Theory of CoarseGraining and Multiscale Phenomena
The Voth group develops theoretical and computational frameworks to study multiscale phenomena in biology and materials science. We work on both new theoreticallyinformed conceptual models as well as more quantitative, systematic, bottomup modeling methods. Since 2005, our group has been one of the leaders in the development of methods for defining coarsegrained (CG) interactions from atomistic simulations in the condensed phase. We have since contributed to systematic methods for defining optimal choices of coarsegraining mapping, observable representation, and effective interactions for large biomolecules. Also, we have developed new enhanced sampling methods, the ultra coarsegraining framework, and new approach to coarsegrained dynamics. We aim to research novel mapping schemes and reactive coarsegraining methods in the future. The development of these methods is tightly coupled to our work on molecular and reactive simulations.
The Theory of Multiscale CoarseGraining (MSCG)
The multiscale coarsegraining (MSCG) methodology provides a systematic, bottomup way to calculate effective CG interactions based on rigorous statistical mechanics. It seeks to approximate the manybody potential of mean force by variationally minimizing the difference between CG forces at the mapped finegrained reference forces (a.k.a, “force matching”). This method is related to liquid state theory and the YvonBornGreen equation. The code implementing the MSCG methodology is available for download here and is available as a fix in LAMMPS through the OpenMSCG package.
Recent methodological work on MSCG has included the inclusion of threebody interactions as well as formulations for both the constant NVT and constant NPT ensembles. We have also explored centerofcharge mappings as an alternative to the more traditional centerofmass and centerofgeometry mappings. MSCG models have been applied to wide range of systems including common solvents (e.g., methanol, hexane, water, ionic liquids), membrane systems, carbohydrates, polyglutamine aggregation, peptide secondary structures, and larger proteins.
Using MSCG, the sensitivity of coarsegrained models to changes in the underlying FG model from which it was derived can be studied. This method provides a lownoise, computationally efficient way to calculate this sensitivity. The sensitivity can be used to accurately calculate alchemical transferability across interaction parameters to first order at low computational cost. Additionally, we used MSCG to investigate the challenges of representing observables in CG models. We present a condition that can ensure that a CG observable reproduces the distribution of the FG observable projected onto CG model.
Recently, we extended the MSCG methodology by explicitly including the order parameter dependent interactions to better reproduce the structural correlations at the inhomogeneous system. Another extension was to develop a theoretical methodology of coarsegraining for the quantum mechanical regime based on the MSCG methodology. For the quantum MSCG (qMSCG) method, the Feynman path integral description of quantum statistical mechanics was combined with the variational forcematching method.
Relevant Papers:

Han, Y., Jin, J., Wagner, J. W., Voth, G. A. (2018). Quantum Theory of Multiscale CoarseGraining. Journal of Chemical Physics, 148, 102335. doi: 10.1063/1.5010270

Wagner, J. W., DannenhofferLafage, T., Jin, J., Voth, G. A. (2017). Extending the Range and Physical Accuracy of CoarseGrained Models: Order Parameter Dependent Interactions. Journal of Chemical Physics, 147, 044113. doi: 10.1063/1.4995946

Wagner, J. W., Dama, J. F., Voth, G. A. (2016). On the representability problem and the physical meaning of coarsegrained models. Journal of Chemical Physics, 145, 044108. doi: 10.1063/1.4959168

Wagner, J. W., Dama, J. F., Voth, G. A. (2015). Predicting the Sensitivity of Multiscale CoarseGrained Models to their Underlying FineGrained Model Parameters. Journal of Chemical Theory and Computation, 11(8), 35473560. doi: 10.1021/acs.jctc.5b00180

Cao, Z., Voth, G. A. (2015). The Multiscale CoarseGraining Method. XI. Accurate Interactions Based on the Centers of Charge of CoarseGrained Sites. Journal of Chemical Physics. 143, 243116. doi: 10.1063/1.4933249

Noid, W. G., Liu, P., Wang, Y., Chu, J.W., Ayton, G. S., Izvekov, S., Andersen, H. C., Voth, G. A., (2008). The multiscale coarsegraining method. II. Numerical implementation for coarsegrained molecular models. Journal of Chemical Physics, 128, 244115. doi: 10.1063/1.2938857

