Computational and Systems Biology Advances to Enable Bioagent Agnostic Signatures.

Enumerated threat agent lists have long driven biodefense priorities. The global SARS-CoV-2 pandemic demonstrated the limitations of searching for known threat agents as compared to a more agnostic approach. Recent technological advances are enabling agent-agnostic biodefense, especially through the integration of multi-modal observations of host-pathogen interactions directed by a human immunological model. Although well-developed technical assays exist for many aspects of human-pathogen interaction, the analytic methods and pipelines to combine and holistically interpret the results of such assays are immature and require further investments to exploit new technologies. In this manuscript, we discuss potential immunologically based bioagent-agnostic approaches and the computational tool gaps the community should prioritize filling.

Solvation Thermodynamics of Solutes in Water and Ionic Liquids Using the Multiscale Solvation-Layer Interface Condition Continuum Model.

Molecular assembly processes are generally driven by thermodynamic properties in solutions. Atomistic modeling can be very helpful in designing and understanding complex systems, except that bulk solvent is very inefficient to treat explicitly as discrete molecules. In this work, we develop and assess two multiscale solvation models for computing solvation thermodynamic properties. The new SLIC/CDC model combines continuum solvent electrostatics based on the solvent layer interface condition (SLIC) with new statistical thermodynamic models for hydrogen bonding and nonpolar modes: cavity formation, dispersion interactions, combinatorial mixing (CDC). Given the structures of 500 solutes, the SLIC/CDC model predicts Gibbs energies of solvation in water with an average accuracy better than 1 kcal/mol, when compared to experimental measurements, and better than 0.8 kcal/mol, when compared to explicit-solvent molecular dynamics simulations. The individual SLIC/CDC energy mode values agree quantitatively with those computed from explicit-solvent molecular dynamics. The previously published SLIC/SASA multiscale model combines the SLIC continuum electrostatic model with the solvent-accessible surface area (SASA) nonpolar energy mode. With our new, improved parametrization method, the SLIC/SASA model now predicts Gibbs energies of solvation with better than 1.4 kcal/mol average accuracy in aqueous systems, compared to experimental and explicit-solvent molecular dynamics, and better than 1.6 kcal/mol average accuracy in ionic liquids, compared to explicit-solvent molecular dynamics. Both models predict solvation entropies, and are the first implicit-solvation models capable of predicting solvation heat capacities.

High-performance transformation of protein structure representation from internal to Cartesian coordinates.

We present a highly parallel algorithm to convert internal coordinates of a polymeric molecule into Cartesian coordinates. Traditionally, converting the structures of polymers (e.g., proteins) from internal to Cartesian coordinates has been performed serially, due to an inherent linear dependency along the polymer chain. We show this dependency can be removed using a tree-based concatenation of coordinate transforms between segments, and then parallelized efficiently on graphics processing units (GPUs). The conversion algorithm is applicable to protein engineering and fitting protein structures to experimental data, and we observe an order of magnitude speedup using parallel processing on a GPU compared to serial execution on a CPU.

Effects of Catalytic Action and Ligand Binding on Conformational Ensembles of Adenylate Kinase.

Crystal structures of adenylate kinase (AdK) from Escherichia coli capture two states: an "open" conformation (apo) obtained in the absence of ligands and a "closed" conformation in which ligands are bound. Other AdK crystal structures suggest intermediate conformations that may lie on the transition pathway between these two states. To characterize the transition from open to closed states in solution, X-ray solution scattering data were collected from AdK in the apo form and with progressively increasing concentrations of five different ligands. Scattering data from apo AdK are consistent with scattering predicted from the crystal structure of AdK in the open conformation. In contrast, data from AdK samples saturated with Ap5A do not agree with that calculated from AdK in the closed conformation. Using cluster analysis of available structures, we selected representative structures in five conformational states: open, partially open, intermediate, partially closed, and closed. We used these structures to estimate the relative abundances of these states for each experimental condition. X-ray solution scattering data obtained from AdK with AMP are dominated by scattering from AdK in the open conformation. For AdK in the presence of high concentrations of ATP and ADP, the conformational ensemble shifts to a mixture of partially open and closed states. Even when AdK is saturated with Ap5A, a significant proportion of AdK remains in a partially open conformation. These results are consistent with an induced-fit model in which the transition of AdK from an open state to a closed state is initiated by ATP binding.

