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Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), previously known as 2019 novel coronavirus (2019-nCoV), has spread rapidly across the globe, creating an unparalleled global health burden and spurring a deepening economic crisis. As of July 7th, 2020, almost seven months into the outbreak, there are no approved vaccines and few treatments available. Developing drugs that target multiple points in the viral life cycle could serve as a strategy to tackle the current as well as future coronavirus pandemics. Here we leverage the power of our recently developed in silico screening platform, VirtualFlow, to identify inhibitors that target SARS-CoV-2. VirtualFlow is able to efficiently harness the power of computing clusters and cloud-based computing platforms to carry out ultra-large scale virtual screens. In this unprecedented structure-based multi-target virtual screening campaign, we have used VirtualFlow to screen an average of approximately 1 billion molecules against each of 40 different target sites on 17 different potential viral and host targets in the cloud. In addition to targeting the active sites of viral enzymes, we also target critical auxiliary sites such as functionally important protein-protein interaction interfaces. This multi-target approach not only increases the likelihood of finding a potent inhibitor, but could also help identify a collection of anti-coronavirus drugs that would retain efficacy in the face of viral mutation. Drugs belonging to different regimen classes could be combined to develop possible combination therapies, and top hits that bind at highly conserved sites would be potential candidates for further development as coronavirus drugs. Here, we present the top 200 in silico hits for each target site. While in-house experimental validation of some of these compounds is currently underway, we want to make this array of potential inhibitor candidates available to researchers worldwide in consideration of the pressing need for fast-tracked drug development.

Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. By determining almost invariant sets of the associated Markov operator, the Monte Carlo sampling splits by a hierarchical annealing process into the essential regions of the state space; therefore UCMC aims at avoiding the typical metastable behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. The correct weighting factors for the various Markov chains are obtained via a coupling matrix, that connects the samplings from the different almost invariant sets. The underlying mathematical structure of this approach is given by a general examination of the uncoupling-coupling procedure. Furthermore, the overall algorithmic scheme of UCMC is applied to the $n$-pentane molecule, a well-known example from molecular dynamics.

Recently, a novel concept for the computation of essential features of the dynamics of Hamiltonian systems (such as molecular dynamics) has been proposed. The realization of this concept had been based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework. This approach allows to define the phrase ``conformation'' in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator $T$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of $T$ via specific hybrid Monte Carlo techniques is shown to lead to a stochastic matrix $P$. With these theoretical preparations, an identification algorithm for conformations is applicable. It is demonstrated that the discretization of $T$ can be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked. Numerical results for the n-pentane molecule and the triribonucleotide adenylyl\emph{(3'-5')}cytidylyl\emph{(3'-5')}cytidin are given and interpreted.

A hybrid Monte Carlo method with adaptive temperature choice is presented, which exactly generates the distribution of a mixed-canonical ensemble composed of two canonical ensembles at low and high temperature. The analysis of resulting Markov chains with the reweighting technique shows an efficient sampling of the canonical distribution at low temperature, whereas the high temperature component facilitates conformational transitions, which allows shorter simulation times. \\The algorithm was tested by comparing analytical and numerical results for the small n-butane molecule before simulations were performed for a triribonucleotide. Sampling the complex multi-minima energy landscape of these small RNA segments, we observed enforced crossing of energy barriers.

The topic of the present paper bas been motivated by a recent computational approach to identify chemical conformations and conformational changes within molecular systems. After proper discretization, the conformations show up as almost invariant aggregates in reversible nearly uncoupled Markov chains. Most of the former work on this subject treated the direct problem: given the aggregates, analyze the loose coupling in connection with the computation of the stationary distribution (aggregation/disaggregation techniques). In contrast to that the present paper focuses on the inverse problem: given the system as a whole, identify the almost invariant aggregates together with the associated transition probabilites. A rather simple and robust algorithm is suggested and illustrated by its application to the n-pentane molecule.

Recently, a novel concept for the computation of essential features of Hamiltonian systems (such as those arising in molecular dynamics) has been proposed. The realization of that concept was based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept based on statistical mechanics, which allows to attack realistic molecular systems. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator $T$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of $T$ via hybrid Monte Carlo techniques (based on short term subtrajectories only) is shown to lead to a stochastic matrix $P$. With these theoretical preparations, an identification algorithm for conformations is applicable (to be presented elsewhere). Numerical results for the n-pentane molecule are given and interpreted.

Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. UCMC aims at avoiding the typical metastable or trapping behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. Therefore, the state space of the chain has to be hierarchically decomposed into its metastable conformations. This is done by means of combining the technique of conformation analysis as recently introduced by the authors, and appropriate annealing strategies. We present a detailed examination of the uncoupling-coupling procedure which uncovers its theoretical background, and illustrates the hierarchical algorithmic approach. Furthermore, application of the UCMC algorithm to the $n$-pentane molecule allows us to discuss the effect of its crucial steps in a typical molecular scenario.