About

William Noid is a Professor of Chemistry at Penn State University, affiliated with the Department of Chemistry. He holds a B.S. from the University of Tennessee, Knoxville, obtained in 2000, and a Ph.D. from Cornell University in 2005. His research primarily focuses on developing theories and computational methods for multiscale modeling of soft materials, including liquids, peptides, polymers, and complex molecular systems. He specializes in creating rigorous statistical mechanical theories and efficient computational methodologies, such as coarse-grained models, to address the challenges of atomically detailed simulations that are often prohibitively time-consuming. His work aims to improve the accuracy and transferability of coarse-grained models, which simplify molecular representations to enable the study of larger systems over longer timescales. He has contributed to the generalization of the Yvon-Born-Green theory, providing a variational framework for determining potentials that approximate many-body interactions. Additionally, Noid collaborates with experimentalists to interpret biophysical phenomena, including the effects of osmolytes on protein stability and the properties of intrinsically disordered proteins. His research integrates theory, simulation, and experimental data to advance understanding in biochemistry, active materials, and complex molecular systems.

Research topics

• Computer Science
• Machine Learning
• Artificial Intelligence
• Mathematics
• Physics
• Statistical physics
• Engineering
• Econometrics
• Data science
• Management science
• Geography
• Cartography
• Theoretical computer science
• Environmental science
• Statistics

Selected publications

• Predicting energetic and entropic driving forces with coarse-grained models

  The Journal of Chemical Physics · 2025-08-26 · 1 citations

  articleSenior author

  Low resolution coarse-grained (CG) models provide exceptional computational efficiency for simulating soft materials. Consequently, many studies employ CG models to determine free energy surfaces along order parameters or reaction coordinates of interest. However, because CG models average over atomic details, it is challenging to determine the energetic and entropic contributions to the resulting free energy surfaces. In this work, we present a rigorous and predictive CG framework for computing these energetic and entropic driving forces based upon simulations at a single temperature. This dual approach employs distinct variational principles to independently approximate the exact CG interaction potential, W(R), and its energetic component, EW(R). This dual approach determines the free energy surface, aφ(x), along an order parameter, φ(x), via simulations with W(R). The dual approach then determines the energetic driving force, ūφ(x), by evaluating EW(R) for the sampled configurations. The entropic driving force, s̄φ(x), is indirectly inferred, s̄φ(x)=ūφ(x)-aφ(x)/T. Importantly, this entropic contribution reflects both the CG configuration distribution and the atomic details that have been eliminated from the CG model. We demonstrate that the dual approach reasonably describes the energetic and entropic driving forces between a pair of nonpolar solutes in a polar solvent. In contrast, naïvely estimating energetics with the CG interaction potential provides a qualitatively incorrect description for these driving forces.

  PublisherDOI

• A Tribute to Gregory A. Voth

  The Journal of Physical Chemistry B · 2024-08-15

  articleOpen accessCorresponding
  PublisherOA PDFDOI

• Rigorous Progress in Coarse-Graining

  Annual Review of Physical Chemistry · 2024-06-28 · 34 citations

  articleOpen access1st authorCorresponding

  Low-resolution coarse-grained (CG) models provide remarkable computational and conceptual advantages for simulating soft materials. In principle, bottom-up CG models can reproduce all structural and thermodynamic properties of atomically detailed models that can be observed at the resolution of the CG model. This review discusses recent progress in developing theory and computational methods for achieving this promise. We first briefly review variational approaches for parameterizing interaction potentials and their relationship to machine learning methods. We then discuss recent approaches for simultaneously improving both the transferability and thermodynamic properties of bottom-up models by rigorously addressing the density and temperature dependence of these potentials. We also briefly discuss exciting progress in modeling high-resolution observables with low-resolution CG models. More generally, we highlight the essential role of the bottom-up framework not only for fundamentally understanding the limitations of prior CG models but also for developing robust computational methods that resolve these limitations in practice.

  PublisherDOI

• Insight into the Density-Dependence of Pair Potentials for Predictive Coarse-Grained Models

  The Journal of Physical Chemistry B · 2024-01-25 · 1 citations

  articleSenior authorCorresponding

  We investigate the temperature- and density-dependence of effective pair potentials for 1-site coarse-grained (CG) models of two industrial solvents, 1,4-dioxane and tetrahydrofuran. We observe that the calculated pair potentials are much more sensitive to density than to temperature. The generalized-Yvon-Born–Green framework reveals that this striking density-dependence reflects corresponding variations in the many-body correlations that determine the environment-mediated indirect contribution to the pair mean force. Moreover, we demonstrate, perhaps surprisingly, that this density-dependence is not important for accurately modeling the intermolecular structure. Accordingly, we adopt a density-independent interaction potential and transfer the density-dependence of the calculated pair potentials into a configuration-independent volume potential. Furthermore, we develop a single global potential that accurately models the intermolecular structure and pressure–volume equation of state across a very wide range of liquid state points. Consequently, this work provides fundamental insight into the density-dependence of effective pair potentials and also provides a significant step toward developing predictive CG models for efficiently modeling industrial solvents.

