arXiv subjects

Thomas L. Beck

Publications and source records attributed to Thomas L. Beck.

15 recordsLinked to original sources

arXiv2026

Exploring the use of quantum computing for facilitating spatially and temporally resolved models of a biological cell

Whole-cell simulation, modeling all of a cell's functional systems over its life cycle, is an outstanding challenge in computational biology. Even the simplest living cell contains thousands of interacting proteins and metabolites (on the order of trillions of atoms) whose full functional dynamics spans roughly five orders of magnitude in space (nm to $\mu$m) and nearly nineteen in time (fs to hours). Further, many of the governing physical and chemical properties remain incompletely characterized. Simulating such complex systems at fully atomistic resolution over a full cell cycle is computationally intractable on classical architectures, raising a central question: Can quantum computing offer a viable path to whole-cell simulations that integrate molecular- and systems-level complexity? This Perspective examines the potential of quantum computing across three hierarchical scales: atomistic-molecular modeling, metabolic and regulatory networks, and whole-cell spatial modeling. We present a complexity analysis comparing classical and quantum algorithms for representative biological problems, identifying regimes of substantial theoretical speedup under specified algorithmic assumptions. We highlight algorithmic developments designed to leverage both near-term exploratory and fault-tolerant quantum architectures, and discuss practical bottlenecks: data encoding overhead, system conditioning, measurement constraints, and hybrid quantum-HPC integration. Together, these results outline a roadmap for quantum-accelerated whole-cell modeling and the biological insights such multiscale frameworks may eventually enable.

quant-ph↗

arXiv2025

Equipartition and the temperature of maximum density of TIP4/2005 water

We simulate TIP4P/2005 water in the temperature range of 257 K to 318 K with time-steps $δ=$ 0.25, 0.50, 2.00, and 4.00 fs. The density-temperature behavior obtained using 0.25 or 0.50 fs are in excellent agreement with each other but differ from those obtained using time-steps that have been shown earlier to lead to a breakdown of equipartition. The temperature of maximum density (TMD) is 277.15 K with $δt = 0.25\;\mathrm{or}\; 0.50$ fs, but is shifted to progressively lower values for longer time-steps, a trend that holds for different thermostat/barostat combinations. Enhancing the water-water dispersion interaction, as has been recommended for simulating disordered proteins in TIP4P/2005, degrades the description of the liquid-vapor phase envelope. A key takeaway from this study is that using sufficiently short time-steps ($\leq 0.5$ fs) to preserve equipartition is essential for obtaining meaningful liquid water properties and for producing reliable data to parametrize biomolecular simulation models, as correct-ensemble sampling is fundamental to ensure reproducibility across codes and simulation alogrithms.

cond-mat.soft↗

arXiv2025

Consequences of the failure of equipartition for the p-V behavior of liquid water and the hydration free energy components of a small protein

Earlier we showed that in the molecular dynamics simulation of a rigid model of water it is necessary to use an integration time-step $δt \leq 0.5$ fs to ensure equipartition between translational and rotational modes. Here we extend that study in the $NVT$ ensemble to $NpT$ conditions and to an aqueous protein. We study neat liquid water with the rigid, SPC/E model and the protein BBA (PDB ID: 1FME) solvated in the rigid, TIP3P model. We examine integration time-steps ranging from $0.5$ fs to $4.0$ fs for various thermostat plus barostat combinations. We find that a small $δt$ is necessary to ensure consistent prediction of the simulation volume. Hydrogen mass repartitioning alleviates the problem somewhat, but is ineffective for the typical time-step used with this approach. The compressibility, a measure of volume fluctuations, and the dielectric constant, a measure of dipole moment fluctuations, are also seen to be sensitive to $δt$. Using the mean volume estimated from the $NpT$ simulation, we examine the electrostatic and van der Waals contribution to the hydration free energy of the protein in the $NVT$ ensemble. These contributions are also sensitive to $δt$. In going from $δt = 2$ fs to $δt = 0.5$ fs, the change in the net electrostatic plus van der Waals contribution to the hydration of BBA is already in excess of the folding free energy reported for this protein.

cond-mat.soft↗

arXiv2023

Equilibration between Translational and Rotational Modes in Molecular Dynamics Simulations of Rigid Water Requires a Smaller Integration Time-Step Than Often Used

In simulations of aqueous systems it is common to freeze the bond vibration and angle bending modes in water to allow for a longer time-step $δt$ for integrating the equations of motion. Thus $δt = 2$ fs is often used in simulating rigid models of water. We simulate the SPC/E model of water using $δt$ from 0.5 fs to 3.0 fs. We find that for all but $δ= 0.5$ fs, equipartition between translational and rotational modes is violated: the rotational modes are at a lower temperature than the translation modes. The autocorrelation of the velocities corresponding to the respective modes shows that the rotational relaxation occurs at a time-scale comparable to vibrational periods, invalidating the original assumption for freezing vibrations. $δt$ also influences thermodynamic properties: the mean system potential energies are not converged until $δt = 0.5$ fs, and the excess entropy of hydration of a soft, repulsive cavity is also sensitive to $δt$.

