### Organizers

Electrostatic interactions are fundamental in nature and ubiquitous in all biomolecules, including proteins, nucleic acids, lipid bilayers, sugars, etc. Electrostatic interactions are inherently of long range, which leads to computational challenges. Since 65-90 percent of cellular mass is water under physiological condition, biomolecules live in a heterogeneous environment, where they interact with a wide range of aqueous ions, counterions, and other molecules. As a result, electrostatic interactions often manifest themselves in a vast variety of different forms, due to polarization, hyperpolarization, vibrational and rotational averages, screening effect, etc, to mention just a few. The importance of electrostatics in biomolecular systems cannot be overemphasized because they underpin the molecular mechanism for almost all important biological processes, including signal transduction, DNA recognition, transcription, post-translational modification, translation, protein folding and protein ligand binding. In general, electrostatics is often the fundamental mechanism for macromolecular structure, function, dynamics and transport. Modeling and understanding the role of electrostatics in biomolecular systems are challenging tasks, since these systems are very complicated, made of macromolecules composed of hundreds of thousands or millions of atoms, and at the same time, surrounded by millions of water molecules, which in turn constantly change their positions and orientations. The number of degrees of freedom in explicit modeling of biomolecular systems is so large that it is frequently computationally prohibited for large systems or cases involving extremely large dimensions. Implicit models and multiscale approaches offer an alternative approach that dramatically reduces the computational cost, while being accurate enough to predict experimentally measurable quantities. Despite enormous efforts in the past two decades, important challenges remain in electrostatic modeling and computation. These include the definition of solvent-solute interfaces, nonlocal dielectric effects, finite size effects, nonlinear solvent response to solute perturbation, the representation of solvent microstructures, the solution of the corresponding nonlinear partial differential equations (PDEs) for irregularly shaped molecular boundaries, the treatment of solvent polarization and multi-valent ions, the formulation and solution of nonlinear integral equations (IEs), liquid density functional theory, and variational multiscale modeling of the dynamics and transport of biomolecular systems. The advantages and limitations of various methodologies are to be explored. Successful approaches to these challenges require combined efforts of physicists, mathematicians, computer scientists and biologists. This workshop will enable interactions between scientists from a diverse set of relevant disciplines. In particular, it will be of interest to mathematicians working in the areas of multiscale modeling, differential geometry of surfaces, PDE analysis, numerical PDE, and fast algorithm, to name a few. It will significantly strengthen the leading role that the US researchers can play in mathematical molecular biosciences by pursuing cutting-edge research and collaboratively training a new generation of mathematicians in this emerging interdisciplinary field.

### Accepted Speakers

Monday, October 12, 2015 | |
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Time | Session |

07:45 AM | Shuttle to MBI |

08:00 AM 08:30 AM | Breakfast |

08:30 AM 08:45 AM | Welcome, overview, introduction: MG |

08:45 AM 09:00 AM | Introduction by workshop organizers |

09:00 AM 09:45 AM | John Zhang - Multi-level theory for protein structure and dynamics Abstract not submitted. |

09:45 AM 10:30 AM | Nathan Baker - Quantifying the influence of conformational uncertainty in biomolecular solvation Biomolecules exhibit conformational fluctuations near equilibrium states, inducing uncertainty in various biological properties in a dynamic way. We have developed a general method to quantify the uncertainty of target properties induced by conformational fluctuations. Using a generalized polynomial chaos (gPC) expansion, we construct a surrogate model of the target property with respect to varying conformational states. We also propose a method to increase the sparsity of the gPC expansion by defining a set of conformational "active space" random variables. With the increased sparsity, we employ the compressive sensing method to accurately construct the surrogate model. We demonstrate the performance of the surrogate model by evaluating fluctuation-induced uncertainty in solvent-accessible surface area for the bovine trypsin inhibitor protein system and show that the new approach offers more accurate statistical information than standard Monte Carlo approaches. Further more, the constructed surrogate model also enables us to directly evaluate the target property under various conformational states, yielding a more accurate response surface than standard sparse grid collocation methods. In particular, the new method provides higher accuracy in high-dimensional systems, such as biomolecules, where sparse grid performance is limited by the accuracy of the computed quantity of interest. Our new framework is generalizable and can be used to investigate the uncertainty of a wide variety of target properties in biomolecular systems. |

10:30 AM 11:00 AM | Break |

11:00 AM 11:45 AM | Dongping Zhong - Watching water motions at biological interfaces Water is a universal lubricant in life and plays a critical role in biomolecular structure, dynamics and function. Here, we report the systematic characterization of water motions around protein surfaces and protein-DNA interfaces in real time. Hydration water is found to strongly slave protein fluctuations. A series of correlations between the dynamics and protein properties was observed. These results revealed the wide range of heterogeneous water dynamics on the picosecond time scales but are well correlated with the protein structures, dynamics and even function. Such water dynamics could be general at any other nanointerfaces. |

