Electrostatic Point Charge Fitting as an Inverse Problem: Revealing the Underlying Ill-Conditioning

Atom-centered point charge model of the molecular electrostatics---a major workhorse of the atomistic biomolecular simulations---is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. Here, to reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem, and construct an analytically soluble model with the point charges spherically arranged according to Lebedev quadrature naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field

Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields

Protein Control of S-Nitrosothiol Reactivity: Interplay of Antagonistic Resonance Structures

There is currently great interest in S-nitrosothiols (RSNOs) because formation of protein-based RSNOs—protein S-nitrosation—has been recently recognized as a major pathway of the biological function of nitric oxide, NO. Despite the growing number of S-nitrosated proteins identified in vivo, enzymatic processes that control reactions of biological RSNOs are still not well understood. In this article, we use a range of models to computationally demonstrate that specific interactions of RSNOs with charged and polar residues in proteins can result in dramatic modification of RSNO structure, stability, and reactivity. This unprecedented sensitivity of the −SNO group toward interactions with charged species is related to their unusual electronic structure that can be elegantly expressed in terms of antagonistic resonance structures. We propose a ‘ligand effect map’ (LEM) approach as an efficient way to estimate the environment effects on the −SNO groups in proteins without performing electronic structure calculations. Furthermore, the calculated 15N NMR signatures of these specific interactions suggest that 15N NMR spectroscopy can be an effective technique to identify and study these interactions experimentally. Overall, the results of this study suggest that RSNO reactions in vivo should be tightly controlled by the protein environment via modulation of the RSNO electronic structure

Extension of Lorenz Unpredictability

It is found that Lorenz systems can be unidirectionally coupled such that the chaos expands from the drive system. This is true if the response system is not chaotic, but admits a global attractor, an equilibrium or a cycle. The extension of sensitivity and period-doubling cascade are theoretically proved, and the appearance of cyclic chaos as well as intermittency in interconnected Lorenz systems are demonstrated. A possible connection of our results with the global weather unpredictability is provided.Comment: 32 pages, 13 figure

Proteinase 3 contributes to endothelial dysfunction in an experimental model of sepsis

In sepsis-induced inflammation, polymorphonuclear neutrophils (PMNs) contribute to vascular dysfunction. The serine proteases proteinase 3 (PR3) and human leukocyte elastase (HLE) are abundant in PMNs and are released upon degranulation. While HLE’s role in inflammation-induced endothelial dysfunction is well studied, PR3’s role is largely uninvestigated. We hypothesized that PR3, similarly to HLE, contributes to vascular barrier dysfunction in sepsis. Plasma PR3 and HLE concentrations and their leukocyte mRNA levels were measured by ELISA and qPCR, respectively, in sepsis patients and controls. Exogenous PR3 or HLE was applied to human umbilical vein endothelial cells (HUVECs) and HUVEC dysfunction was assessed by FITC-dextran permeability and electrical resistance. Both PR3 and HLE protein and mRNA levels were significantly increased in sepsis patients (P \u3c 0.0001 and P \u3c 0.05, respectively). Additionally, each enzyme independently increased HUVEC monolayer FITC-dextran permeability (P \u3c 0.01), and decreased electrical resistance in a time- and dose-dependent manner (P \u3c 0.001), an effect that could be ameliorated by novel treatment with carbon monoxide-releasing molecule 3 (CORM-3). The serine protease PR3, in addition to HLE, lead to vascular dysfunction and increased endothelial permeability, a hallmark pathological consequence of sepsis-induced inflammation. CORMs may offer a new strategy to reduce serine protease-induced vascular dysfunction

Transcriptional profiling of leukocytes in critically ill COVID19 patients: implications for interferon response and coagulation

BACKGROUND: COVID19 is caused by the SARS-CoV-2 virus and has been associated with severe inflammation leading to organ dysfunction and mortality. Our aim was to profile the transcriptome in leukocytes from critically ill patients positive for COVID19 compared to those negative for COVID19 to better understand the COVID19-associated host response. For these studies, all patients admitted to our tertiary care intensive care unit (ICU) suspected of being infected with SARS-CoV-2, using standardized hospital screening methodologies, had blood samples collected at the time of admission to the ICU. Transcriptome profiling of leukocytes via ribonucleic acid sequencing (RNAseq) was then performed and differentially expressed genes as well as significantly enriched gene sets were identified. RESULTS: We enrolled seven COVID19 + (PCR positive, 2 SARS-CoV-2 genes) and seven age- and sex-matched COVID19- (PCR negative) control ICU patients. Cohorts were well-balanced with the exception that COVID19- patients had significantly higher total white blood cell counts and circulating neutrophils and COVID19 + patients were more likely to suffer bilateral pneumonia. The mortality rate for this cohort of COVID19 + ICU patients was 29%. As indicated by both single-gene based and gene set (GSEA) approaches, the major disease-specific transcriptional responses of leukocytes in critically ill COVID19 + ICU patients were: (i) a robust overrepresentation of interferon-related gene expression; (ii) a marked decrease in the transcriptional level of genes contributing to general protein synthesis and bioenergy metabolism; and (iii) the dysregulated expression of genes associated with coagulation, platelet function, complement activation, and tumour necrosis factor/interleukin 6 signalling. CONCLUSIONS: Our findings demonstrate that critically ill COVID19 + patients on day 1 of admission to the ICU display a unique leukocyte transcriptional profile that distinguishes them from COVID19- patients, providing guidance for future targeted studies exploring novel prognostic and therapeutic aspects of COVID19

Multiwavelength approach to classifying transient events in the direction of M31

Context. In the hunt for rare time-domain events, it is important to consider confusing exotic extragalactic phenomena with more common Galactic foreground events. Aims. We show how observations from multiple wavebands, in this case optical and X-ray observations, can be used to facilitate the distinction between the two. Methods. We discovered an extremely bright and rapid transient event during optical observations of the M 31 galaxy taken by the intermediate Palomar Transient Factory (iPTF). The persistent optical counterpart of this transient was previously thought to be a variable star in M 31 without any dramatic flux excursions. The iPTF event initially appeared to be an extraordinarily rapid and energetic extragalactic transient, which had a ≈3 mag positive flux excursion in less than a kilosecond; one of the exciting possibilities was this event could be a very fast nova in M 31. The nature of the source was resolved with the help of Chandraarchival data, where we found an X-ray counterpart and obtained its X-ray spectrum. Results. We find the X-ray spectrum of the quiescent emission can be described by a model of optically thin plasma emission with a temperature of ≈7 MK, typical for coronal emission from an active star. The combination of the X-ray luminosity, which is calculated assuming the source is located in M 31 (~3 × 10^(36) erg s^(−1)), and the color temperature exclude any type of known accreting compact object or active star in M 31. We argue instead that the optical transient source is an M-type main-sequence, active star located in the disk of the Milky Way at a distance of ~0.5–1 kpc. Its persistent X-ray luminosity is in the ≈1.3–5 × 10^(30)erg s^(−1) range and it has the absolute optical magnitude of 9.5–11.0 mag in the R band. The observed optical flare has the equivalent duration of ≈95 min and total energy of ≈(0.3–1) × 10^(35) erg in the R band, which places it among the brightest flares ever observed from an M-type star. This case can serve as an example for the classification of Galactic and extragalactic events in upcoming high-cadence time-domain projects, such as the Zwicky Transient Facility and the Large Synoptic Survey Telescope