Evaluating the use of absolute binding free energy in the fragment optimization process.

Key to the fragment optimization process is the need to accurately capture the changes in affinity that are associated with a given set of chemical modifications. Due to the weakly binding nature of fragments, this has proven to be a challenging task, despite recent advancements in leveraging experimental and computational methods. In this work, we evaluate the use of Absolute Binding Free Energy (ABFE) calculations in guiding fragment optimization decisions, retrospectively calculating binding free energies for 59 ligands across 4 fragment elaboration campaigns. We first demonstrate that ABFEs can be used to accurately rank fragment-sized binders with an overall Spearman’s r of 0.89 and a Kendall τ of 0.67, although often deviating from experiment in absolute free energy values with an RMSE of 2.75 kcal/mol. We then also show that in several cases, retrospective fragment optimization decisions can be supported by the ABFE calculations. Cases that were not supported were often limited by large uncertainties in the free energy estimates, however generally the right direction in ΔΔG is still observed. Comparing against cheaper endpoint methods, namely Nwat-MM/GBSA, we find that ABFEs offer better outcomes in ranking binders, improving correlation metrics, although a similar confidence in retrospective synthetic decisions is achieved. Our results indicate that ABFE calculations are currently at the level of accuracy that can be usefully employed to gauge which fragment elaborations are likely to offer the best gains in affinity.

One-dimensional periodic fractional Schrödinger equations with exponential critical growth

In the present paper, we study the existence of nontrivial solutions of the following one-dimensional fractional Schr\“{o}dinger equation $$ (-\Delta)^{1/2}u+V(x)u=f(x,u), \ \ x\in \R, $$ where $(-\Delta)^{1/2}$ stands for the $1/2$-Laplacian, $V(x)\in \mathcal{C}(\R, (0,+\infty))$, and $f(x,u):\R\times\R\to \R$ is a continuous function with an exponential critical growth. Comparing with the existing works in the field of exponential-critical-growth fractional Schr\”{o}dinger equations, we encounter some new challenges due to the weaker assumptions on the reaction term $f$. By using some sharp energy estimates, we present a detailed analysis of the energy level, which allows us to establish the existence of nontrivial solutions for a wider class of nonlinear terms. Furthermore, we use the non-Nehari manifold method to establish the existence of Nehari-type ground state solutions of the one-dimensional fractional Schr\”{o}dinger equations.

Experimental multiblast craters and ejecta — seismo-acoustics, jet characteristics, craters, and ejecta deposits and implications for volcanic explosions

Blasting experiments were performed that investigate multiple explosions that occur in quick succession in the ground and their effects on host material and atmosphere. Such processes are known to occur during volcanic eruptions at various depths, lateral locations, and energies. The experiments follow a multi-instrument approach in order to observe phenomena in the atmosphere and in the ground, and measure the respective energy partitioning. The experiments show significant coupling of atmospheric (acoustic)- and ground (seismic) signal over a large range of (scaled)distances (30--330\m, 1--10\(\m\J^{-1/3}\)). The distribution of ejected material strongly depends on the sequence of how the explosions occur. The overall crater sizes are in the expected range of a maximum size for many explosions and a minimum for one explosion at a given lateral location. The experiments also show that peak atmospheric over-pressure decays exponentially with scaled depth at a rate of \bar{d}_0 = 6.47x10^{-4} mJ^{-1/3}; at a scaled explosion depth of \(4x10^{-3} mJ^{-1/3} ca. 1% of the blast energy is responsible for the formation of the atmospheric pressure pulse; at a more shallow scaled depth of 2.75x10^{-3 \mJ^{-1/3} this ratio lies at ca. 5.5–7.5%. A first order consideration of seismic energy estimates the sum of radiated airborne and seismic energy to be up to 20\% of blast energy.

Computational study of the furin cleavage domain of SARS-CoV-2: delta binds strongest of extant variants

We demonstrate that AlphaFold and AlphaFold Multimer, implemented within the ColabFold suite, can accurately predict the structures of the furin enzyme with known six residue inhibitory peptides. Noting the similarity of the peptide inhibitors to polybasic furin cleavage domain insertion region of the SARS-CoV-2, which begins at P681, we implement this approach to study the wild type furin cleavage domain for the virus and several mutants. We introduce mutations in silico for alpha, omicron, and delta variants, for several sequences which have been rarely observed, for sequences which have not yet been observed, for other coronaviruses (NL63, OC43, HUK1a, HUK1b, MERS, and 229E), and for the H5N1 flu. We show that interfacial hydrogen bonds between the furin cleavage domain and furin are a good measure of binding strength that correlate well with endpoint binding free energy estimates, and conclude that among all candidate viral sequences studied, delta is near the very top binding strength within statistical accuracy. However, the binding strength of several rare sequences match delta within statistical accuracy. We find that the furin S1 pocket is optimized for binding arginine as opposed to lysine. This residue, typically at sequence position five, contains the most hydrogen bonds to the furin, and hydrogen bond count for just this residue shows a strong positive correlation with the overall hydrogen bond count . We demonstrate that the root mean square backbone C-alpha fluctuation of the first residue in the furin cleavage domain has a strong negative correlation with the interfacial hydrogen bond count. We show by considering the variation with the number of basic residues that the maximum mean number of interfacial hydrogen bonds expected is 15.7 at 4 basic residues.