Extending the Solvation-Layer Interface Condition Continum Electrostatic Model to a Linearized Poisson-Boltzmann Solvent.

We extend the linearized Poisson-Boltzmann (LPB) continuum electrostatic model for molecular solvation to address charge-hydration asymmetry. Our new solvation-layer interface condition (SLIC)/LPB corrects for first-shell response by perturbing the traditional continuum-theory interface conditions at the protein-solvent and the Stern-layer interfaces. We also present a GPU-accelerated treecode implementation capable of simulating large proteins, and our results demonstrate that the new model exhibits significant accuracy improvements over traditional LPB models, while reducing the number of fitting parameters from dozens (atomic radii) to just five parameters, which have physical meanings related to first-shell water behavior at an uncharged interface. In particular, atom radii in the SLIC model are not optimized but uniformly scaled from their Lennard-Jones radii. Compared to explicit-solvent free-energy calculations of individual atoms in small molecules, SLIC/LPB is significantly more accurate than standard parametrizations (RMS error 0.55 kcal/mol for SLIC, compared to RMS error of 3.05 kcal/mol for standard LPB). On parametrizing the electrostatic model with a simple nonpolar component for total molecular solvation free energies, our model predicts octanol/water transfer free energies with an RMS error 1.07 kcal/mol. A more detailed assessment illustrates that standard continuum electrostatic models reproduce total charging free energies via a compensation of significant errors in atomic self-energies; this finding offers a window into improving the accuracy of Generalized-Born theories and other coarse-grained models. Most remarkably, the SLIC model also reproduces positive charging free energies for atoms in hydrophobic groups, whereas standard PB models are unable to generate positive charging free energies regardless of the parametrized radii. The GPU-accelerated solver is freely available online, as is a MATLAB implementation.

Theory of wavelet-based coarse-graining hierarchies for molecular dynamics.

We present a multiresolution approach to compressing the degrees of freedom and potentials associated with molecular dynamics, such as the bond potentials. The approach suggests a systematic way to accelerate large-scale molecular simulations with more than two levels of coarse graining, particularly applications of polymeric materials. In particular, we derive explicit models for (arbitrarily large) linear (homo)polymers and iterative methods to compute large-scale wavelet decompositions from fragment solutions. This approach does not require explicit preparation of atomistic-to-coarse-grained mappings, but instead uses the theory of diffusion wavelets for graph Laplacians to develop system-specific mappings. Our methodology leads to a hierarchy of system-specific coarse-grained degrees of freedom that provides a conceptually clear and mathematically rigorous framework for modeling chemical systems at relevant model scales. The approach is capable of automatically generating as many coarse-grained model scales as necessary, that is, to go beyond the two scales in conventional coarse-grained strategies; furthermore, the wavelet-based coarse-grained models explicitly link time and length scales. Furthermore, a straightforward method for the reintroduction of omitted degrees of freedom is presented, which plays a major role in maintaining model fidelity in long-time simulations and in capturing emergent behaviors.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

Constrained Maximum Likelihood Estimation of Relative Abundances of Protein Conformation in a Heterogeneous Mixture from Small Angle X-Ray Scattering Intensity Measurements.

In this paper, we describe a model for maximum likelihood estimation (MLE) of the relative abundances of different conformations of a protein in a heterogeneous mixture from small angle X-ray scattering (SAXS) intensities. To consider cases where the solution includes intermediate or unknown conformations, we develop a subset selection method based on k-means clustering and the Cramér-Rao bound on the mixture coefficient estimation error to find a sparse basis set that represents the space spanned by the measured SAXS intensities of the known conformations of a protein. Then, using the selected basis set and the assumptions on the model for the intensity measurements, we show that the MLE model can be expressed as a constrained convex optimization problem. Employing the adenylate kinase (ADK) protein and its known conformations as an example, and using Monte Carlo simulations, we demonstrate the performance of the proposed estimation scheme. Here, although we use 45 crystallographically determined experimental structures and we could generate many more using, for instance, molecular dynamics calculations, the clustering technique indicates that the data cannot support the determination of relative abundances for more than 5 conformations. The estimation of this maximum number of conformations is intrinsic to the methodology we have used here.

