Classical non-polarizable force fields. Computing physical properties that can be compared to experiment. Introducing quantum corrections.

All-atom molecular dynamics applied to DNA and DNA-protein complexes.

1. Purpose and overview of history and applications of coarse-grained force fields for proteins. 2. Representation of polypeptide chains in coarse-grained force fields. 3. Connection between statistical mechanics and coarse-grained force field 4. Types of potentials (physics-based, statistical, structure-based, engineered, elastic network). 5. Coarse-grained force fields from potentials of mean force: emergence and role of multibody terms. 6. Equations of motion with coarse-grained force field and algorithms for their solving. 7. Generalized-ensemble sampling with coarse-grained force field. 8. Examples (UNRES, CABS, MARTINI).

Parametrization strategy in biomolecular atomistic force field. Design strategies to build a coarse grained model (mapping scheme, potentials, solvent description). Approach used to parametrize CG potentials (with attention to non-bonded interactions). Backmapping. Transferability problems. Example from a fragment-based coarse grained model for peptide. Brief introduction of possible approach to access multi-scale modeling.

continued

Stochastic motion of a set of coupled harmonic oscillators. Applications to proteins' internal dynamics. Principal component analysis of MD trajectories.

Comparing the internal dynamics of proteins with different fold: dynamics-based protein alignment.

The packing of DNA inside bacteriophages arguably yields the simplest example of genome organisation in living organisms [1, 2]. An indirect indication of how DNA is packaged is provided by the detected spectrum of knots formed by DNA that is circularised inside the P4 viral capsid [3, 4]. The experimental results on the knot spectrum of the P4 DNA are compared to results of coarse-grained simulation of DNA knotting in confined volumes. We start by considering a standard coarse-grained model for DNA which is known to be capable of reproducing the salient physical aspects of free (unconstrained) DNA [5]. Specificallty the model accounts for DNA bending rigidity and excluded volume interactions. By subjecting the model DNA molecules to spatial confinement it is found that confinement favours chiral knots over achiral ones, as found in the P4 experiments. However, no significant bias of torus over twist knots is found, contrary to what found in P4 experiments [6, 7]. A good agreement with experiment is found, instead, upon introducing an additional interaction potential that accounts for tendency of contacting DNA portions to order as in cholesteric liquid crystals. Accounting for this local potential allows us to reproduce the main experimental data on DNA organisation in phages, including the cryo-EM observations and detailed features of the spectrum of DNAknots formed inside viral capsids. The DNA knots we observe are strongly delocalized and, intriguingly, this is shown not to interfere with genome ejection out of the phage [8]. [1] Earnshaw WC, Harrison SC (1977) DNA arrangement in isometric phage heads. Nature 268:598-602. [2] Gelbart WM, Knobler CM (2009) Virology. pressurized viruses. Science 323:1682-1683. [3] Arsuaga J, Vazquez M, Trigueros S, Sumners D, Roca J (2002) Proc Natl Acad Sci U S A 99:5373-5377. [4] Arsuaga, J et al. (2005) Proc Natl Acad Sci U S A 102:9165-9169. [5] Rybenkov VV, Cozzarelli NR, Vologodskii AV (1993) Proc Natl Acad Sci U S A 90:5307-5311. [6] Micheletti C, Marenduzzo D, Orlandini E, Sumners DW (2006) J Chem Phys 124:64903-64903. [7] Micheletti C, Marenduzzo D, Orlandini E, Sumners DW (2008) Biophys J 95:3591-3599. [8] Marenduzzo D, Orlandini E, Stasiak A, Sumners DW, Tubiana L, Micheletti C (2009) Proc Natl Acad Sci U S A 106:22269-22274.

Instead of making incremental steps in science, one should aim for breakthroughs that really make a difference. That is, while there are numerous interesting topics to explore, how many of them are really important. One logical way to approach this question is to think of biologically relevant phenomena that due to limited computing power cannot be unresolved today, but whose detailed considerations will be within reach, say, 2-5 years from now. Considering this, what are the main limitations in current simulation models and approaches that we should fix in order to make a difference, to clarify some of the related grand questions. In this contribution, I would like to use the opportunity to create some discussion in this spirit, examples of current limitations including hydrodynamics, non-equilibrium, and crowding.