11:45 AM 12:30 PM | Huan-Xiang Zhou - Electrostatic Interactions in Protein Structure, Folding, Binding, and Assembly Amino acids with ionizable side chains, e.g., Asp, Glu, His, Lys, and Arg, impart important properties to proteins. Modulation of the charges on these amino acids, e.g., by pH, may result in significant changes such as protein unfolding. Charged residues can play critical roles in regulating protein assembly, as illustrated by the Glu6 ? Val mutation in the |

12:30 PM 02:00 PM | Lunch Break |

02:00 PM 02:45 PM | Julie Mitchell - What Data-Driven Models of Biophysics Tell Us About Protein Electrostatics No abstract has been provided. |

02:45 PM 03:00 PM | Break |

03:00 PM 04:00 PM | Sharon Hammes-Schiffer - Probing Electrostatics and Conformational Motions in Enzyme Catalysis Electrostatic interactions play an important role in enzyme catalysis. These effects are modulated by the conformational changes that occur over the catalytic cycle. To elucidate the catalytic roles of these effects, thiocyanate probes were introduced at site-specific positions in the enzymes ketosteroid isomerase (KSI) and dihydrofolate reductase (DHFR). In KSI, the impact of electrostatics on ligand binding was explored. In DHFR, the impact of electrostatics on the catalytic cycle involving five different complexes was investigated. The shifts in the vibrational stretching frequencies of the nitrile probes report on the electrostatics of the microenvironments surrounding the probes. Mixed quantum mechanical/molecular mechanical molecular dynamics simulations reproduced the experimental vibrational frequency shifts and provided atomic-level insight into the roles that key residues play in determining the electrostatics of the microenvironments. The electrostatic contributions were decomposed into the major components from individual residues, ligands, and water molecules. For DHFR, calculation of the electric field along the hydride donor-acceptor axis, along with decomposition of this field into specific contributions, indicates that the cofactor and substrate, as well as the enzyme, impose a substantial electric field that facilitates hydride transfer. Overall, experimental and theoretical data provide evidence for significant electrostatic changes in the active site microenvironments due to conformational motions occurring over the catalytic cycles of enzymes. |

04:00 PM 06:00 PM | Reception and poster session in MBI Lounge |

06:00 PM | Shuttle pick-up from MBI |

Tuesday, October 13, 2015 | |
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Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:45 AM | Teresa Head-Gordon - Atomistic and coarse-grained models and methods for electrostatics Abstract not submitted. |

09:45 AM 10:30 AM | Maria Sushko - Ionic atmosphere around DNA: role of ion correlatios and solvation Abstract not submitted. |

10:30 AM 11:00 AM | Break |

11:00 AM 11:45 AM | Duan Chen - Modeling and computation of heterogeneous implicit solvent and its applications for biomolecules Description of inhomogeneous dielectric properties of a solvent in the vicinity of ions has been attracting research interests in mathematical modeling for many years. From many experimental results, it has been concluded that the dielectric response of a solvent linearly depends on the ionic strength within a certain range. Based on this assumption, a new implicit solvent model is proposed in the form of total free energy functional and a quasi-linear Poisson-Boltzmann equation (QPBE) is derived. Classical Newton’s iteration can be used to solve the QPBE numerically but the corresponding Jacobian matrix is complicated due to the quasi-linear term. In the current work, a systematic formulation of the Jacobian matrix is derived. As an alternative option, an algorithm mixing the Newton’s iteration and the fixed point method is proposed to avoid the complicated Jacobian matrix, and it is a more general algorithm for equation with discontinuous coefficients. Computational efficiency and accuracy for these two methods are investigated based on a set of equation parameters. At last, the QPBE with singular charge source and piece-wisely defined dielectric functions has been applied to analyze electrostatics of macro biomolecules in a complicated solvent. A set of computational algorithms such as interface method, singular charge removal technique and the Newton- fixed-point iteration are employed to solve the QPBE. Biological applications of the proposed model and algorithms are provided, including calculation of electrostatic solvation free energy of proteins, investigation of physical properties of channel pore of an ion channel, and electrostatics analysis for the segment of a DNA strand. |