  PublisherDOI

• Surveying the energy landscape of coarse-grained mappings

  The Journal of Chemical Physics · 2024-02-02 · 3 citations

  articleSenior author

  Simulations of soft materials often adopt low-resolution coarse-grained (CG) models. However, the CG representation is not unique and its impact upon simulated properties is poorly understood. In this work, we investigate the space of CG representations for ubiquitin, which is a typical globular protein with 72 amino acids. We employ Monte Carlo methods to ergodically sample this space and to characterize its landscape. By adopting the Gaussian network model as an analytically tractable atomistic model for equilibrium fluctuations, we exactly assess the intrinsic quality of each CG representation without introducing any approximations in sampling configurations or in modeling interactions. We focus on two metrics, the spectral quality and the information content, that quantify the extent to which the CG representation preserves low-frequency, large-amplitude motions and configurational information, respectively. The spectral quality and information content are weakly correlated among high-resolution representations but become strongly anticorrelated among low-resolution representations. Representations with maximal spectral quality appear consistent with physical intuition, while low-resolution representations with maximal information content do not. Interestingly, quenching studies indicate that the energy landscape of mapping space is very smooth and highly connected. Moreover, our study suggests a critical resolution below which a "phase transition" qualitatively distinguishes good and bad representations.

  PublisherDOI

• Analysis of mapping atomic models to coarse-grained resolution

  The Journal of Chemical Physics · 2024-10-04 · 9 citations

  articleSenior author

  Low-resolution coarse-grained (CG) models provide significant computational and conceptual advantages for simulating soft materials. However, the properties of CG models depend quite sensitively upon the mapping, M, that maps each atomic configuration, r, to a CG configuration, R. In particular, M determines how the configurational information of the atomic model is partitioned between the mapped ensemble of CG configurations and the lost ensemble of atomic configurations that map to each R. In this work, we investigate how the mapping partitions the atomic configuration space into CG and intra-site components. We demonstrate that the corresponding coordinate transformation introduces a nontrivial Jacobian factor. This Jacobian factor defines a labeling entropy that corresponds to the uncertainty in the atoms that are associated with each CG site. Consequently, the labeling entropy effectively transfers configurational information from the lost ensemble into the mapped ensemble. Moreover, our analysis highlights the possibility of resonant mappings that separate the atomic potential into CG and intra-site contributions. We numerically illustrate these considerations with a Gaussian network model for the equilibrium fluctuations of actin. We demonstrate that the spectral quality, Q, provides a simple metric for identifying high quality representations for actin. Conversely, we find that neither maximizing nor minimizing the information content of the mapped ensemble results in high quality representations. However, if one accounts for the labeling uncertainty, Q(M) correlates quite well with the adjusted configurational information loss, Îmap(M), that results from the mapping.

  PublisherDOI

• Relating the artificial chemotaxis of catalysts to a gradient descent of the free energy

  The Journal of Chemical Physics · 2023-06-02 · 1 citations

  articleSenior author

  Recent experiments suggest that mesoscale catalysts are active materials that power their motion with chemical free energy from their environment and also "chemotax" with respect to substrate gradients. In the present work, we explore a thermodynamic framework for relating this chemotaxis to the evolution of a system down the gradient of its free energy. This framework builds upon recent studies that have employed the Wasserstein metric to describe diffusive processes within the Onsager formalism for irreversible thermodynamics. In this work, we modify the Onsager dissipation potential to explicitly couple the reactive flux to the diffusive flux of catalysts. The corresponding gradient flow is a modified reaction-diffusion equation with an advective term that propels the chemotaxis of catalysts with the free energy released by chemical reactions. In order to gain first insights into this framework, we numerically simulate a simplified model for spherical catalysts undergoing artificial chemotaxis in one dimension. These simulations investigate the thermodynamic forces and fluxes that drive this chemotaxis, as well as the resulting dissipation of free energy. Additionally, they demonstrate that chemotaxis can delay the relaxation to equilibrium and, equivalently, prolong the duration of nonequilibrium conditions. Although future simulations should consider a more realistic coupling between reactive and diffusive fluxes, this work may provide insight into the thermodynamics of artificial chemotaxis. More generally, we hope that this work may bring attention to the importance of the Wasserstein metric for relating nonequilibrium relaxation to the thermodynamic free energy and to large deviation principles.

  PublisherDOI

• A temperature-dependent length-scale for transferable local density potentials

  The Journal of Chemical Physics · 2023-08-17 · 8 citations

  articleSenior author

  Recent coarse-grained (CG) models have often supplemented conventional pair potentials with potentials that depend upon the local density around each particle. In this work, we investigate the temperature-dependence of these local density (LD) potentials. Specifically, we employ the multiscale coarse-graining (MS-CG) force-matching variational principle to parameterize pair and LD potentials for one-site CG models of molecular liquids at ambient pressure. The accuracy of these MS-CG LD potentials quite sensitively depends upon the length-scale, rc, that is employed to define the local density. When the local density is defined by the optimal length-scale, rc*, the MS-CG potential often accurately describes the reference state point and can provide reasonable transferability across a rather wide range of temperatures. At ambient pressure, the optimal LD length-scale varies linearly with temperature over a very wide range of temperatures. Moreover, if one adopts this temperature-dependent LD length-scale, then the MS-CG LD potential appears independent of temperature, while the MS-CG pair potential varies linearly across this temperature range. This provides a simple means for predicting pair and LD potentials that accurately model new state points without performing additional atomistic simulations. Surprisingly, at certain state points, the predicted potentials provide greater accuracy than MS-CG potentials that were optimized for the state point.