Biological membranes compartmentalize cells and form the interface between the cell and its environment. Lipid bilayers are fundamental components of cell membranes. Due to their fluidity, it is very difficult to obtain experimentally atomic level structural information on lipid bilayers in their physiologically relevant state. One property that is difficult to explore in experiments is the membrane ability to dissolve different solutes, including transmembrane peptides and synthetic compounds. We investigated the solubility of fullerene in lipid bilayers, and compared it to its solubility in alkanes. Fullerenes and their derivatives have unique properties that make them interesting for a number of technological applications. Moreover, they are biologically active and can enter easily liposomes and different kinds of cells. Despite numerous studies on both synthetic and biological systems, it is yet unclear how these materials interact with lipid bilayers, and their aggregation in membranes is controversial. I will present results on the validation of all-atom models for C60 fullerene, and on the development of a coarse-grained (CG) model compatible with the MARTINI CG force field for lipids and proteins [1-2]. Using both unbiased and non-equilibrium MD techniques, we characterize the thermodynamics and the kinetics of fullerene aggregation in lipid bilayers and in alkanes. We find that, despite the apparent similarity between alkanes and the bilayer interior, membranes are much better solvents for fullerene. Our results are compatible with experiments showing small perturbations of membrane properties upon addition of fullerene. [1] SJ Marrink et al., J Phys Chem B, 111 (2007) 7812 [2] L Monticelli et al., J Chem Theory Comput, 4 (2008) 819

The disease-linked amyloid β and α-synuclein proteins are currently subject to intense research. I will discuss ongoing studies, where we use implicit solvent all-atom Monte Carlo methods to explore the conformational ensembles sampled by these proteins. We study the full-length forms with 42 and 140 residues, respectively, and compare our results with existing experimental data. The aim is to identify and characterize conformational mechanisms involved in aggregation, and gain insight into the effects of, for instance, mutations and aggregation-inhibiting small molecules. I will also discuss a study of oligomer growth for a fibril-forming 6-residue fragment of protein tau, based on the same methods.

Folding and aggregation of molecules, as well as the adsorption of soft organic matter to solid inorganic substrates belong to the most interesting challenges in studies of structure formation and function of complex macromolecules. The substantially grown interest in the understanding of basic physical mechanisms underlying these processes is caused by their impact in a broad field that ranges from the molecular origin of the loss of biological functionality as, for example, in Alzheimer's disease, to the development of nanotechnological applications such as biosensors. Most of these systems are necessarily of finite size, but molecular structure formation exhibits cooperative effects that resemble similar processes in thermodynamic phase transitions. Inspired by the fact that the density of states, and with it the microcanonical entropy, is the natural result of any generalized-ensemble Monte Carlo simulation, we have introduced a method that allows for a systematic and unique identification and Ehrenfest-like classification of structural transitions in small systems by means of microcanonical analysis. This computational approach to phase transitions, which is hardly accessible in theoretical studies, is particularly useful for the analysis of cooperative behavior in folding, aggregation, and adsorption processes of polymers and proteins. In this talk, I am going to discuss background and application of this method.

Some of the emerging goals in biological sciences are to uncover the roles of molecular structure and dynamics in certain cellular processes and the ability to rationally manipulate these processes. Despite recent revolutionary advances in experimental methodologies, we are still limited in our ability to sample and decipher the structural and dynamic aspects of single molecules that are critical for their biological function. Thus, there is a crucial need for new and unorthodox techniques to uncover the fundamentals of molecular structure and interactions. We developed a multiscale approach, utilizing rapid Discrete Molecular Dynamics (DMD) simulations, that allows us to study large- and small-scale conformational dynamics of molecules and molecular complexes. Using this approach we demonstrate the ability to control protein stability as well as manipulate protein allostery with computational protein design.