11:45 AM 12:30 PM | Zhen-Gang Wang - Electrostatics beyond Poisson-Boltzmann: Effects of Self Energy Ions are essential in physical chemistry, colloidal science, electrochemistry, biology and many other areas of science and engineering. While their role is commonly described in terms of screening and translational entropy, many phenomena, ranging from some classical experimental observations made many decades ago to some new systems of current interest, cannot be explained, even qualitatively, by these concepts. A key effect that is often ignored or inadequately treated in the main literature on electrolytes and polyelectrolytes is the self-energy of the ions. In this talk, I will discuss several self-energy effects in macromolecular and interfacial systems. First, we show that the preferential solvation energy of the ions provides a significant driving force for phase separation. This concept is used to develop a theory to explain the dramatic shift in the order-disorder transition temperature in PEO-PS diblock copolymers upon the addition of salt. Second, we show that the dielectric contrast between the polymer backbone and the solvent significantly affects the conformation and charge condensation in dilute polyelectrolyte solutions. Third, we show that the image force has qualitative effects on the double layer structure and forces, such as like charge attraction and charge inversion. Finally we present a simple model for understanding the specific ion effects in the interfacial activity for air/water and oil/water interfaces. |

12:30 PM 02:00 PM | Lunch Break |

02:00 PM 02:45 PM | Xueyu Song - Beyond Poisson-Boltzmann approach in macromolecules electrostatics In this presentation a molecular Debye-Huckel theory for ionic fluids is developed. Starting from the macroscopic Maxwell equations for bulk systems, the dispersion relation leads to a generalized Debye-Huckel theory which is related to the dressed ion theory in the static case.Due to the multi-pole structure of the dielectric function of ionic fluids, the electric potential around a single solute has a multi-Yukawa form. Given the dielectric function, the multi-Yukawa potential can be determined from our molecular Debye-Huckel theory, hence, the electrostatic contributions to thermodynamic properties of ionic fluids can be obtained. Applications to solutes with arbitrary shapes in model electrolyte solutions demonstrated the accuracy of our approach. In combination with cavity formation energy a variational approach can be used to define the boundary between a solute and its continuum solvent. Thus, our approach provides a simple and efficient path to go beyond the traditional Poisson-Boltzmann model in biophysics. |

02:45 PM 03:00 PM | Break |

03:00 PM 03:45 PM | Weihua Geng - A treecode-accelerated boundary integral Poisson-Botlzmann solver: modeling, algorithm and application. The Poisson-Boltzmann model is an extended model of the classical Gauss's law involving additionally multiple dielectrics (thus interface problem), solvent effects (thus continuum model) and dissolved electrolytes (thus nonlinearity). In this talk, I will introduce our recent progress in developing a numerical Poisson-Boltzmann solver with tree-code algorithms (for efficiency) and boundary integral formulation (for accuracy). Following that, I will briefly touch the attractive performance computing feature of this solver including parallelization and GPUs. I will conclude the talk with a report for the potential and established application of the Poisson-Botlzmann model/solver for computing quantities with biological significance such as electrostatic solvation energy, electrostatic forces, pKa values, etc. |

03:45 PM 04:30 PM | Informal discussions/daily wrap-up |

04:30 PM | Shuttle pick-up from MBI |

Wednesday, October 14, 2015 | |
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Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:45 AM | Robert Krasny - A Treecode-Accelerated Boundary Integral Poisson-Boltzmann Solver for Electrostatics of Solvated Proteins Electrostatic effects play an important role in determining protein structure and function. Here we present a treecode-accelerated boundary integral (TABI) solver for the electrostatic potential of a solvated protein described by the linear Poisson-Boltzmann equation. In this model the solvent is a continuum dielectric material with screening due to dissolved ions and the protein is a set of charged particles. The method employs a well-conditioned boundary integral formulation for the electrostatic potential and its normal derivative on the molecular surface. The surface is triangulated by MSMS and the integral equations are discretized by centroid collocation. The linear system is solved by GMRES and the matrix-vector product is carried out by a tree code which reduces the computational cost from $O(N^2)$ to $O(Nlog N)$, where $N$ is the number of faces in the triangulated molecular surface. We compare TABI results to those obtained using the finite-difference APBS code. The TABI solver exhibits good serial and parallel performance, with relatively simple implementation, efficient memory usage, and geometric adaptability. This is joint work with Weihua Geng (Southern Methodist University). |

09:45 AM 10:30 AM | Tyler Luchko - Partial Molar Volume Corrected Solvation Energies, Entropies and Free Energies from 3D-RISM No abstract has been provided. |

10:30 AM 11:00 AM | Break |

11:00 AM 11:45 AM | Alexey Onufriev - Why Multivalent Ions Condense DNA but Not RNA? No abstract has been submitted. |

11:45 AM 12:30 PM | Stephen White - Electrostatics inside the SecY translocon protein that guides membrane protein assembly SecY constitutes the core of the highly conserved SecYEG translocon complex that governs the translocation or integration of proteins across or into cytoplasmic membranes. Besides its role of guiding nascent membrane protein chains into the lipid bilayer, it also plays an important role in determining transmembrane topology via the so-called positive-inside rule. Site-directed mutations of translocons are known to modify the topology of nascent α-helical segments [1]. We performed molecular dynamics simulations of SecYE from |

