Exploring the Free Energy Landscape: From Dynamics to Networks and Back

Abstract

Knowledge of the Free Energy Landscape topology is the essential key to understanding many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers there are, what the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times and rate constants, or hierarchical relationships among basins, completes the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.

Dynamical community structure of populations evolving on genotype networks

“…A variety of network community detection methods based on meaningful underlying dynamical processes have been proposed in different contexts [27][28][29], and all of them share the feature that detected communities can be very different from those based solely on network connectivity. The identification of relevant dynamical indicators of community structure (as were here time to equilibrium or population of nodes) may be system-dependent, and thus remains at present as an open problem worth pursuing.…”

The OH stretch vibration of liquid water reveals hydrogen-bond clusters

“…Towards a more quantitative analysis of the free-energy surface in terms of kinetically homogeneous regions, or substates, we use a recently introduced procedure to partition the landscape into free-energy basins [31] (which is a simpler version of the Stochastic Steepest Descent algorithm introduced in [32]). To that end, we build a transition-gradient-network from the original one by keeping only one link per node, the one with the highest weight (excluding self links).…”

Decoding the energy landscape: extracting structure, dynamics and thermodynamics

“…For example, visualizing the connectivity of stationary point databases, which constitute kinetic transition networks [14,16,57], enables us to connect the selforganizing properties of a diverse range of systems. In this sense, disconnectivity graphs [17,18] provide a distinct 'phenotype' for a zeroth-order prediction of observable properties, such as heat capacity features, and competing time scales for relaxation.…”

“…This software includes tools for global optimization [47] via basin-hopping [48][49][50], location of transition states and characterization of pathways [51], and methods for expanding connected stationary point databases [52] using discrete path sampling [53,54], combined with kinetic analysis [55,56]. Here, we will focus on the insight that can be gained from visualizing the network [14,57] defined by a database of local minima and transition states, and on the emergence of characteristic thermodynamic and kinetic properties as a consequence of particular motifs.…”

“…A connected database of local minima and transition states not only defines a kinetic transition network [14,16,57], but also provides the information required to visualize the landscape using disconnectivity graphs [17]. Constructing such graphs for a wide range of atomic and molecular clusters, biomolecules and condensed matter systems has enabled us to understand how observable properties are governed by the organization of the landscape [2,58,59].…”