Communication: modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions.

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.

A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers.

The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known apbs finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the apbs solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is in the order of 1-2% error, when running on one gpu card (nvidia Tesla C2075), compared with apbs running on six Intel Xeon cpu cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using gpus via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.

Gradient Models in Molecular Biophysics: Progress, Challenges, Opportunities.

In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g. molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding features such as nonlocal dielectric response, and nonlinearities resulting from dielectric saturation. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost forty years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The paper concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics.

Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding.

We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins-a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions in protein-protein binding, using the widely studied model system of trypsin and bovine pancreatic trypsin inhibitor (BPTI). Finding that the BIBEE/I model performs surprisingly less well in this task than simpler BIBEE models, we seek to explain this behavior in terms of the models' differing spectral approximations of the exact boundary-integral operator. Calculations of analytically solvable systems (spheres and tri-axial ellipsoids) suggest two possibilities for improvement. The first is a modified BIBEE/I approach that captures the asymptotic eigenvalue limit correctly, and the second involves the dipole and quadrupole modes for ellipsoidal approximations of protein geometries. Our analysis suggests that fast, rigorous approximate models derived from reduced-basis approximation of boundary-integral equations might reach unprecedented accuracy, if the dipole and quadrupole modes can be captured quickly for general shapes.

Affine-response model of molecular solvation of ions: Accurate predictions of asymmetric charging free energies.

Two mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquid-vapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use free-energy perturbation molecular-dynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solute-solvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular "linear response" model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewise-linear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicit-solvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewise-linear response (due to the steric contribution).

Cost and quality implications of discrepancies between admitting and discharge diagnoses.

BACKGROUND: Presenting and discharge diagnoses of hospitalized patients may differ as a result of patient complexity, diagnostic dilemmas, or errors in clinical judgment at the time of primary assessment. When diagnoses at admission and discharge are not in agreement, this discrepancy may indicate more complex processes of care and resultant costs. It is unclear whether surrogate measures reflecting quality of care are impacted by discrepant diagnoses. OBJECTIVE: To assess whether an association exists between admitting and discharge International Classification of Diseases, Ninth Revision (ICD-9) diagnosis codes and other quality markers including hospital length of stay, total cost of care, and 30-day readmission rate. METHODS: This was a retrospective, cross-sectional analysis of general internal medicine patients aged 18 years and older. Diagnosis discrepancy was defined as a difference between the 3-digit ICD-9 diagnosis code at admission and the principal 3-digit ICD-9 diagnosis code at discharge. RESULTS: Sixty-eight percent of patients had a diagnosis discrepancy. Diagnosis discrepancy was associated with a 0.41-day increase in length of stay (P < .001), $663 increase in direct costs (P < .001), and a 1.55 times greater odds of readmission within 30 days (P < .001). CONCLUSION: Diagnosis discrepancy was associated with hospital quality outcome measures. This finding likely reflects variations in patients' diagnostic complexity.

Comparison of three-dimensional poisson solution methods for particle-based simulation and inhomogeneous dielectrics.

Particle-based simulation represents a powerful approach to modeling physical systems in electronics, molecular biology, and chemical physics. Accounting for the interactions occurring among charged particles requires an accurate and efficient solution of Poisson's equation. For a system of discrete charges with inhomogeneous dielectrics, i.e., a system with discontinuities in the permittivity, the boundary element method (BEM) is frequently adopted. It provides the solution of Poisson's equation, accounting for polarization effects due to the discontinuity in the permittivity by computing the induced charges at the dielectric boundaries. In this framework, the total electrostatic potential is then found by superimposing the elemental contributions from both source and induced charges. In this paper, we present a comparison between two BEMs to solve a boundary-integral formulation of Poisson's equation, with emphasis on the BEMs' suitability for particle-based simulations in terms of solution accuracy and computation speed. The two approaches are the collocation and qualocation methods. Collocation is implemented following the induced-charge computation method of D. Boda et al. [J. Chem. Phys. 125, 034901 (2006)]. The qualocation method is described by J. Tausch et al. [IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 20, 1398 (2001)]. These approaches are studied using both flat and curved surface elements to discretize the dielectric boundary, using two challenging test cases: a dielectric sphere embedded in a different dielectric medium and a toy model of an ion channel. Earlier comparisons of the two BEM approaches did not address curved surface elements or semiatomistic models of ion channels. Our results support the earlier findings that for flat-element calculations, qualocation is always significantly more accurate than collocation. On the other hand, when the dielectric boundary is discretized with curved surface elements, the two methods are essentially equivalent; i.e., they have comparable accuracies for the same number of elements. We find that ions in water--charges embedded in a high-dielectric medium--are harder to compute accurately than charges in a low-dielectric medium.