12:30 PM 02:00 PM | Break |

02:00 PM 02:45 PM | Yingkai Zhang - Role of Water and Ions in Enzyme Catalysis: from Mechanistic Insights to Modulator Design Water and ions are an integral part of biological systems. In this talk, I will use several medically important enzymes to illustrate versatile roles of water and ions in enzyme function. Our computational approaches center on Born-Oppenheimer ab initio QM/MM molecular dynamics simulation (aiQM/MM-MD) with umbrella sampling. Under the guidance of our elucidated insights, we have discovered a novel time-dependent HDAC2-selective inhibitor. In addition, I will briefly describe AlphaSpace – fragment centric topographical mapping to target protein-protein interaction (PPI) interfaces. The resulting high-resolution map of underutilized, targetable pocket space can be used to guide the rational design and optimization of synthetic PPI modulators. |

02:45 PM 03:00 PM | Break |

03:00 PM 03:45 PM | Chia-en (Angelina) Chang - Modeling of enhanced catalysis in multienzyme nanostructures: effect of molecular scaffolds, spatial organization, and concentration No abstract has been provided. |

03:45 PM 04:30 PM | Informal discussions/daily wrap-up |

04:30 PM | Shuttle pick-up from MBI |

Thursday, October 15, 2015 | |
---|---|

Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:45 AM | Zhan Chen - Differential geometry based Multiscale solvation models and their computation The understanding of solvation is an essential prerequisite for the quantitative description and analysis of many sophisticated chemical, biological and biomolecular processes.. Implicit solvent models, particularly those based on the Poisson-Boltzmann (PB) equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces and complex solutions of nonlinear equations post some severe limitations on their applications. We have introduced differential geometry (DG) based multiscale solvation models, which allow the solvent-solute interface, electrostatic potential, and even electron densities to be determined by the variation of a total free energy functional. In addition, our models is able to significantly reduce the number of free parameters and to avoid complicated interface problems raised by sharp solvent-solute interface. Finally, our DG based models have shown promising power in blind prediction of solvation as well as other applications. This is primarily joint work with Prof. Guowei Wei and Prof. Nathan Baker. |

09:45 AM 10:30 AM | John Herbert - What can quantum-inspired electrostatics methods contribute to biomolecular applications? My group is primarily interested in electrostatics calculations from the quantum-mechanical or QM/MM perspective, but I will describe two projects in which our methods might play a role in biomolecular electrostatics calculations. First, we have developed new and better versions of dielectric continuum solvation models ("PCMs", in the language of quantum chemistry) that circumvent long-standing problems with discontinuities in the energy as the atoms are moved. For classical biomolecular calculations in implicit solvent, these methods are formally equivalent to solution of Poisson's equation but potentially much more efficient, as they require only 2-dimensional discretization of the cavity surface rather than 3-dimensional discretization of all space. Second, I will describe a relatively efficient quantum chemistry algorithm for applying symmetry-adapted perturbation theory to many-body systems. This allows for accurate interaction energy calculations (and their decomposition into physically-meaningful components) for systems composed of multiple fragments, such as the interaction between a ligand and the nearby amino acid residues of the protein to which it is bound. |

10:30 AM 11:00 AM | Break |

11:00 AM 11:45 AM | Pengyu Ren - Improving Short-range Electrostatic Model for Molecular Interaction Ab initio energy decomposition schemes such as symmetry adapted perturbation theory (SAPT) provide physically meaningful decomposition of intermolecular interaction energy into the electrostatic, polarization, dispersion and repulsion-exchange components. By systematically investigating a large number of molecular clusters using SAPT, we have developed a general and transferable empirical model to capture the short range electrostatic penetration effect. This improvement significantly enhances the accuracy in modeling electrostatic interaction energy from using atomic point multipoles alone. We expect that incorporation of such penetration correction will lead to more balanced and transferable classical potential energy functions for describing molecular binding and assembly in general. |

11:45 AM 12:30 PM | Irina Moreira - Structural/energetic analysis of protein-based interactions: highlighting the electrostatics contribution No abstract has been provided. |

12:30 PM 02:00 PM | Lunch Break |

02:00 PM 02:45 PM | Marharyta Petukh - BION webserver: electrostatics based prediction of surface bound ions Ions play significant role in all living cells. They are involved in multiple biological processes by maintaining the unique fold of macromolecules; participating in their enzymatic activity; and screening electrostatic interactions. While experimental methods are not always able to assign the exact location of ions, computational methods are in demand. Although the majority of computational methods are successful in predicting the position of ions buried inside macromolecules, they are less effective in deciphering positions of surface bound ions. The new BION algorithm (compbio.clemson.edu/bion_server_pH/) predicts the location of ions of the surface of proteins based on electrostatic and geometrical properties of both ions and proteins. The advanced clustering procedure in combination with pairing rules improves both the efficiency and the accuracy of the method. The webserver allows specifying the pH and the salt concentration in predicting ions positions. The example of BION application is demonstrated in the study of the origin of the Chronic Berillium Disease and functionality of TAR/TSR bacterial chemoreceptors. |

