arXiv subjects
Publications and source records attributed to Francesco Rao.
A kinetic over-relaxation minimizer, based on a lattice version of the Boltzmann equation is presented. The method is validated against standard Metropolis Monte Carlo, and proves very effective in attaining (global) minima of classical pair potentials, involving solid body rotations. Linear scaling of the computational time to minimum with the system size is demonstrated.
Coherent transport promises to be the basis for an emerging new technology. Notwithstanding, a mechanistic understanding of the fundamental principles behind optimal scattering media is still missing. Here, complex network analysis is applied for the characterization of geometries that result in optimal coherent transport. The approach is tailored towards the elucidation of the subtle relationship between transport and geometry. Investigating systems with a different number of elementary units allows us to identify classes of structures which are common to all system sizes and which possess distinct robustness features. In particular, we find that small groups of two or three sites closely packed together that do not carry excitation at any time are fundamental to realize efficient and robust excitation transport. Features identified in small systems recur also in larger systems, what suggests that such strategy can efficiently be used to construct close-to-optimal transport properties irrespective of the system size.
Introduction of polarizability in classical molecular simulations holds the promise to increase accuracy as well as prediction power to computer modeling. To introduce polarizability in a straight-forward way one strategy is based on Drude particles: dummy atoms whose displacements mimic polarizability. In this work, molecular dynamics simulations of SWM4-NDP, a Drude-based water model, were performed for a wide range of temperatures going from 170 K to 340 K. We found that the density maximum is located far down in the supercooled region at around 200 K, roughly 80 K below the experimental value. Very long relaxation times together with a new increase in the density were found at even lower temperatures. On the other hand, both hydrogen-bond coordination up to the second solvation shell and tetrahedral order resembled very much what was found for TIP4P/2005, a very good performer at the reproduction of the density curve and other properties of bulk water in temperature space. Such a discrepancy between the density curve and the hydrogen bond propensity was not observed in other conventional water models. Our results suggest that while the simplicity of the SWM4 model is appealing, its current parametrization needs improvements in order to correctly reproduce water behavior beyond ambient conditions.
In the last decades several hydrogen-bond definitions were proposed by classical computer simulations. Aiming at validating their self-consistency on a wide range of conditions, here we present a comparative study of six among the most common hydrogen-bond definitions for temperatures ranging from 220K to 400K and six classical water models. Our results show that, in the interval of temperatures investigated, a generally weak agreement among definitions is present. Moreover, cutoff choice for geometrically based definitions depends on both temperature and water model. As such, analysis of the same water model at different temperatures as well as different water models at the same temperature would require the development of specific cutoff values. Interestingly, large discrepancies were found between two hydrogen-bond definitions which were recently introduced to improve on more conventional methods. Our results anticipate that a more universal way to characterize hydrogen-bonds in classical molecular systems is needed.
At the fundamental level, our understanding of water hydrogen-bond dynamics has been largely built on the detailed analysis of classical molecular simulations. The latter served to develop a plethora of hydrogen bond definitions based on different properties, including geometrical distances, topology and energetics. Notwithstanding, no real consensus emerged from these approaches, making the development of a consistent and reliable definition elusive. In this contribution, a framework to study hydrogen bonds in liquid water based purely on kinetics is presented. This approach makes use of the analysis of commitment probabilities without relying on arbitrarily chosen order parameters and cutoffs. Our results provide evidence for a self-consistent description, resulting in a clear multi-exponential behavior of the kinetics.
Quantum transport is strongly influenced by interference with phase relations that depend sensitively on the scattering medium. Since even small changes in the geometry of the medium can turn constructive interference to destructive, a clear relation between structure and fast, efficient transport is difficult to identify. Here we present a complex network analysis of quantum transport through disordered systems to elucidate the relationship between transport efficiency and structural organization. Evidence is provided for the emergence of structural classes with different geometries but similar high efficiency. Specifically, a structural motif characterised by pair sites which are not actively participating to the dynamics renders transport properties robust against perturbations. Our results pave the way for a systematic rationalization of the design principles behind highly efficient transport which is of paramount importance for technological applications as well as to address transport robustness in natural light harvesting complexes.
