The Weak Coupling Method for Coupling Continuum Mechanics with Molecular Dynamics

For the global behavior of solids in structural mechanics of nonlinear processes, local effects on the atomistic level play an important role. Often a direct numerical simulation of the macroscopic behavior by a complete resolution of the microscale is for computational reason not possible. Thus, employing a multiscale strategy for an efficient and accurate modelling seems favorable since by separating the problem into two different frameworks, the accuracy of a fine scale model can be combined with the advantages of a computationally efficient model. More precisely a comparably small region of atoms e.g. surrounding the tip of a crack is modelled by molecular dynamics. Outside of this region, we take advantage of the fact that the displacement is almost homogeneous and can thus be modelled efficiently by a linear elastic continuum dynamical simulation. Clearly, both scales offer fundamentally different descriptions of the matter and they use different simulation methods. Whereas on the continuum scale the finite element method and a function space setting is used, the molecular dynamics is based on the movement of particles in the Euclidean space. Additionally, dynamical simulations with a transition zone (handshake region) between atomistic systems and the coarser finite element mesh suffer from unwanted (spurious) reflections, since the finite element method can not represent short wave length vibrational modes. Here a completely new approach is presented, which takes advantage of an infinite dimensional function space for the information transfer between the scales. Starting from a handshake region, the key idea is to construct a transfer operator between the different scales. This transfer operator is based on local averaging taken values. In order to construct the local weight functions, a partition of unity is assigned to the molecular degree of freedom. This allows us to decompose the micro scale displacement in the handshake region into a small and large wave number part by means of a weighted $L^2$ projection. In the first instance, this function space oriented interpretation of the atomistic displacement is applied in the context of a completely overlapping decomposition. More precisely, we consider the case, when the domain of the handshake region is conform with the domain of the molecular dynamics. In order to identify the displacements pertaining to the atomistic or continuum level respectively, we employ a multiscale decomposition. In particular, we decompose the micro scale displacement into a "low frequency'' and a "high frequency'' part in a weak sense. This new approach is also used in the context of a partly overlapping decomposition. Therein, the coarse and the fine scale simulation are matched by constraining the two displacements in the handshake region. The key issue in this context is, that our function space oriented approach allows us to interpret the constraints in a weak sense. Thus the "low frequent'' part can be captured by the coarse scale, whereas the "high frequent'' part of the displacement which has no meaning on the coarse scale is damped in the handshake region. Moreover numerical examples in 1d,2d and 3d show that this approach allows molecular displacements for entering into the continuum domain and the other way round flawlessly

Set-free Markov state model building

Molecular dynamics (MD) simulations face challenging problems since the time scales of interest often are much longer than what is possible to simulate; and even if sufficiently long simulations are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant time scales accessible via coarse grained representations that also allow for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows us to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM

Augmented ant colony algorithm for virtual drug discovery

Docking is a fundamental problem in computational biology and drug discovery that seeks to predict a ligand’s binding mode and affinity to a target protein. However, the large search space size and the complexity of the underlying physical interactions make docking a challenging task. Here, we review a docking method, based on the ant colony optimization algorithm, that ranks a set of candidate ligands by solving a minimization problem for each ligand individually. In addition, we propose an augmented version that takes into account all energy functions collectively, allowing only one minimization problem to be solved. The results show that our modification outperforms in accuracy and efficiency

Qualitative Euclidean embedding of Disjoint Sets of Points

We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean embedding, the distances between the points are generated by a specific relation-preserving function. Consequently, the mutual distances between two points of the same set are specific qualitative transformations of their mutual distances in their original space; the pairwise distances between the points of different sets can be constructed from an arbitrary proximity function.Comment: 16 pages. Included substantial revisions of Theorem 2.1 and 3.1. and readjusted the abstract. Corrected the proof of Theorem 3.1. Elaborated on the solution of the problem in Remark 3.1. Corrected typos. Some changes in notation

Soft versus hard metastable conformations in molecular simulations

Particle methods have become indispensible in conformation dynamics to compute transition rates in protein folding, binding processes and molecular design, to mention a few. Conformation dynamics requires at a decomposition of a molecule’s position space into metastable conformations. In this paper, we show how this decomposition can be obtained via the design of either “soft” or “hard” molecular conformations. We show, that the soft approach results in a larger metastabilitiy of the decomposition and is thus more advantegous. This is illustrated by a simulation of Alanine Dipeptide

Novel multi-objective affinity approach allows to identify pH-specific μ-opioid receptor agonists

Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the -opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported -fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a >50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale

A multi-pronged approach targeting SARS-CoV-2 proteins using ultra-large virtual screening.

The unparalleled global effort to combat the continuing severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic over the last year has resulted in promising prophylactic measures. However, a need still exists for cheap, effective therapeutics, and targeting multiple points in the viral life cycle could help tackle the current, as well as future, coronaviruses. Here, we leverage our recently developed, ultra-large-scale in silico screening platform, VirtualFlow, to search for inhibitors that target SARS-CoV-2. In this unprecedented structure-based virtual campaign, we screened roughly 1 billion molecules against each of 40 different target sites on 17 different potential viral and host targets. In addition to targeting the active sites of viral enzymes, we also targeted critical auxiliary sites such as functionally important protein-protein interactions

Search for new particles in events with energetic jets and large missing transverse momentum in proton-proton collisions at root s=13 TeV

A search is presented for new particles produced at the LHC in proton-proton collisions at root s = 13 TeV, using events with energetic jets and large missing transverse momentum. The analysis is based on a data sample corresponding to an integrated luminosity of 101 fb(-1), collected in 2017-2018 with the CMS detector. Machine learning techniques are used to define separate categories for events with narrow jets from initial-state radiation and events with large-radius jets consistent with a hadronic decay of a W or Z boson. A statistical combination is made with an earlier search based on a data sample of 36 fb(-1), collected in 2016. No significant excess of events is observed with respect to the standard model background expectation determined from control samples in data. The results are interpreted in terms of limits on the branching fraction of an invisible decay of the Higgs boson, as well as constraints on simplified models of dark matter, on first-generation scalar leptoquarks decaying to quarks and neutrinos, and on models with large extra dimensions. Several of the new limits, specifically for spin-1 dark matter mediators, pseudoscalar mediators, colored mediators, and leptoquarks, are the most restrictive to date.Peer reviewe