02:45 PM 03:00 PM | Break |

03:00 PM 03:45 PM | Lin Li - Electrostatic interactions play important roles in kinesin proceeding on microtubule One of the most important roles of Kinesins is transporting cargo and organelles along microtubules. N-kinesins proceeding toward the plus-end of microtubule while C-kinesin proceeding toward the minus end. Many experimental researches and few computational efforts have been performed to investigate the mechanism of kinesins’ proceeding. However, many details of the mechanism for the kinesins’ proceeding are still unknown. One of the reason is the size of the kinesin-microtubule system is too large for simulations. A Monte Carlo simulation approach with discrete conformational sampling algorithm is developed to reveal the role of electrostatic interactions in kinesins’ proceeding on microtubule. We find that the electrostatic profile on microtubule forms potential valleys around the microtubule, which keeps kinesin walking along the longitudinal direction of microtubule rather than lateral direction. The simulated pathways on N-kinesin, C-kinesin and nanoparticle show that the electrostatic interactions guide the kinesins walking toward their directions. |

03:45 PM 04:30 PM | Informal discussions/daily wrap-up |

04:30 PM | Shuttle pick-up from MBI |

06:30 PM 07:00 PM | Cash bar |

07:00 PM 07:00 PM | Banquet in the Fusion Room @ Crowne Plaza Hotel |

Friday, October 16, 2015 | |
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Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:45 AM | Ridgway Scott - Dipolar materials Dipoles are ubiquitous in nature. Many materials are made of dipolar molecules, such as water. Thus it is of interest to know how large collections of dipoles can interact on a macro scale. One measure of this is called the Madelung constant. Materials whose dipoles coordinate on a global scale are called ferro-electric, by analogy with ferro-magnets. Ferro-electric materials can store a permanent charge. We describe how it is possible for water ice to become ferro-electric, and we discuss how to interpret Madelung constants in cases where the corresponding sum of dipoles appears divergent. |

09:45 AM 10:30 AM | Patrice Koehl - Biomolecular electrostatics beyond Poisson-Boltzmann In this talk I will describe a new way to calculate the electrostatic properties of macromolecules that goes beyond the classical Poisson-Boltzmann treatment. The solvent region is no longer modeled as a homogeneous dielectric media but rather as an assembly of self-orienting interacting dipoles of variable density. The method effectively unifies both the Poisson-centric view and the Langevin Dipole model. The model results in a variable dielectric constant in the solvent region and also in a variable solvent density that depends on the nature of the closest exposed solute atoms. I will discuss the limits of this new model, as well as the solutions we are developing to extend its field of applications. |

10:30 AM 11:00 AM | Break |

11:00 AM 11:45 AM | Donald Jacobs - Free Energy Driven Geometrical Simulation of Protein Dynamics Proteins are macromolecules consisting of myriad intramolecular interactions together with interactions with solvent that determine their conformational ensemble, stability and dynamics. Global constraints such as temperature and solvent composition play an essential role in defining equilibrium properties. Similarly, covalent bonding and other intramolecular interactions such as hydrogen bonds impose local mechanical constraints. Application of graph-rigidity has played an important role in predicting protein flexibility, exploring conformational dynamics through geometrical simulation (GS) and predicting thermodynamic stability via a Distance Constraint Model (DCM) that accounts for non-additivity in conformational entropy. A DCM/GS hybrid method is presented that rapidly explores conformational dynamics guided by changes in free energy by successively solving a free energy functional. A critical part of the free energy functional is modeling the solvation contribution to balance accuracy and speed so as to enable rapid exploration of conformational space that is scalable to a collection of proteins in a multi-component solvent to investigate protein-protein interactions in specific formulations and the cellular environment. Among the many implicit solvation models available in the literature, two approaches are being pursued currently which will be used to generate discussions among the experts. |

11:45 AM 12:00 PM | Informal discussions/workshop wrap-up |

12:00 PM | Shuttle pick-up from MBI (One to airport and one back to hotel) |

Name | Affiliation | |
---|---|---|

Alexov, Emil | ealexov@clemson.edu | Computational Biophysics and Bioinformatics, Clemson University |

Baker, Nathan | nathan.baker@pnl.gov | Computational and Statistical Analytics Division, Pacific Northwest National Laboratory |

Barba, Lorena | labarba@bu.edu | Mechanical and Aerospace Engineering, George Washington University |

Brooks, Charles | brookscl@umich.edu | Biophysics Program, University of Michigan |

Chang, Chia-en | chiaenc@ucr.edu | Chemistry, University of California, Riverside |

Chen, Zhan | zchen@georgiasouthern.edu | Mathematics, Michigan State University |

