A community effort in SARS-CoV-2 drug discovery.

The COVID-19 pandemic continues to pose a substantial threat to human lives and is likely to do so for years to come. Despite the availability of vaccines, searching for efficient small-molecule drugs that are widely available, including in low- and middle-income countries, is an ongoing challenge. In this work, we report the results of an open science community effort, the "Billion molecules against COVID-19 challenge", to identify small-molecule inhibitors against SARS-CoV-2 or relevant human receptors. Participating teams used a wide variety of computational methods to screen a minimum of 1 billion virtual molecules against 6 protein targets. Overall, 31 teams participated, and they suggested a total of 639,024 molecules, which were subsequently ranked to find 'consensus compounds'. The organizing team coordinated with various contract research organizations (CROs) and collaborating institutions to synthesize and test 878 compounds for biological activity against proteases (Nsp5, Nsp3, TMPRSS2), nucleocapsid N, RdRP (only the Nsp12 domain), and (alpha) spike protein S. Overall, 27 compounds with weak inhibition/binding were experimentally identified by binding-, cleavage-, and/or viral suppression assays and are presented here. Open science approaches such as the one presented here contribute to the knowledge base of future drug discovery efforts in finding better SARS-CoV-2 treatments.

DENVIS: Scalable and High-Throughput Virtual Screening Using Graph Neural Networks with Atomic and Surface Protein Pocket Features.

Computational methods for virtual screening can dramatically accelerate early-stage drug discovery by identifying potential hits for a specified target. Docking algorithms traditionally use physics-based simulations to address this challenge by estimating the binding orientation of a query protein-ligand pair and a corresponding binding affinity score. Over the recent years, classical and modern machine learning architectures have shown potential for outperforming traditional docking algorithms. Nevertheless, most learning-based algorithms still rely on the availability of the protein-ligand complex binding pose, typically estimated via docking simulations, which leads to a severe slowdown of the overall virtual screening process. A family of algorithms processing target information at the amino acid sequence level avoid this requirement, however, at the cost of processing protein data at a higher representation level. We introduce deep neural virtual screening (DENVIS), an end-to-end pipeline for virtual screening using graph neural networks (GNNs). By performing experiments on two benchmark databases, we show that our method performs competitively to several docking-based, machine learning-based, and hybrid docking/machine learning-based algorithms. By avoiding the intermediate docking step, DENVIS exhibits several orders of magnitude faster screening times (i.e., higher throughput) than both docking-based and hybrid models. When compared to an amino acid sequence-based machine learning model with comparable screening times, DENVIS achieves dramatically better performance. Some key elements of our approach include protein pocket modeling using a combination of atomic and surface features, the use of model ensembles, and data augmentation via artificial negative sampling during model training. In summary, DENVIS achieves competitive to state-of-the-art virtual screening performance, while offering the potential to scale to billions of molecules using minimal computational resources.

Variational model for the delayed collapse of Bose-Einstein condensates.

We present an action that can be used to study variationally the collapse of Bose-Einstein condensates. This action is real, even though it includes dissipative terms. It adopts long-range interactions between the atoms, so that there is always a stable minimum of the energy, even if the remaining number of atoms is above the number that in the case of local interactions is the critical one. The proposed action incorporates the time needed for the abrupt and delayed onset of collapse, yielding in fact its dependence on the scattering length. We show that the evolution of the condensate is equivalent to the motion of a particle in an effective potential. The particle begins its motion far from the point of stable equilibrium and it then proceeds to oscillate about that point. We prove that the resulting large oscillations in the shape of the wave function after the collapse have frequencies equal to twice the frequencies of the traps. Our results agree with the experimental observations.

Evolution of a Bose-Einstein condensate in a rapidly expanding circular box.

We examine the evolution of the ground state of a Bose-Einstein condensate in a two-dimensional circular box, the wall of which is initially at rest and then recedes with large and constant speed. The final state of the condensate depends on the rapidity of the expansion of the box. If the number of atoms in the condensate is small compared to the dimensionless speed of the wall, then the condensate becomes a mixture of excitations and follows the expansion of the box, leaving empty though an increasingly larger region between the condensate boundary and the wall. If, on the other hand, the number of atoms is large compared to the dimensionless speed of the wall, then the condensate is always in the ground state and spreads uniformly in all of the expanding box, the condensate boundary always coinciding with the receding wall. Approximate analytic expressions are found for the evolving wave function.

Piecewise linear emulation of propagating fronts as a method for determining their speeds.

We use piecewise linear terms to emulate the polynomial nonlinear terms in a typical reaction-diffusion equation, replacing it thus with a set of simple linear inhomogeneous differential equations. The resulting analytic solution constitutes an excellent approximation to the exact propagating front, as is explicitly shown in the case of cubic and quintic nonlinearities, yielding also the correct value for the physically selected speed of the observable front. Such a piecewise linear emulation can be used for any nonlinearity, giving therefore a very reliable and accurate method for determining the selected speed of fronts invading unstable states, especially pushed fronts.

Piecewise linear emulator of the nonlinear Schrödinger equation and the resulting analytic solutions for Bose-Einstein condensates.

We emulate the cubic term Psi(3) in the nonlinear Schrödinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a delta function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Psi(3) one. In particular, it can be used for the nonlinear Schrödinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions.

Speed selection mechanism for propagating fronts in reaction-diffusion systems with multiple fields.

We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large finite intervals in the comoving frames of reference. The unique velocity for which the center of a monotonic solution for a particular field is insensitive to the location of the ends of the finite interval is the velocity that is physically selected for that field, making thus the solution approximately translation invariant. The fronts for the various fields may propagate at different speeds, all of them being determined though through this mechanism. We present analytic results for the case of piecewise parabolic potentials, and numerical results for other cases.