A goal in the kinetic characterization of a macromolecular system is the description of its slow relaxation processes, involving (i) identification of the structural changes involved in these processes, and (ii) estimation of the rates or timescales at which these slow processes occur. Most of the approaches to this task, including Markov models, Master-equation models, and kinetic network models, start by discretizing the high-dimensional state space and then characterize relaxation processes in terms of the eigenvectors and eigenvalues of a discrete transition matrix. The practical success of such an approach depends very much on the ability to finely discretize the slow order parameters. How can this task be achieved in a high-dimensional configuration space without relying on subjective guesses of the slow order parameters? In this paper, we use the variational principle of conformation dynamics to derive an optimal way of identifying the "slow subspace" of a large set of prior order parameters -either generic internal coordinates (distances and dihedral angles), or a user-defined set of parameters. It is shown that a method to identify this slow subspace exists in statistics: the time-lagged independent component analysis (TICA). Furthermore, optimal indicators-order parameters indicating the progress of the slow transitions and thus may serve as reaction coordinates-are readily identified. We demonstrate that the slow subspace is well suited to construct accurate kinetic models of two sets of molecular dynamics simulations, the 6-residue fluorescent peptide MR121-GSGSW and the 30-residue natively disordered peptide KID. The identified optimal indicators reveal the structural changes associated with the slow processes of the molecular system under analysis.

The understanding of protein-ligand binding is of critical importance for biomedical research, yet the process itself has been very difficult to study because of its intrinsically dynamic character. Here, we have been able to quantitatively reconstruct the complete binding process of the enzyme-inhibitor complex trypsin-benzamidine by performing 495 molecular dynamics simulations of free ligand binding of 100 ns each, 187 of which produced binding events with an rmsd less than 2 Å compared to the crystal structure. The binding paths obtained are able to capture the kinetic pathway of the inhibitor diffusing from solvent (S0) to the bound (S4) state passing through two metastable intermediate states S2 and S3. Rather than directly entering the binding pocket the inhibitor appears to roll on the surface of the protein in its transition between S3 and the final binding pocket, whereas the transition between S2 and the bound pose requires rediffusion to S3. An estimation of the standard free energy of binding gives ΔG°¼ −5.2 AE 0.4 kcal∕mol (cf. the experimental value −6.2 kcal∕mol), and a two-states kinetic model k on ¼ ð1.5 AE 0.2Þ × 10 8 M −1 s −1 and k off ¼ ð9.5 AE 3.3Þ× 10 4 s −1 for unbound to bound transitions. The ability to reconstruct by simple diffusion the binding pathway of an enzyme-inhibitor binding process demonstrates the predictive power of unconventional high-throughput molecular simulations. Moreover, the methodology is directly applicable to other molecular systems and thus of general interest in biomedical and pharmaceutical research.binding affinity | distributed computing | Markov state model | transition-state kinetics | association rates U nderstanding protein-ligand binding processes is undoubtedly of critical importance in structure-based drug design, and much effort is being invested in experimental and computational methods to resolve binding. The focus has generally resided on predicting the lowest energy binding pose of a ligand (1, 2), but resolving the kinetic mechanisms and structure activity relationships of the ligand has increasingly been recognized to provide additional mechanisms for elucidating therapeutically safe and differentiated responses (3, 4). The kinetics of binding depend on the characteristic transition states of a system. Hence, characterizing the binding pathway is crucial to understanding how to control and reengineer the process of binding.Commonly used methods to experimentally determine kinetic data for biomolecular interactions are available (5), but fast timescale resolution of a binding mechanism with atomic resolution remains difficult due to the intrinsic dynamic and volatile nature of the process of binding. From a computational perspective, the difficulty lies in accurately measuring binding affinities and kinetic parameters, but it has become easier to try to predict binding free energies on a limited number of targets and to qualitatively interpret binding mechanisms using molecular dynamics. Although it still requires substantial computational reso...

Dynamic time warping is a popular technique for comparing time series, providing both a distance measure that is insensitive to local compression and stretches and the warping which optimally deforms one of the two input series onto the other. A variety of algorithms and constraints have been discussed in the literature. The dtw package provides an unification of them; it allows R users to compute time series alignments mixing freely a variety of continuity constraints, restriction windows, endpoints, local distance definitions, and so on. The package also provides functions for visualizing alignments and constraints using several classic diagram types.

Polycythemia vera (PV) and essential thrombocythemia (ET) are myeloproliferative neoplasms with variable risk of evolution into post-PV and post-ET myelofibrosis, from now on referred to as secondary myelofibrosis (SMF). No specific tools have been defined for risk stratification in SMF. To develop a prognostic model for predicting survival, we studied 685 JAK2, CALR, and MPL annotated patients with SMF. Median survival of the whole cohort was 9.3 years (95% CI: 8-not reached-NR-). Through penalized Cox regressions we identified negative predictors of survival and according to beta risk coefficients we assigned 2 points to hemoglobin level <11 g/dl, to circulating blasts ⩾3%, and to CALR-unmutated genotype, 1 point to platelet count <150 × 10/l and to constitutional symptoms, and 0.15 points to any year of age. Myelofibrosis Secondary to PV and ET-Prognostic Model (MYSEC-PM) allocated SMF patients into four risk categories with different survival (P<0.0001): low (median survival NR; 133 patients), intermediate-1 (9.3 years, 95% CI: 8.1-NR; 245 patients), intermediate-2 (4.4 years, 95% CI: 3.2-7.9; 126 patients), and high risk (2 years, 95% CI: 1.7-3.9; 75 patients). Finally, we found that the MYSEC-PM represents the most appropriate tool for SMF decision-making to be used in clinical and trial settings.