Hospital care may not affect the risk of readmission.

BACKGROUND: : Thirty-day readmissions have become a focal point for reducing health care spending, because they are viewed as a marker of the quality of hospital care. However, if increased time in the hospital is associated with better care, attempts to shorten length of stay (LOS) may result in increased rates of readmission. As such, we sought to explore the association of an incremental added day in LOS with the rate of readmission. METHODS: : We examined the rate of readmission at 30 and 120 days for 4151 patients admitted to a general internal medicine unit between July 2004 and March 2006. We used binary logistic regression to examine the relationship between an incremental added day in LOS and the probability of readmission. RESULTS: : Readmission rates were 8.7% at 30 days and 21.0% at 120 days, respectively. After controlling for demographic characteristics and severity of illness, we found that the probability of readmission varied little for an incremental added day in LOS. CONCLUSIONS: : Our findings suggest that more hospital care may not affect the likelihood of readmission and thus denying payment for readmission may be unwarranted.

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements.

Nonlocal continuum electrostatic theory predicts surprisingly small energetic penalties for charge burial in proteins.

We study the energetics of burying charges, ion pairs, and ionizable groups in a simple protein model using nonlocal continuum electrostatics. Our primary finding is that the nonlocal response leads to markedly reduced solvent screening, comparable to the use of application-specific protein dielectric constants. Employing the same parameters as used in other nonlocal studies, we find that for a sphere of radius 13.4 Šcontaining a single +1e charge, the nonlocal solvation free energy varies less than 18 kcal/mol as the charge moves from the surface to the center, whereas the difference in the local Poisson model is ∼35 kcal/mol. Because an ion pair (salt bridge) generates a comparatively more rapidly varying Coulomb potential, energetics for salt bridges are even more significantly reduced in the nonlocal model. By varying the central parameter in nonlocal theory, which is an effective length scale associated with correlations between solvent molecules, nonlocal-model energetics can be varied from the standard local results to essentially zero; however, the existence of the reduction in charge-burial penalties is quite robust to variations in the protein dielectric constant and the correlation length. Finally, as a simple exploratory test of the implications of nonlocal response, we calculate glutamate pK(a) shifts and find that using standard protein parameters (ε(protein) = 2-4), nonlocal results match local-model predictions with much higher dielectric constants. Nonlocality may, therefore, be one factor in resolving discrepancies between measured protein dielectric constants and the model parameters often used to match titration experiments. Nonlocal models may hold significant promise to deepen our understanding of macromolecular electrostatics without substantially increasing computational complexity.

Streaming current and wall dissolution over 48 h in silica nanochannels.

We present theoretical and experimental studies of the streaming current induced by a pressure-driven flow in long, straight, electrolyte-filled nanochannels. The theoretical work builds on our recent one-dimensional model of electro-osmotic and capillary flow, which self-consistently treats both the ion concentration profiles, via the nonlinear Poisson-Boltzmann equation, and the chemical reactions in the bulk electrolyte and at the solid-liquid interface. We extend this model to two dimensions and validate it against experimental data for electro-osmosis and pressure-driven flows, using eight 1-µm-wide nanochannels of heights varying from 40 nm to 2000 nm. We furthermore vary the electrolyte composition using KCl and borate salts, and the wall coating using 3-cyanopropyldimethylchlorosilane. We find good agreement between prediction and experiment using literature values for all parameters of the model, i.e., chemical reaction constants and Stern-layer capacitances. Finally, by combining model predictions with measurements over 48 h of the streaming currents, we develop a method to estimate the dissolution rate of the silica walls, typically around 0.01 mg/m(2)/h, equal to 45 pm/h or 40 nm/yr, under controlled experimental conditions.