cond-mat.soft↗

arXiv2012

The influence of water interfacial potentials on ion hydration free energies and density profiles near the surface

The surface or contact potential at the water liquid-vapor interface is discussed in relation to determinations of absolute ion hydration free energies and distributions of ions near the interface. It is shown that, rather than the surface potential itself, the net electrostatic potential at the center of an uncharged solute can aid both in relating differences between tabulations of hydration free energies and in explaining differing classical and quantum surface potential estimates. Quantum mechanical results are consistent with conclusions from classical simulations that there is a net driving force that enhances anion density at the surface relative to cations.

cond-mat.soft↗

arXiv2011

Information Theory and Statistical Mechanics Revisited

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

cond-mat.stat-mech↗

arXiv2010

Resolution and Scale Independent Function Matching Using a String Energy Penalized Spline Prior

The extension of the classical Bayesian penalized spline method to inference on vector-valued functions is considered, with an emphasis on characterizing the suitability of the method for general application.We show that the standard quadratic penalty is exactly analogous to the energy of a stretched string, with the penalty parameter corresponding to its tension. This physical analogy motivates a discussion of resolution independence, which we define as the convergence of a computational function estimate to arbitrary accuracy with increasing resolution.The multidimensional context makes direct application of standard procedures for choosing the penalty parameter difficult, and a new method is proposed and compared to the established generalized cross-validation (GCV) and Akaike information criterion (AIC) functions.Our Bayesian method for choosing this parameter is derived by introducing a scal e independence criterion to ensure that simultaneously scaling the function samples and their variances does not significantly change the posterior parameter distribution. Due to the possibility of an exact polynomial fit, numerical issues prevent the use of this prior, and a solution is presented based on adding a st ring zero-point energy. This makes more complicated approaches recently propose d in the literature unnecessary, and eliminates the requirement for sensitivity analysis when the function deviates from the above mentioned polynomial. An important class of problems which can be analyzed by this method are stochastic numerical integrators, which are considered as an example problem. This work represents the first extension of penalized spline methods to inference on multidimensional numerical integrators reported in the literature. Several numerical calculations illustrate the above points and address practical application issues.

stat.ML↗

arXiv2009

Quasi-Chemical and Structural Analysis of Polarizable Anion Hydration

Quasi-chemical theory is utilized to analyze the roles of solute polarization and size in determining the structure and thermodynamics of bulk anion hydration for the Hofmeister series Cl$^-$, Br$^-$, and I$^-$. Excellent agreement with experiment is obtained for whole salt hydration free energies using the polarizable AMOEBA force field. The quasi-chemical approach exactly partitions the solvation free energy into inner-shell, outer-shell packing, and outer-shell long-ranged contributions by means of a hard-sphere condition. Small conditioning radii, even well inside the first maximum of the ion-water(oxygen) radial distribution function, result in Gaussian behavior for the long-ranged contribution that dominates the ion hydration free energy. The spatial partitioning allows for a mean-field treatment of the long-ranged contribution, leading to a natural division into first-order electrostatic, induction, and van der Waals terms. The induction piece exhibits the strongest ion polarizability dependence, while the larger-magnitude first-order electrostatic piece yields an opposing but weaker polarizability dependence. In addition, a structural analysis is performed to examine the solvation anisotropy around the anions. As opposed to the hydration free energies, the solvation anisotropy depends more on ion polarizability than on ion size: increased polarizability leads to increased anisotropy. The water dipole moments near the ion are similar in magnitude to bulk water, while the ion dipole moments are found to be significantly larger than those observed in quantum mechanical studies. Possible impacts of the observed over-polarization of the ions on simulated anion surface segregation are discussed.

cond-mat.soft↗

arXiv2009

Polarization and Charge Transfer in the Hydration of Chloride Ions

A theoretical study of the structural and electronic properties of the chloride ion and water molecules in the first hydration shell is presented. The calculations are performed on an ensemble of configurations obtained from molecular dynamics simulations of a single chloride ion in bulk water. The simulations utilize the polarizable AMOEBA force field for trajectory generation, and MP2-level calculations are performed to examine the electronic structure properties of the ions and surrounding waters in the external field of more distant waters. The ChelpG method is employed to explore the effective charges and dipoles on the chloride ions and first-shell waters. The Quantum Theory of Atoms in Molecules (QTAIM) is further utilized to examine charge transfer from the anion to surrounding water molecules. From the QTAIM analysis, 0.2 elementary charges are transferred from the ion to the first-shell water molecules. The default AMOEBA model overestimates the average dipole moment magnitude of the ion compared with the estimated quantum mechanical value. The average magnitude of the dipole moment of the water molecules in the first shell treated at the MP2 level, with the more distant waters handled with an AMOEBA effective charge model, is 2.67 D. This value is close to the AMOEBA result for first-shell waters (2.72 D) and is slightly reduced from the bulk AMOEBA value (2.78 D). The magnitude of the dipole moment of the water molecules in the first solvation shell is most strongly affected by the local water-water interactions and hydrogen bonds with the second solvation shell, rather than by interactions with the ion.

