Single Proteoliposome High-Content Analysis Reveals Differences in the Homo-Oligomerization of GPCRs.

G-protein-coupled receptors (GPCRs) control vital cellular signaling pathways. GPCR oligomerization is proposed to increase signaling diversity. However, many reports have arrived at disparate conclusions regarding the existence, stability, and stoichiometry of GPCR oligomers, partly because of cellular complexity and ensemble averaging of intrareconstitution heterogeneities that complicate the interpretation of oligomerization data. To overcome these limitations, we exploited fluorescence-microscopy-based high-content analysis of single proteoliposomes. This allowed multidimensional quantification of intrinsic monomer-monomer interactions of three class A GPCRs (ß2-adrenergic receptor, cannabinoid receptor type 1, and opsin). Using a billion-fold less protein than conventional assays, we quantified oligomer stoichiometries, association constants, and the influence of two ligands and membrane curvature on oligomerization, revealing key similarities and differences for three GPCRs with decidedly different physiological functions. The assays introduced here will assist with the quantitative experimental observation of oligomerization for transmembrane proteins in general.

Big Data Analytic, Big Step for Patient Management and Care in Puerto Rico.

This letter provides an overview of the application of big data in health care system to improve quality of care, including predictive modelling for risk and resource use, precision medicine and clinical decision support, quality of care and performance measurement, public health and research applications, among others. The author delineates the tremendous potential for big data analytics and discuss how it can be successfully implemented in clinical practice, as an important component of a learning health-care system.

Optimizing transition interface sampling simulations.

We demonstrate that a recently proposed adaptive optimization algorithm for forward flux sampling simulations [E. E. Borrero and F. A. Escobedo, J. Chem. Phys. 129, 024115 (2008)] can be easily applied within the framework of transition interface sampling. This optimization algorithm systematically identifies the kinetic bottlenecks along the order parameter used to partition phase space via interfaces and improves the statistical accuracy of the reaction rate constant estimate. In different versions of the algorithm, the number or the placement of the interfaces (or both) are varied in order to allocate the numerical effort in a balanced way. The algorithm is demonstrated for a simple two-dimensional model and for the dipole flip transition of icelike structures inside carbon nanotubes. For these test systems, the optimization yielded an efficiency increase by a factor of 2-15.

Kinetics and reaction coordinates of the reassembly of protein fragments via forward flux sampling.

We studied the mechanism of the reassembly and folding process of two fragments of a split lattice protein by using forward flux sampling (FFS). Our results confirmed previous thermodynamics and kinetics analyses that suggested that the disruption of the critical core (of an unsplit protein that folds by a nucleation mechanism) plays a key role in the reassembly mechanism of the split system. For several split systems derived from a parent 48-mer model, we estimated the reaction coordinates in terms of collective variables by using the FFS least-square estimation method and found that the reassembly transition is best described by a combination of the total number of native contacts, the number of interchain native contacts, and the total conformational energy of the split system. We also analyzed the transition path ensemble obtained from FFS simulations using the estimated reaction coordinates as order parameters to identify the microscopic features that differentiate the reassembly of the different split systems studied. We found that in the fastest folding split system, a balanced distribution of the original-core amino acids (of the unsplit system) between protein fragments propitiates interchain interactions at early stages of the folding process. Only this system exhibits a different reassembly mechanism from that of the unsplit protein, involving the formation of a different folding nucleus. In the slowest folding system, the concentration of the folding nucleus in one fragment causes its early prefolding, whereas the second fragment tends to remain as a detached random coil. We also show that the reassembly rate can be either increased or decreased by tuning interchain cooperativeness via the introduction of a single point mutation that either strengthens or weakens one of the native interchain contacts (prevalent in the transition state ensemble).

Overcoming barriers in trajectory space: mechanism and kinetics of rare events via Wang-Landau enhanced transition path sampling.