Ground States for Mass Critical Two Coupled Semi-Relativistic Hartree Equations with Attractive Interactions

We prove the existence and nonexistence of $L^{2}(\mathbb R^3)$-normalized solutions of two coupled semi-relativistic Hartree equations, which arisen from the studies of boson stars and multi-component Bose–Einstein condensates. Under certain condition on the strength of intra-specie and inter-specie interactions, by proving some delicate energy estimates, we give a precise description on the concentration behavior of ground state solutions of the system. Furthermore, an optimal blowing up rate for the ground state solutions of the system is also proved.

An Efficient Hybrid Numerical Scheme for Nonlinear Multiterm Caputo Time and Riesz Space Fractional-Order Diffusion Equations with Delay

In this paper, we construct and analyze a linearized finite difference/Galerkin–Legendre spectral scheme for the nonlinear multiterm Caputo time fractional-order reaction-diffusion equation with time delay and Riesz space fractional derivatives. The temporal fractional orders in the considered model are taken as 0 < β 0 < β 1 < β 2 < ⋯ < β m < 1 . The problem is first approximated by the L 1 difference method on the temporal direction, and then, the Galerkin–Legendre spectral method is applied on the spatial discretization. Armed by an appropriate form of discrete fractional Grönwall inequalities, the stability and convergence of the fully discrete scheme are investigated by discrete energy estimates. We show that the proposed method is stable and has a convergent order of 2 − β m in time and an exponential rate of convergence in space. We finally provide some numerical experiments to show the efficacy of the theoretical results.

Experimental 3-dimensional tracking of the dynamics of a single electron in the Fermilab Integrable Optics Test Accelerator (IOTA)

We present the results of experimental studies on the transverse and longitudinal dynamics of a single electron in the IOTA storage ring. IOTA is a flexible machine dedicated to beam physics experiments with electrons and protons. A method was developed to reliably inject and circulate a controlled number of electrons in the ring. A key beam diagnostic system is the set of sensitive high-resolution digital cameras for the detection of synchrotron light emitted by the electrons. With 60–130 electrons in the machine, we measured beam lifetime and derived an absolute calibration of the optical system. At exposure times of 0.5 s, the cameras were sensitive to individual electrons. Camera images were used to reconstruct the time evolution of oscillation amplitudes of a single electron in all 3 degrees of freedom. The evolution of amplitudes directly showed the interplay between synchrotron-radiation damping, quantum excitations, and scattering with the residual gas. From the distribution of measured single-electron oscillation amplitudes, we deduced transverse emittances, momentum spread, damping times, and beam energy. Estimates of residual-gas density and composition were calculated from the measured distributions of vertical scattering angles. Combining scattering and lifetime data, we also provide an estimate of the aperture of the ring. To our knowledge, this is the first time that the dynamics of a single electron are tracked in all three dimensions with digital cameras in a storage ring.

Weak Damping of Propagating MHD Kink Waves in the Quiescent Corona

Propagating transverse waves are thought to be a key transporter of Poynting flux throughout the Sun’s atmosphere. Recent studies have shown that these transverse motions, interpreted as the magnetohydrodynamic kink mode, are prevalent throughout the corona. The associated energy estimates suggest the waves carry enough energy to meet the demands of coronal radiative losses in the quiescent Sun. However, it is still unclear how the waves deposit their energy into the coronal plasma. We present the results from a large-scale study of propagating kink waves in the quiescent corona using data from the Coronal Multi-channel Polarimeter (CoMP). The analysis reveals that the kink waves appear to be weakly damped, which would imply low rates of energy transfer from the large-scale transverse motions to smaller scales via either uniturbulence or resonant absorption. This raises questions about how the observed kink modes would deposit their energy into the coronal plasma. Moreover, these observations, combined with the results of Monte Carlo simulations, lead us to infer that the solar corona displays a spectrum of density ratios, with a smaller density ratio (relative to the ambient corona) in quiescent coronal loops and a higher density ratio in active-region coronal loops.

Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system

In this paper we are concerned with the existence, nonexistence and bifurcation of nontrivial solution of the nonlinear Schrödinger-Korteweg-de Vries type system(NLS-NLS-KdV). First, we find some conditions to guarantee the existence and nonexistence of positive solution of the system. Second, we study the asymptotic behavior of the positive ground state solution. Finally, we use the classical Crandall-Rabinowitz local bifurcation theory to get the nontrivial positive solution. To get these results we encounter some new challenges. By combining the Nehari manifolds constraint method and the delicate energy estimates, we overcome the difficulties and find the two bifurcation branches from one semitrivial solution. This is an new interesting phenomenon but which have not previously been found.

Large deviation principles of 2D stochastic Navier–Stokes equations with Lévy noises

Taking the consideration of two-dimensional stochastic Navier–Stokes equations with multiplicative Lévy noises, where the noises intensities are related to the viscosity, a large deviation principle is established by using the weak convergence method skillfully, when the viscosity converges to 0. Due to the appearance of the jumps, it is difficult to close the energy estimates and obtain the desired convergence. Hence, one cannot simply use the weak convergence approach. To overcome the difficulty, one introduces special norms for new arguments and more careful analysis.