cond-mat.soft↗

arXiv2008

Modeling molecular and ionic absolute solvation free energies with quasi-chemical theory bounds

A recently developed statistical mechanical Quasi-Chemical Theory (QCT) has led to significant insights into solvation phenomena for both hydrophilic and hydrophobic solutes. The QCT exactly partitions solvation free energies into three components: 1) inner-shell chemical, 2) outer-shell packing, and 3) outer-shell long-ranged contributions. In this paper, we discuss efficient methods for computing each of the three parts of the free energy. A Bayesian estimation approach is developed to compute the inner-shell chemical and outer-shell packing contributions. We derive upper and lower bounds on the outer-shell long-ranged portion of the free energy by expressing this component in two equivalent ways. Local, high energy contacts between solute and solvent are eliminated by spatial conditioning in this free energy piece, leading to near-Gaussian distributions of solute-solvent interactions energies. Thus, the average of the two mean-field bounds yields an accurate and efficient free energy estimate. Aqueous solvation free energy results are presented for several solutes, including methane, perfluoromethane, water, and the sodium and chloride ions. The results demonstrate the accuracy and efficiency of the methods. The approach should prove useful in computing solvation free energies in inhomogeneous, restricted environments.

cond-mat.stat-mech↗

arXiv2003

Multiscale Algorithms for Eigenvalue Problems

Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and self-consistent eigenvalue problems. In principle, the expensive orthogonalization and Ritz projection operations can be moved to coarse levels, thus substantially reducing the overall computational expense. Results of the nonlinear multiscale approach are presented for simple fixed potential problems and for self-consistent pseudopotential calculations on large molecules. It is shown that, while excellent efficiencies can be obtained for problems with small numbers of states or well-defined eigenvalue cluster structure, the algorithm in its original form stalls for large-molecule problems with tens of occupied levels. Work is in progress to attempt to alleviate those difficulties.

cond-mat.mtrl-sci↗

arXiv2000

Real-Space Mesh Techniques in Density Functional Theory

This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling electrostatics and electronic structure methods is first discussed. Then the basic aspects of real-space representations are presented. Multigrid techniques for solving the discretized problems are covered; these numerical schemes allow for highly efficient solution of the grid-based equations. Applications to problems in electrostatics are discussed, in particular numerical solutions of Poisson and Poisson-Boltzmann equations. Next, methods for solving self-consistent eigenvalue problems in real space are presented; these techniques have been extensively applied to solutions of the Hartree-Fock and Kohn-Sham equations of electronic structure, and to eigenvalue problems arising in semiconductor and polymer physics. Finally, real-space methods have found recent application in computations of optical response and excited states in time-dependent density functional theory, and these computational developments are summarized. Multiscale solvers are competitive with the most efficient available plane-wave techniques in terms of the number of self-consistency steps required to reach the ground state, and they require less work in each self-consistency update on a uniform grid. Besides excellent efficiencies, the decided advantages of the real-space multiscale approach are 1) the near-locality of each function update, 2) the ability to handle global eigenfunction constraints and potential updates on coarse levels, and 3) the ability to incorporate adaptive local mesh refinements without loss of optimal multigrid efficiencies.

cond-mat.mtrl-sci↗

arXiv1999

Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques

We present a multigrid algorithm for self consistent solution of the Kohn-Sham equations in real space. The entire problem is discretized on a real space mesh with a high order finite difference representation. The resulting self consistent equations are solved on a heirarchy of grids of increasing resolution with a nonlinear Full Approximation Scheme, Full Multigrid algorithm. The self consistency is effected by updates of the Poisson equation and the exchange correlation potential at the end of each eigenfunction correction cycle. The algorithm leads to highly efficient solution of the equations, whereby the ground state electron distribution is obtained in only two or three self consistency iterations on the finest scale.

cond-mat.mtrl-sci↗

arXiv1998

Multigrid High Order Mesh Refinement Techniques

A method for performing high order mesh refinement multigrid computations is presented. The Full Approximation Scheme (FAS) multigrid technique is utilized for a sequence of nested patches of increasing resolution. Conservation forms are generated on coarse scales by additional defect correction terms which counter the local excess fluxes at the boundaries. Formulas are given for arbitrary order, extending the existing technique of Bai and Brandt. Test calculations are presented for a singular source in three dimensions which illustrate the multigrid convergence properties, numerical accuracy, and correct order of the approach. Applications for all electron quantum chemical computations are discussed.

physics.chem-ph↗

arXiv1995

Application of A Distributed Nucleus Approximation In Grid Based Minimization of the Kohn-Sham Energy Functional

In the distributed nucleus approximation we represent the singular nucleus as smeared over a smallportion of a Cartesian grid. Delocalizing the nucleus allows us to solve the Poisson equation for theoverall electrostatic potential using a linear scaling multigrid algorithm.This work is done in the context of minimizing the Kohn-Sham energy functionaldirectly in real space with a multiscale approach. The efficacy of the approximation is illustrated bylocating the ground state density of simple one electron atoms and moleculesand more complicated multiorbital systems.

chem-ph↗