Recent advances in molecular biology have revealed that many proteins do not fold spontaneously into stable native state, instead exist in a highly dynamic state without a specific structure. These disordered proteins, often termed as Intrinsically Disordered or Natively Unstructured Proteins, play a pivot role in various cellular mechanisms by interacting with different proteins. However, little is known about their binding mechanism in atomistic details. With a simple but atomistically detailed protein model, we explore the free-energy landscape of pairs of interacting sequences and how it is impacted by 1), variations in the binding mechanism; and 2), the addition of disordered flanks to the binding region. In particular, we focus on various small helical systems and study how different modes of associations impact kinetic and thermodynamic aspects of the interaction.

Globally the energy landscape of a folding protein resembles a partially rough funnel with reduced energetic frustration. A consequence of minimizing energetic frustration is that the topology of the native fold also plays a major role in the folding mechanism. Some folding motifs are easier to design than others suggesting the possibility that evolution not only selected sequences with sufficiently small energetic frustration but also selected more easily designable native structures. The overall structures of the on-route and off-route (traps) intermediates for the folding of more complex proteins are also strongly influenced by topology. Going beyond folding, the power of reduced models to study the physics of protein assembly, protein binding and recognition, and larger biomolecular machines has also proven impressive. Since energetic frustration is sufficiently small, native structure-based models, which correspond to perfectly unfrustrated energy landscapes, have shown to be a powerful approach to explore larger proteins and protein complexes, not only folding but also function associated to large conformational motions. Therefore a discussion of how global motions control the mechanistic processes in the ribosome and molecular motors will be presented. For example, this conceptual framework is allowing us to envisage the dynamics of molecular motors from the structural perspective and it provides the means to make several quantitative predictions that can be tested by experiments.

The Levinthal paradox of protein folding is commonly perceived as a statement about the impossibility of folding by a completely random conformational search. Often missed in such narratives is the fact that the question raised by Levinthal was in response to the experimental discovery of two-state, switch-like cooperative folding in the late 1960s, rather than to the problem of conformational search per se. The implication of this understanding on the notion of a funnel-like energy landscape will be discussed. Comparisons between theory and experiment on cooperative folding indicate a prominent role of desolvation barriers, which contribute to an apparent general organizing principle entailing a coupling between local conformational preferences and nonlocal packing interactions. Investigations into the role of desolvation in protein folding also resolves an apparent inconsistency between experimental observations of enthalpic folding barriers and the theoretical funnel picture of folding. Examples will be given to illustrate how important folding principles have been gleaned from studies using native-centric models and how nonnative interactions may be treated perturbatively in essentially the same conceptual framework.