  PublisherDOI

• Perspective: Advances, Challenges, and Insight for Predictive Coarse-Grained Models

  The Journal of Physical Chemistry B · 2023 · 136 citations

  1st authorCorresponding
  • Computer Science
  • Computer Science
  • Artificial Intelligence

  By averaging over atomic details, coarse-grained (CG) models provide profound computational and conceptual advantages for studying soft materials. In particular, bottom-up approaches develop CG models based upon information obtained from atomically detailed models. At least in principle, a bottom-up model can reproduce all the properties of an atomically detailed model that are observable at the resolution of the CG model. Historically, bottom-up approaches have accurately modeled the structure of liquids, polymers, and other amorphous soft materials, but have provided lower structural fidelity for more complex biomolecular systems. Moreover, they have also been plagued by unpredictable transferability and a poor description of thermodynamic properties. Fortunately, recent studies have reported dramatic advances in addressing these prior limitations. This Perspective reviews this remarkable progress, while focusing on its foundation in the basic theory of coarse-graining. In particular, we describe recent insights and advances for treating the CG mapping, for modeling many-body interactions, for addressing the state-point dependence of effective potentials, and even for reproducing atomic observables that are beyond the resolution of the CG model. We also outline outstanding challenges and promising directions in the field. We anticipate that the synthesis of rigorous theory and modern computational tools will result in practical bottom-up methods that not only are accurate and transferable but also provide predictive insight for complex systems.

  PublisherDOI

• A simple theory for interfacial properties of dilute solutions

  The Journal of Chemical Physics · 2022-06-27 · 5 citations

  articleOpen accessSenior authorCorresponding

  Recent studies suggest that cosolute mixtures may exert significant non-additive effects upon protein stability. The corresponding liquid-vapor interfaces may provide useful insight into these non-additive effects. Accordingly, in this work, we relate the interfacial properties of dilute multicomponent solutions to the interactions between solutes. We first derive a simple model for the surface excess of solutes in terms of thermodynamic observables. We then develop a lattice-based statistical mechanical perturbation theory to derive these observables from microscopic interactions. Rather than adopting a random mixing approximation, this dilute solution theory (DST) exactly treats solute-solute interactions to lowest order in perturbation theory. Although it cannot treat concentrated solutions, Monte Carlo (MC) simulations demonstrate that DST describes the interactions in dilute solutions with much greater accuracy than regular solution theory. Importantly, DST emphasizes a fundamental distinction between the "intrinsic" and "effective" preferences of solutes for interfaces. DST predicts that three classes of solutes can be distinguished by their intrinsic preference for interfaces. While the surface preference of strong depletants is relatively insensitive to interactions, the surface preference of strong surfactants can be modulated by interactions at the interface. Moreover, DST predicts that the surface preference of weak depletants and weak surfactants can be qualitatively inverted by interactions in the bulk. We also demonstrate that DST can be extended to treat surface polarization effects and to model experimental data. MC simulations validate the accuracy of DST predictions for lattice systems that correspond to molar concentrations.

  PublisherOA PDFDOI

Recent grants

• Systematic coarse-graining of inhomogeneous systems

  NSF · $450k · 2019–2023

• CAREER: Variational Bridge between Knowledge-based and Physics-based Models - Applications to Ubiquilin Interactions

  NSF · $685k · 2011–2017

• Towards Predictive Coarse-grained Models

  NSF · $501k · 2022–2026

• NIH Grant F32GM076839

  NIH · $74k · 2007

• Van der Waals Approach to Systematic Coarse-Graining

  NSF · $420k · 2016–2020

Frequent coauthors

• Roger F. Loring

  Cornell University

  15 shared

• Joseph F. Rudzinski

  12 shared

• Ryo Akiyama

  9 shared

• M. D. Fayer

  Stanford University

  8 shared

• Kusai A. Merchant

  National Institute of Diabetes and Digestive and Kidney Diseases

  8 shared

• Jhih‐Wei Chu

  7 shared

• Gregory A. Voth

  Chicago Institute for Psychoanalysis

  6 shared

• David E. Thompson

  Sam Houston State University

  6 shared

Awards & honors

• Camille Dreyfus Teacher-Scholar Award 2012
• NSF Career Award 2011
• Alfred P. Sloan Foundation Research Fellow 2011
• Penn State Institute for CyberScience Faculty Fellow 2011
• HP Outstanding Junior Faculty Award from the ACS Division of…