Chen, Jiahui | jiahuic@smu.edu | mathematics, Southern Methodist University |

Chen, Duan | dchen10@uncc.edu | Department of Mathematics, University of North Carolina, Charlotte |

Cisneros, Gerardo Andres | andres@chem.wayne.edu | Chemistry, Wayne State University |

Clementi, Natalia | ncclementi@gwu.edu | Mechanical and Aerospace Engineering, The George Washington University |

Eisenberg, Robert | beisenbe@rush.edu | Molecular Biophysics and Physiology, Rush University Medical Center |

Fenley, Marcia | mfenley@fsu.edu | IMB, FSU |

Geng, Weihua | wgeng@mail.smu.edu | Mathematics, University of Michigan |

Hammes-Schiffer, Sharon | shs3@illinois.edu | Department of Chemistry, University of Illinois at Urbana-Champaign |

Hazra, Tania | thazra@crimson.ua.edu | Mathematics, University of Alabama |

Head-Gordon, Teresa | thg@berkeley.edu | Chemistry, University of California, Berkeley |

Herbert, John | herbert@chemistry.ohio-state.edu | Chemistry, The Ohio State University |

Hohn, Maryann | maryann.hohn@uconn.edu | Mathematics, University of Connecticut |

Im, Wonpil | wonpil@ku.edu | Molecular Biosciences and Center for Computational Biology, The University of Kansas |

Jacobs, Donald | djacobs1@uncc.edu | Physics and Optical Science, University of North Carolina, Charlotte |

Koehl, Patrice | koehl@cs.ucdavis.edu | Computer Science, University of California, Davis |

Krasny, Robert | krasny@umich.edu | Department of Mathematics, University of Michigan |

Li, Bo | bli@math.ucsd.edu | Department of Mathematics, University of California, San Diego |

Li, Lin | lli5@clemson.edu | Department of Physics, Clemson University |

Luchko, Tyler | tyler.luchko@csun.edu | Physics and Astronomy, California State University, Northridge |

Luo, Ray | ray.luo@uci.edu | Molecular Biology and Biochemistry, University of California, Irvine |

Matyushov, Dmitry | dmitrym@asu.edu | Physics, Arizona State University |

Mitchell, Julie | jcmitchell@wisc.edu | Mathematics and Biochemistry, University of Wisconsin |

Moreira, Irina | irina.moreira@fc.up.pt | Medicine, Center for Neuroscience and Cell Biology |

Mori, Yoichiro | ymori@math.umn.edu | School of Mathematics, University of Minnesota |

Onufriev, Alexey | alexey@cs.vt.edu | Computer Science and Physics, Virginia Tech |

Pettitt, B. Montgomery | pettitt@uh.edu | Sealy Center for Structural Biology, University of Texas Medical Branch |

Petukh, Marharyta | mpetukh@clemson.edu | Physics and Astronomy, Clemson University |

Ren, Pengyu | pren@mail.utexas.edu | Biomedical Engineering, The University of Texas at Austin |

Scott, Ridgway | ridg@uchicago.edu | Computer Science and Mathematics, University of Chicago |

Song, Xueyu | xsong@iastate.edu | Chemistry, Iowa State University |

Sun, Weitao | sunwt@mail.tsinghua.edu.cn | Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University |

Sushko, Maria | Maria.Sushko@pnnl.gov | Physical Sciences Directorate, Battelle Pacific Northwest Laboratories |

Wang, Zhen-Gang | zgw@cheme.caltech.edu | Division of Chemistry and Chemical Engineering, California Institute of Technology |

Wang, Bao | wangbao@msu.edu | Department of Mathematics, Michigan State University |

Wei, Guowei | wei@math.msu.edu | Department of Mathematics, Michigan State University |

White, Stephen | stephen.white@uci.edu | Dept. of Physiology & Biophysics, University of California, Irvine |

Wilson, Leighton | lwwilson@umich.edu | |

Wong, Chung | wongch@msx.umsl.edu | Chemistry and Biochemistry, University of Missouri-St. Louis |

Xie, Dexuan | dxie@uwm.edu | Department of Mathematical Sciences, University of Wisconsin |

Yan, Jue | jyan@iastate.edu | Mathematics, Iowa State University |

Zhang, Yingkai | yingkai.zhang@nyu.edu | Chemistry, New York University |

Zhang, John | john.zhang@nyu.edu | College of Arts of Science, New York University Shanghai |

Zhao, Zhixiong | zhaozx@msu.edu | Maths, Michigan State University |

Zhong, Dongping | zhong.28@asc.ohio-state.edu | Physics, Chemistry, & Biochemistry, The Ohio State University |

Zhou, Huan-Xiang | hzhou4@fsu.edu | Institute of Molecular Biophysics, Florida State University |

Electrolyte and cell volume regulation is essential in physiological systems. After a brief introduction to cell volume control and electrophysiology, I will discuss the classical pump-leak model of electrolyte and cell volume control. I will then generalize this to a PDE model that allows for the modeling of tissue-level electrodiffusive, convective and osmotic phenomena. This model will then be applied to the study of cortical spreading depression, a wave of ionic homeostasis breakdown, that is the basis for migraine aura and other brain pathologies.