Within the framework of transition path sampling (TPS), activation energies can be computed as path ensemble averages without a priori information about the reaction mechanism [C. Dellago and P. G. Bolhuis, Mol. Simul. 30, 795 (2004)]. Activation energies computed for different conditions can then be used to determine by numerical integration the rate constant for a system of interest from the rate constant known for a reference system. However, in systems with complex potential energy surfaces, multiple reaction pathways may exist making ergodic sampling of trajectory space difficult. Here, we present a combination of TPS with the Wang-Landau (WL) flat-histogram algorithm for an efficient sampling of the transition path ensemble. This method, denoted by WL-TPS, has the advantage that from one single simulation, activation energies at different temperatures can be determined even for systems with multiple reaction mechanisms. The proposed methodology for rate constant calculations does not require the knowledge of the reaction coordinate and is generally applicable to Arrhenius and non-Arrhenius processes. We illustrate the applicability of this technique by studying a two-dimensional toy system consisting of a triatomic molecule immersed in a fluid of repulsive soft disks. We also provide an expression for the calculation of activation volumes from path averages such that the pressure dependence of the rate constant can be obtained by numerical integration.

Kinetics and mechanism of the unfolding native-to-loop transition of Trp-cage in explicit solvent via optimized forward flux sampling simulations.

The native-to-loop (N-L) unfolding transition of Trp-cage protein was studied via optimized forward flux sampling (FFS) methods with trajectories evolved using molecular dynamics. The rate constant calculated from our simulations is in good agreement with the experimental value for the native-to-unfolded transition of this protein; furthermore, the trajectories sampled a phase region consistent with that reported in previous studies for the N-L transition using transition path sampling and transition interface sampling. A new variant of FFS is proposed and implemented that allows a better control of a constant flux of partial paths. A reaction coordinate model was obtained, at no extra cost, from the transition path ensemble generated by FFS, through iterative use of the FFS-least-square estimation method [E. E. Borrero and F. A. Escobedo, J. Chem. Phys. 127, 164101 (2007)] and an adaptive staging optimization algorithm [E. E. Borrero and F. A. Escobedo, J. Chem. Phys. 129, 024115 (2008)]. Finally, we further elucidate the unfolding mechanism by correlating the unfolding progress with changes in the root mean square deviation from the α carbons of the native state, the root mean square deviation from an ideal α-helix, and other structural properties of the protein.

Simulating the kinetics and thermodynamics of transitions via forward flux/umbrella sampling.

First, a technique is introduced for computing equilibrium probability distributions for transitional rare-event simulations by combining the ensemble of trajectories generated by forward flux sampling (FFS) and by umbrella sampling (US) in multiple windows along an order parameter of interest; this method is denoted FFS-US. Second, the FFS algorithm is extended to obtain rate constants of partial transitions involving intermediate states from a single simulation; this is denoted "multiple state" FFS. For the FFS-US method, a FFS algorithm (preoptimized for order parameter and staging) is used to take advantage of its zero potential bias of phase-space sampling to gather histogram data with which to jump start the US and get the equilibrium distributions. In this way, kinetic data (like the rate constants and the transition path ensemble) and the underlying free-energy landscape (or probability distribution) of the system are obtained efficiently and concurrently. The applicability of these techniques is illustrated by studying several test systems, including two that involve potential energy surfaces having multiple metastable states and transition pathways, representative of complex kinetic behavior.

Kinetics and reaction coordinate for the isomerization of alanine dipeptide by a forward flux sampling protocol.

Forward flux sampling (FFS) simulations were used to study the kinetics of alanine dipeptide both in vacuum and in explicit solvent. The recently proposed FFS least-squares estimation approach and an algorithm that optimizes the position of the interfaces were implemented to determine a reaction coordinate that adequately describes the transition dynamics. A new method is also introduced to try to ensure that the ensemble of "starting points" (for the trial trajectories) is properly sampled. The rate constant estimates for the C7(eq)-->C5 transition of alanine dipeptide in vacuum were used to demonstrate the consistency between Monte Carlo and molecular dynamics (MD) simulations. FFS-MD simulations were then performed for the study of the beta(2)/alpha(R)-->C5/C7(eq) transition in explicit solvent. The kinetic results for both systems in vacuum and explicit solvent are in general agreement with previous experimental and computational studies for this peptide. In vacuum, an additional dihedral angle besides the one typically used as order parameter is identified as a significant variable in the reaction coordinate model. In solution, several dihedral angles and variables that describe the solvent action on the molecule's dynamics are found to play a significant role in the description of the system's dynamics.

Optimizing the sampling and staging for simulations of rare events via forward flux sampling schemes.

