>.</p

Normal mode computations and applications

Proteins are fundamental functional units in cells. Proteins form stable and yet somewhat flexible 3D structures and often function by interacting with other molecules. Their functional behaviors are determined by their 3-D structures as well as their flexibilities. In this thesis, I focus my study on protein dynamics and its role in protein function. One of the most powerful computational methods for studying protein dynamics is normal mode analysis (NMA). Especially its low frequency modes having the intrinsic dynamics of proteins are of interest for most of protein dynamics studies. Although NMA provides analytical solutions to a protein\u27s collective motions, it is inconvenient to use because of its requirement of energy minimization, and it is prohibitive due to the large memory consumption and the long computation time especially when the system is too large. Additionally, it is unclear what meanings the frequencies of normal modes have, and if those meanings can be validated by comparison with the experimental results. The majority of this thesis resolves the above issues. I have addressed following sequence of questions and developed several simplified NMAs as answers: (1) what is the role of inter residue forces; (2) how to remove the energy minimization requirement in NMA yet to keep most of accuracy; (3) how to efficiently build the coarse-grained model from the all-atomic model with keeping atomic accuracy. Additionally, using newly developed models and traditional NMA, I have examined the meaning of normal modes in all frequency range, and have found the connection with experimental results. The last part of this thesis addresses, as an application of normal modes, how the normal modes can depict the sequence of breathing motion of myoglobin to find the transition pathway that dynamically opens ligand migration channels. The results have an excellent agreement with molecular dynamics simulation results and experimentally determined reaction rate constants