Recent advances in computational power and simulation programs finally delivered the first examples of reversible folding for small proteins with an all-atom description. But having at hand the atomistic details of the process did not lead to a straightforward interpretation of the mechanism. For the case of the Fip35 WW-domain where multiple long trajectories of 100 μs are available from D. E. Shaw Research, different interpretations emerged. Some of those are in clear contradiction with each other while others are in qualitative agreement. Here, we present a network-based analysis of the same data by looking at the local fluctuations of conventional order parameters for folding. We found that folding occurs through two major pathways, one almost four times more populated than the other. Each pathway involves the formation of an intermediate with one of the two hairpins in a native configuration. The quantitative agreement of our results with a state-of-the-art reaction coordinate optimization procedure as well as qualitative agreement with other Markov-state-models and different simulation schemes provides strong evidence for a multiple folding pathways scenario with the presence of intermediates.
Molecular simulations as well as single molecule experiments have been widely analyzed in terms order parameters, the latter representing candidate probes for the relevant degrees of freedom. Notwithstanding this approach is very intuitive, mounting evidence showed that such description is not accurate, leading to ambiguous definitions of states and wrong kinetics. To overcome these limitations a framework making use of order parameter fluctuations in conjunction with complex network analysis is investigated. Derived from recent advances in the analysis of single molecule time traces, this approach takes into account of the fluctuations around each time point to distinguish between states that have similar values of the order parameter but different dynamics. Snapshots with similar fluctuations are used as nodes of a transition network, the clusterization of which into states provides accurate Markov-State-Models of the system under study. Application of the methodology to theoretical models with a noisy order parameter as well as the dynamics of a disordered peptide illustrates the possibility to build accurate descriptions of molecular processes on the sole basis of order parameter time series without using any supplementary information.
Ion channels form pores across the lipid bilayer, selectively allowing inorganic ions to cross the membrane down their electrochemical gradient. While the study of ion desolvation free-energies have attracted much attention, the role of water inside the pore is less clear. Here, molecular dynamics simulations of a reduced model of the KcsA selectivity filter indicate that the equilibrium position of Na+, but not of K+, is strongly influenced by confined water. The latter forms a stable complex with Na+, moving the equilibrium position of the ion to the plane of the backbone carbonyls. Almost at the centre of the binding site, the water molecule is trapped by favorable electrostatic interactions and backbone hydrogen-bonds. In the absence of confined water the equilibrium position of both Na+ and K+ is identical. Our observations strongly suggest a previously unnoticed active role of confined water in the selectivity mechanism of ion channels.
Free-energy landscape theory is often used to describe complex molecular systems. Here, a microscopic description of water structure and dynamics based on configuration-space-networks and molecular dynamics simulations of the TIP4P/2005 model is applied to investigate the free-energy landscape of water. The latter is built on top of a large set of water microstates describing the kinetic stability of local hydrogen-bond arrangements up to the second solvation shell. In temperature space, the landscape displays three regions with an overall different organization. At ambient conditions, the free-energy surface is characterized by structural inhomogeneities with multiple, structurally well defined, short-lived basins of attraction. Below around ambient temperature, the liquid rapidly becomes homogeneous. In this regime, the landscape is funneled-like, with fully-coordinated water arrangements at the bottom of the funnel. Finally, a third region develops below the temperature of maximal compressibility (Widom line) where the funnel becomes steeper with few interconversions between microstates other than the fully coordinated ones. Our results present a viable a way to manage the complexity of water structure and dynamics, connecting microscopic properties to its ensemble behavior.
Supercooled water is a metastable phase of liquid water below the melting temperature. An interesting discussion recently developed on the relationship between crystallization rate and the time scales of equilibration within the liquid phase. Calculations using a coarse grained monatomic model of water, the mW model, suggested that equilibration of the liquid below the temperature of homogeneous nucleation $T_H\approx225$ K is slower than ice nucleation. Here, a 3 $μ$s long molecular dynamics simulation of the TIP4P-Ew water model is presented to investigate the relaxation properties of an atomistic model in the supercooled region below $T_H$. Evidence is provided that the liquid phase of the TIP4P-Ew model is at equilibrium in the supercooled regime before ice nucleation.