Noid, W. G., Chu, J.W., Ayton, G. S., Krishna, V., Izvekov, S., Voth, G. A., Das, A., & Andersen, H. C. (2008). The multiscale coarsegraining method. I. A rigorous bridge between atomistic and coarsegrained models. Journal of Chemical Physics, 128(24), 244114. doi: 10.1063/1.2938860
Researchers: Thomas DannenhofferLafage, Jaehyeok Jin, Yining Han
The Theory of UltraCoarseGraining (UCG)
We developed a new systematic framework for coarsegraining by incorporating internal state variables with configurational variables into CG beads. This UCG he development of this method is actively ongoing. In the current UCG framework, two different internal dynamics are rigorously explored: rapidly equilibrating (in a local equilibrium) or rarely switching (Markovstate). For the rarely switching dynamics, we constructed the UCG model at ultralow resolution that combines particlebased and Markovstatebased modeling to allow for dynamics both of and within coarsegrained beads. From the developed UCG model, we studied the limit where state switching is rare compared to the time scale of particle motion.
For the other extreme where the internal CG states are in a rapid local equilibrium, the UCG force field is obtained by mixing standard CG force fields in terms of local order parameters where the degree of mixing is regulated. We designed the UCG theory for this limit to embed an environmental dependence and manybody effects to the CG force field. To modulate the interactions between the UCG beads, we focused on order parameters in various systems ranging from hydrophobic association to inhomogeneous interfacial systems. Compared to the standard CG approach, the developed UCG models can faithfully recapitulate the structural correlations more accurately. More fascinatingly, we recently demonstrated that this UCG approach can impart transferable CG interactions from the bulk system to the interfacial systems (liquidvapor or liquidliquid interfaces). Currently, we are working on applying the UCG methodology to complex biomolecules or liquid phenomena.
Relevant Papers:

Jin, J., Voth, G. A. (2018). UltraCoarseGrained Models Allow for an Accurate and Transferable Treatment of Interfacial Systems. Journal of Chemical Theory and Computation, 14(4), 21802197. doi: 10.1021/acs.jctc.7b01173

Dama, J. F., Jin, J., Voth, G. A. (2017). The Theory of UltraCoarseGraining. 3. CoarseGrained Sites with Rapid Local Equilibrium of Internal States. Journal of Chemical Theory and Computation, 13(3), 10101022. doi: 10.1021/acs.jctc.6b01081

Davtyan, A., Dama, J. F., Sinitskiy, A. V., Voth, G. A. (2014) The Theory of UltraCoarseGraining. 2. Numerical Implementation. Journal of Chemical Theory and Computation, 10(12), 5265–5275. doi: 10.1021/ct500834t

Dama, J. F., Sinitskiy, A. V., McCullagh, M., Weare, J., Roux, B., Dinner, A. V., Voth, G. A. (2013). The Theory of UltraCoarseGraining. 1. General Principles. Journal of Chemical Theory and Computation, 9(5), 2466–2480. doi: 10.1021/ct4000444
Researchers: Jaehyeok Jin
CG Dynamics
Due to the dramatic reduction in the number of degrees of freedom (DoF) that is achieved through coarsegraining, the dynamics in the CG system is usually sped up. However, the interpretation of CG dynamics is often difficult due to the inhomogeneous acceleration of diffusion and transitions. This is due to the removal of the fluctuation forces on the CG sites after the DoF reduction. Our dynamic force matching method allows for the reintroduction of those fluctuation forces into the CG model through “fictitious particles” in a way that does not significantly affect the computational efficiency or the equilibrium properties of the CG model. In our first paper, we showed that this method can accurately reproduce the diffusion rate and reasonably represent the shorttime dynamics. Additional developments have allowed us to simultaneously reproduce multiple longtime properties (such as selfdiffusion rate and rotational relaxation rate) as well.
Relevant Papers:

Davtyan, A., Voth, G. A., Andersen, H. C. (2016) Dynamic Force Matching: Construction of Dynamic CoarseGrained Models with Realistic Short Time Dynamics and Accurate Long Time Dynamics. Journal of Chemical Physics. 145, 224107. doi: 10.1063/1.4971430
 Davtyan, A., Dama, J. F., Voth, G. A., Andersen, H. C. (2015). Dynamic force matching: A method for constructing dynamical coarsegrained models with realistic time dependence. Journal of Chemical Physics. 142, 154104. doi: 10.1063/1.4917454
Researchers: Yining Han, Jaehyeok Jin
Enhanced Sampling Development
Creating coarsegrained models that properly reflect the underlying physics and chemistry inherently requires having robustly explored the phase space defined by the finegrained model. Moreover, it is important that the model be parameterized correctly in order to have simulations properly reflect behavior seen in experiments. The Voth group has sought to ameliorate difficulties related to both aspects of the sampling problem.
First, in order to ensure robust sampling, the Voth group makes extensive use of free energy methods, which enhance the exploration of phase space along chosen collective variables (reaction coordinates) in the system. We make extensive use of both umbrella sampling and metadynamics. We have recently put a substantial amount of effort into the development and benchmarking of new metadynamics variants. In particular, our group first proved that the welltempered version of metadynamics converges asymptotically to the exact free energy of the system. Then using the conditions for convergence, we were able to design new methods, such as the transition tempered metadynamics method, which first uses untempered metadynamics to enhance exploration, then tempers after a transition between two specified areas of phase space is detected, giving much more robust results quickly. For example, we have shown this to be a superior method for studying the permeation of small molecules through lipid bilayers. We have also recently developed the metabasin metadynamics method, which restricts the area in which bias is added to a region which is below a freeenergetic threshold, where this region is detected automatically and onthefly. This allows for more careful addition of bias without pushing the system into unphysical regions.
Second, in order to ensure the distribution sampled reflects experimental observations, new linear biasing methods have been developed that ensure experimentally observed averages or target distributions are recovered by a simulation with minimal perturbation. We have developed experimentally directed simulation (EDS) methods which discover the correct biasing parameters on the fly, and show how these can also be used to bias coarsegrained models. We have also developed an experimentally directed metadynamics method (EDM), which uses the same ideas of metadynamics to add bias to the system such that the system samples a target distribution. The EDS method has recently been applied in reactive simulations of water and water with an excess proton. Here we show that by only correcting the oxygenoxygen radial distribution function of DFT water with a poor functional, we can greatly improve the structure and dynamics in the system effectively without additional cost.
All of these new methods are all available and implemented in public repositories:
Transition tempered and metabasin: https://github.com/JFDama/plumed2/tree/pinioncleanup
Relevant Metadynamics Papers:

Sun, R., Han, Y., Swanson, J. M., Tan, J. S., Rose, J. P., Voth, G. A. (2018). Molecular Transport Through Membranes: Accurate Permeability Coefficients From Multidimensional Potentials of Mean Force and Local Diffusion Constants. Journal of Chemical Physics, 149, 072310. doi: 10.1063/1.5027004

Sun, R., Dama, J. F., Tan, J. S., Rose, J. P., Voth, G.A. (2016). TransitionTempered Metadynamics is a Promising Tool for Studying the Permeation of Druglike Molecules through Membranes. Journal of Chemical Theory and Computation. 12(10), 5157–5169. doi: 10.1021/acs.jctc.6b00206

Dama, J. F., Hocky, G. M., Sun, R., Voth, G. A. (2015). Exploring Valleys Without Climbing Every Peak: More Efficient and Forgiving Metabasin Metadynamics via Robust OntheFly Bias Domain Restriction. Journal of Chemical Theory and Computation. 11(12), 5638–5650. doi: 10.1021/acs.jctc.5b00907

Dama, J. F., Rotskoff, J., Parrinello, M., Voth, G.A. (2014). TransitionTempered Metadynamics: Robust, Convergent Metadynamics via OnTheFly Transition Barrier Estimation. Journal of Chemical Theory and Computation. 10(9), 3626–3633. doi: 10.1021/ct500441q

Dama, J. F., Parrinello, M., Voth, G. A. (2014). Welltempered Metadynamics Converges Asymptotically. Physical Review Letters. 112, 16. doi: 10.1103/PhysRevLett.112.240602
Relevant Experiment Directed Papers:

Hocky, G. M., DannenhofferLafage, T., Voth, G. A. (2017). CoarseGrained Directed Simulation. Journal of Chemical Theory and Computation, 13(9), 45934603. doi: 10.1021/acs.jctc.7b00690

White, A. D., Knight, C., Hocky, G. M., Voth, G.A. (2017). Improved Ab Initio Molecular Dynamics by Minimally Biasing with Experimental Data. Journal of Chemical Physics. 146, 041102. doi: 10.1063/1.4974837

DannenhofferLafage, T., White, A. D., Voth, G. A. (2016). A Direct Method for Incorporating Experimental Data into Multiscale Coarsegrained Models. Journal of Chemical Theory and Computation. 12(5), 21442153. doi: 10.1021/acs.jctc.6b00043

White, A. D., Dama, J. F., Voth, G. A. (2015). Designing Free Energy Surfaces that Match Experimental Data with Metadynamics. Journal of Chemical Theory and Computation. 11(6), 24512560. doi: 10.1021/acs.jctc.5b00178
 White, A. D., Voth, G. A. (2014). Efficient and Minimal Method to Bias Molecular Simulations with Experimental Data. Journal of Chemical Theory and Computation. 10(8): 3023–3030. doi: 10.1021/ct500320c
Researchers: Thomas DannenhofferLafage, Glen Hocky