Biomolecules exhibit conformational fluctuations near equilibrium states, inducing uncertainty in various biological properties in a dynamic way. We have developed a general method to quantify the uncertainty of target properties induced by conformational fluctuations. Using a generalized polynomial chaos (gPC) expansion, we construct a surrogate model of the target property with respect to varying conformational states. We also propose a method to increase the sparsity of the gPC expansion by defining a set of conformational "active space" random variables. With the increased sparsity, we employ the compressive sensing method to accurately construct the surrogate model. We demonstrate the performance of the surrogate model by evaluating fluctuation-induced uncertainty in solvent-accessible surface area for the bovine trypsin inhibitor protein system and show that the new approach offers more accurate statistical information than standard Monte Carlo approaches. Further more, the constructed surrogate model also enables us to directly evaluate the target property under various conformational states, yielding a more accurate response surface than standard sparse grid collocation methods. In particular, the new method provides higher accuracy in high-dimensional systems, such as biomolecules, where sparse grid performance is limited by the accuracy of the computed quantity of interest. Our new framework is generalizable and can be used to investigate the uncertainty of a wide variety of target properties in biomolecular systems.

No abstract has been provided.

The understanding of solvation is an essential prerequisite for the quantitative description and analysis of many sophisticated chemical, biological and biomolecular processes.. Implicit solvent models, particularly those based on the Poisson-Boltzmann (PB) equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces and complex solutions of nonlinear equations post some severe limitations on their applications.

We have introduced differential geometry (DG) based multiscale solvation models, which allow the solvent-solute interface, electrostatic potential, and even electron densities to be determined by the variation of a total free energy functional. In addition, our models is able to significantly reduce the number of free parameters and to avoid complicated interface problems raised by sharp solvent-solute interface. Finally, our DG based models have shown promising power in blind prediction of solvation as well as other applications. This is primarily joint work with Prof. Guowei Wei and Prof. Nathan Baker.

Description of inhomogeneous dielectric properties of a solvent in the vicinity of ions has been attracting research interests in mathematical modeling for many years. From many experimental results, it has been concluded that the dielectric response of a solvent linearly depends on the ionic strength within a certain range. Based on this assumption, a new implicit solvent model is proposed in the form of total free energy functional and a quasi-linear Poisson-Boltzmann equation (QPBE) is derived. Classical Newton’s iteration can be used to solve the QPBE numerically but the corresponding Jacobian matrix is complicated due to the quasi-linear term. In the current work, a systematic formulation of the Jacobian matrix is derived. As an alternative option, an algorithm mixing the Newton’s iteration and the fixed point method is proposed to avoid the complicated Jacobian matrix, and it is a more general algorithm for equation with discontinuous coefficients. Computational efficiency and accuracy for these two methods are investigated based on a set of equation parameters. At last, the QPBE with singular charge source and piece-wisely defined dielectric functions has been applied to analyze electrostatics of macro biomolecules in a complicated solvent. A set of computational algorithms such as interface method, singular charge removal technique and the Newton- fixed-point iteration are employed to solve the QPBE. Biological applications of the proposed model and algorithms are provided, including calculation of electrostatic solvation free energy of proteins, investigation of physical properties of channel pore of an ion channel, and electrostatics analysis for the segment of a DNA strand.

The Poisson-Boltzmann model is an extended model of the classical Gauss's law involving additionally multiple dielectrics (thus interface problem), solvent effects (thus continuum model) and dissolved electrolytes (thus nonlinearity). In this talk, I will introduce our recent progress in developing a numerical Poisson-Boltzmann solver with tree-code algorithms (for efficiency) and boundary integral formulation (for accuracy). Following that, I will briefly touch the attractive performance computing feature of this solver including parallelization and GPUs. I will conclude the talk with a report for the potential and established application of the Poisson-Botlzmann model/solver for computing quantities with biological significance such as electrostatic solvation energy, electrostatic forces, pKa values, etc.