In this work, we present an adaptive algorithm to optimize the phase space sampling for simulations of rare events in complex systems via forward flux sampling (FFS) schemes. In FFS, interfaces are used to partition the phase space along an order parameter lambda connecting the initial and final regions of interest. Since the kinetic "bottleneck" regions along the order parameter are not usually known beforehand, an adaptive procedure is used that first finds these regions by estimating the rate constants associated with reaching subsequent interfaces; thereafter, the FFS simulation is reset to concentrate the sampling on those bottlenecks. The approach can optimize for either the number and position of the interfaces (i.e., optimized lambda phase staging) or the number M of fired trial runs per interface (i.e., the {M(i)} set) to minimize the statistical error in the rate constant estimation per simulation period. For example, the optimization of the lambda staging leads to a net constant flux of partial trajectories between interfaces and hence a constant flux of connected paths throughout the region between the two end states. The method is demonstrated for several test systems, including the folding of a lattice protein. It is shown that the proposed approach leads to an optimized lambda staging and {M(i)} set which increase the computational efficiency of the sampling algorithm.

Transition path sampling and forward flux sampling. Applications to biological systems.

The last decade has seen a rapid growth in the number of simulation methods and applications dealing with the sampling of transition pathways of rare nanoscale events. Such studies are crucial, for example, for understanding the mechanism and kinetics of conformational transitions and enzymatic events associated with the function of biomolecules. In this review, a broad account of transition path sampling approaches is provided, starting from the general concepts, progressing to the specific principles that underlie some of the most important methods, and eventually singling out the so-called forward flux sampling method for a more detailed description. This is done because forward flux sampling, despite its appealing simplicity and potential efficiency, has thus far received limited attention from practitioners. While path sampling methods have a widespread application to many types of rare transitional events, here only recent applications involving biomolecules are reviewed, including isomerization, protein folding, and enzyme catalysis.

Reaction coordinates and transition pathways of rare events via forward flux sampling.

A new approach is developed for identifying suitable reaction coordinates to describe the progression of rare events in complex systems. The method is based on the forward flux sampling (FFS) technique and standard least-square estimation (LSE) and it is denoted as FFS-LSE. The FFS algorithm generates trajectories for the transition between stable states as chains of partially connected paths, which can then be used to obtain "on-the-fly" estimates for the committor probability to the final region, p(B). These p(B) data are then used to screen a set of candidate collective properties for an optimal order parameter (i.e., reaction coordinate) that depends on a few relevant variables. LSE is used to find the coefficients of the proposed reaction coordinate model and an analysis of variance is used to determine the significant terms in the model. The method is demonstrated for several test systems, including the folding of a lattice protein. It is shown that a simple approximation to p(B) via a model linear on energy and number of native contacts is sufficient to describe the intrinsic dynamics of the protein system and to ensure an efficient sampling of pathways. In addition, since the p(B) surface found from the FFS-LSE approach leads to the identification of the transition state ensemble, mechanistic details of the dynamics of the system can be readily obtained during a single FFS-type simulation without the need to perform additional committor simulations.

Folding kinetics of a lattice protein via a forward flux sampling approach.

We implement a forward flux sampling approach [R. J. Allen et al., J. Chem. Phys. 124, 194111 (2006)] for calculating transition rate constants and for sampling paths of protein folding events. The algorithm generates trajectories for the transition between the unfolded and folded states as chains of partially connected paths, which can be used to obtain the transition-state ensemble and the properties that characterize these intermediates. We apply this approach to Monte Carlo simulations of a model lattice protein in open space and in confined spaces of varying dimensions. We study the effect of confinement on both protein thermodynamic stability and folding kinetics; the former by mapping free-energy landscapes and the latter by the determination of rate constants and mechanistic details of the folding pathway. Our results show that, for the range of temperatures where the native state is stable, confinement of a protein destabilizes the unfolded state by reducing its entropy, resulting in increased thermodynamic stability of the folded state. Relative to the folding in open space, we find that the kinetics can be accelerated at temperatures above the temperature at which the unconfined protein folds fastest and that the rate constant increases with the number of constrained dimensions. By examining the statistical properties of the transition-state ensemble, we detect signs of a classical nucleation folding mechanism for a core of native contacts formed at an early stage of the process. This nucleus acts as folding foci and is composed of those residues that have higher probability to form native contacts in the transition-state intermediates, which can vary depending on the confinement conditions of the system.