The so-called protein folding problem is the loose denominator for an amalgam of closely related, unsolved problems that include protein structure prediction, protein design and the simulation of the protein folding process. We adopt a unique probabilistic approach to modeling bio-molecular structure, based on graphical models and directional statistics [1,2,3,4,5]. Notably, we developed the first probabilistic model of protein structure in full atomic detail [1, 4]. In this talk, I will give an overview of how rigorous probabilistic models of something as complicated as a protein structure can be formulated, focusing on the use of graphical models and directional statistics to model angular degrees of freedom. I will also discuss the reference ratio method [6], a novel statistical method that can be seen as a surprising Bayesian variant of the maximum entropy method. This method also sheds an entirely new light on the in protein structure prediction widely used potentials of mean force, which were up to now poorly understood and justified. Finally, I will describe some applications, including the investigation of protein dynamics and the statistical inference of protein structure from nuclear magnetic resonance (NMR) data [7] and small angle X-ray scattering (SAXS) data [8]. [1] Hamelryck, T., Kent, J., Krogh, A. (2006) Sampling realistic protein conformations using local structural bias. PLoS Comput. Biol., 2(9): e131. [2] W. Boomsma, K.V. Mardia, C.C. Taylor, J. Ferkinghoff-Borg, A. Krogh, and T. Hamelryck. (2008) A generative, probabilistic model of local protein structure. Proc. Natl. Acad. Sci. U S A, 105(26):8932–8937. [3] Frellsen, J., Moltke, I., Thiim, M., Mardia, KV., Ferkinghoff-Borg, J., Hamelryck, T. (2009) A probabilistic model of RNA conformational space. PLoS Computational Biology, 5(6), e1000406. [4] Tim Harder, Wouter Boomsma, Martin Paluszewski, Jes Frellsen, Kristoffer Johansson, and Thomas Hamelryck. (2010) Beyond rotamers: a generative, probabilistic model of side chains in proteins. BMC Bioinformatics, 11(1):306. [5] M. Paluszewski and T. Hamelryck. (2010) Mocapy++ – a toolkit for inference and learning in dynamic bayesian networks. BMC bioinformatics, 11(1):126. [6] Thomas Hamelryck, Mikael Borg, Martin Paluszewski, Jonas Paulsen, Jes Frellsen, Christian Andreetta, Wouter Boomsma, Sandro Bottaro, and Jesper Ferkinghoff-Borg (2010). Potentials of mean force for protein structure prediction vindicated, formalized and generalized. PLoS ONE, 5(11):e13714. [7] Simon Olsson, Wouter Boomsma, Jes Frellsen, Sandro Bottaro, Tim Harder, Jesper Ferkinghoff-Borg, and Thomas Hamelryck. (2011) Generative probabilistic models extend the scope of inferential structure determination. J. Magn. Reson., 213(1):182-6. [8] Stovgaard, K., Andreetta, C., Ferkinghoff-Borg, J., Hamelryck, T. (2010) Calculation of accurate small angle X-ray scattering curves from coarse-grained protein models. BMC Bioinformatics, 11:429.

Geyer, T. and Helms, V. (2006) Biophysical Journal, Vol. 91, p. 927-937. Reconstruction of a Kinetic Model of the Chromatophore Vesicles from Rhodobacter Sphaeroides. Geyer, T. and Helms, V. (2006) Biophysical Journal, Vol. 91, p. 921-926. A Spatial Model of the Chromatophore Vesicles of Rhodobacter Sphaeroides and the Position of the Cytochrome bc1 Complex. Geyer, T., Lauck, F., and Helms, V. (2007) Journal of Biotechnology, Vol. 129, p. 212-228. Molecular Stochastic Simulations of Chromatophore Vesicles from Rhodobacter Sphaeroides. Geyer, T., Mol, X., Blaß, S., and Helms, V. (2010) PLoS ONE 5(11): e14070. Bridging the gap: Linking molecular simulations and systemic descriptions of cellular compartments.

Closed DNA circles can be unknotted, knotted or linked (catenated). Such topological entanglements of DNA molecules have important impact on biological processes. Topoisomerases are a ubiquitous class of enzymes that pass one DNA segment through another, serving critical biological functions in cellular replication and maintenance of genome stability. Experimentally, type-2 topoisomerases (topo II) can reduce knot population by as much as 90 times and catenane population by ~ 16 times. These observations raise a fundamental question of physical principle: How does a relatively small enzyme discern the global topology of a much larger DNA molecule that it acts upon? Because it seems that topo II can work magic, it has even been likened to Maxwell's demon. This talk addresses the statistical mechanical basis of topo II actions. Using coarse-grained lattice and continuum wormlike chain models, we have elucidated the mathematical basis of the hypothesis that topo II recognize and act at specific DNA juxtapositions. We found that selective segment passage at hooked geometries can reduce knot populations as dramatically as seen in experiments. Selective segment passage also provided theoretical underpinning for an intriguing empirical scaling relation between unknotting and decatenating potentials. Such selective segment passage also accounts for supercoil simplification (narrowing linking number distribution) by topo II. The consistent agreement between theory and experiment argues for topo II actions at hooked or twisted-hooked DNA juxtapositions. Our investigation also highlights a general connection between local geometry and global topology in polymer configurations.