A large number of water models exists for molecular simulations. They differ in the ability to reproduce specific features of real water instead of others, like the correct temperature for the density maximum or the diffusion coefficient. Past analysis mostly concentrated on ensemble quantities, while few data was reported on the different microscopic behavior. Here, we compare seven widely used classical water models (SPC, SPC/E, TIP3P, TIP4P, TIP4P-Ew, TIP4P/2005 and TIP5P) in terms of their local structure-forming capabilities through hydrogen bonds for temperatures ranging from 210 K to 350 K by the introduction of a set of order parameters taking into account the configuration of the second solvation shell. We found that all models share the same structural pattern up to a temperature shift. When this shift is applied, all models overlap onto a master curve. Interestingly, increased stabilization of fully coordinated structures extending to at least two solvation shells is found for models that are able to reproduce the correct position of the density maximum. Our results provide a self-consistent atomic-level structural comparison protocol, which can be of help in elucidating the influence of different water models on protein structure and dynamics.
The dynamical characterization of proteins is crucial to understand protein function. From a microscopic point of view, protein dynamics is governed by the local atomic interactions that, in turn, trigger the functional conformational changes. Unfortunately, the relationship between local atomic fluctuations and global protein rearrangements is still elusive. Here, atomistic molecular dynamics simulations in conjunction with complex network analysis show that fast peptide relaxations effectively build the backbone of the global free-energy landscape, providing a connection between local and global atomic rearrangements. A minimum-spanning-tree representation, built on the base of transition gradients networks, results in a high resolution mapping of the system dynamics and thermodynamics without requiring any a priori knowledge of the relevant degrees of freedom. These results suggest the presence of a local mechanism for the high communication efficiency generally observed in complex systems.
For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a real--world network it is therefore crucial to compare the measured results with a null model counterpart. Here we focus on dense and weighted networks, proposing a suitable null model and studying the behaviour of the degree correlations as measured by the rich-club coefficient. Our method solves an existing problem with the randomization of dense unweighted graphs, and at the same time represents a generalization of the rich--club coefficient to weighted networks which is complementary to other recently proposed ones.
The configuration space network (CSN) of a dynamical system is an effective approach to represent the ensemble of configurations sampled during a simulation and their dynamic connectivity. To elucidate the connection between the CSN topology and the underlying free-energy landscape governing the system dynamics and thermodynamics, an analytical soluti on is provided to explain the heavy tail of the degree distribution, neighbor co nnectivity and clustering coefficient. This derivation allows to understand the universal CSN network topology observed in systems ranging from a simple quadratic well to the native state of the beta3s peptide and a 2D lattice heteropolymer. Moreover CSN are shown to fall in the general class of complex networks describe d by the fitness model.
Many complex networks have an underlying modular structure, i.e., structural subunits (communities or clusters) characterized by highly interconnected nodes. The modularity $Q$ has been introduced as a measure to assess the quality of clusterizations. $Q$ has a global view, while in many real-world networks clusters are linked mainly \emph{locally} among each other (\emph{local cluster-connectivity}). Here, we introduce a new measure, localized modularity $LQ$, which reflects local cluster structure. Optimization of $Q$ and $LQ$ on the clusterization of two biological networks shows that the localized modularity identifies more cohesive clusters, yielding a complementary view of higher granularity.
The assumption that similar structures have similar folding probabilities ($p_{fold}$) leads naturally to a procedure to evaluate $p_{fold}$ for every snapshot saved along an equilibrium folding-unfolding trajectory of a structured peptide or protein. The procedure utilizes a structurally homogeneous clustering and does not require any additional simulation. It can be used to detect multiple folding pathways as shown for a three-stranded antiparallel $β$-sheet peptide investigated by implicit solvent molecular dynamics simulations.
The conformation space of a 20-residue antiparallel $β$-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Conformations are nodes of the network, and the transitions between them are links. The conformation space network describes the significant free energy minima and their dynamic connectivity without projections into arbitrarily chosen reaction coordinates. As previously found for the Internet and the World-Wide Web as well as for social and biological networks, the conformation space network is scale-free and contains highly connected hubs like the native state which is the most populated free energy basin. Furthermore, the native basin exhibits a hierarchical organization which is not found for a random heteropolymer lacking a predominant free-energy minimum. The network topology is used to identify conformations in the folding transition state ensemble, and provides a basis for understanding the heterogeneity of the transition state and denaturated state ensemble as well as the existence of multiple pathway