Electrostatic interactions play an important role in enzyme catalysis. These effects are modulated by the conformational changes that occur over the catalytic cycle. To elucidate the catalytic roles of these effects, thiocyanate probes were introduced at site-specific positions in the enzymes ketosteroid isomerase (KSI) and dihydrofolate reductase (DHFR). In KSI, the impact of electrostatics on ligand binding was explored. In DHFR, the impact of electrostatics on the catalytic cycle involving five different complexes was investigated. The shifts in the vibrational stretching frequencies of the nitrile probes report on the electrostatics of the microenvironments surrounding the probes. Mixed quantum mechanical/molecular mechanical molecular dynamics simulations reproduced the experimental vibrational frequency shifts and provided atomic-level insight into the roles that key residues play in determining the electrostatics of the microenvironments. The electrostatic contributions were decomposed into the major components from individual residues, ligands, and water molecules. For DHFR, calculation of the electric field along the hydride donor-acceptor axis, along with decomposition of this field into specific contributions, indicates that the cofactor and substrate, as well as the enzyme, impose a substantial electric field that facilitates hydride transfer. Overall, experimental and theoretical data provide evidence for significant electrostatic changes in the active site microenvironments due to conformational motions occurring over the catalytic cycles of enzymes.

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My group is primarily interested in electrostatics calculations from the quantum-mechanical or QM/MM perspective, but I will describe two projects in which our methods might play a role in biomolecular electrostatics calculations. First, we have developed new and better versions of dielectric continuum solvation models ("PCMs", in the language of quantum chemistry) that circumvent long-standing problems with discontinuities in the energy as the atoms are moved. For classical biomolecular calculations in implicit solvent, these methods are formally equivalent to solution of Poisson's equation but potentially much more efficient, as they require only 2-dimensional discretization of the cavity surface rather than 3-dimensional discretization of all space. Second, I will describe a relatively efficient quantum chemistry algorithm for applying symmetry-adapted perturbation theory to many-body systems. This allows for accurate interaction energy calculations (and their decomposition into physically-meaningful components) for systems composed of multiple fragments, such as the interaction between a ligand and the nearby amino acid residues of the protein to which it is bound.

Proteins are macromolecules consisting of myriad intramolecular interactions together with interactions with solvent that determine their conformational ensemble, stability and dynamics. Global constraints such as temperature and solvent composition play an essential role in defining equilibrium properties. Similarly, covalent bonding and other intramolecular interactions such as hydrogen bonds impose local mechanical constraints. Application of graph-rigidity has played an important role in predicting protein flexibility, exploring conformational dynamics through geometrical simulation (GS) and predicting thermodynamic stability via a Distance Constraint Model (DCM) that accounts for non-additivity in conformational entropy. A DCM/GS hybrid method is presented that rapidly explores conformational dynamics guided by changes in free energy by successively solving a free energy functional. A critical part of the free energy functional is modeling the solvation contribution to balance accuracy and speed so as to enable rapid exploration of conformational space that is scalable to a collection of proteins in a multi-component solvent to investigate protein-protein interactions in specific formulations and the cellular environment. Among the many implicit solvation models available in the literature, two approaches are being pursued currently which will be used to generate discussions among the experts.

In this talk I will describe a new way to calculate the electrostatic properties of macromolecules that goes beyond the classical Poisson-Boltzmann treatment. The solvent region is no longer modeled as a homogeneous dielectric media but rather as an assembly of self-orienting interacting dipoles of variable density. The method effectively unifies both the Poisson-centric view and the Langevin Dipole model. The model results in a variable dielectric constant in the solvent region and also in a variable solvent density that depends on the nature of the closest exposed solute atoms. I will discuss the limits of this new model, as well as the solutions we are developing to extend its field of applications.

Electrostatic effects play an important role in determining protein structure and function. Here we present a treecode-accelerated boundary integral (TABI) solver for the electrostatic potential of a solvated protein described by the linear Poisson-Boltzmann equation. In this model the solvent is a continuum dielectric material with screening due to dissolved ions and the protein is a set of charged particles. The method employs a well-conditioned boundary integral formulation for the electrostatic potential and its normal derivative on the molecular surface. The surface is triangulated by MSMS and the integral equations are discretized by centroid collocation. The linear system is solved by GMRES and the matrix-vector product is carried out by a tree code which reduces the computational cost from $O(N^2)$ to $O(Nlog N)$, where $N$ is the number of faces in the triangulated molecular surface. We compare TABI results to those obtained using the finite-difference APBS code. The TABI solver exhibits good serial and parallel performance, with relatively simple implementation, efficient memory usage, and geometric adaptability. This is joint work with Weihua Geng (Southern Methodist University).

One of the most important roles of Kinesins is transporting cargo and organelles along microtubules. N-kinesins proceeding toward the plus-end of microtubule while C-kinesin proceeding toward the minus end. Many experimental researches and few computational efforts have been performed to investigate the mechanism of kinesins’ proceeding. However, many details of the mechanism for the kinesins’ proceeding are still unknown. One of the reason is the size of the kinesin-microtubule system is too large for simulations. A Monte Carlo simulation approach with discrete conformational sampling algorithm is developed to reveal the role of electrostatic interactions in kinesins’ proceeding on microtubule. We find that the electrostatic profile on microtubule forms potential valleys around the microtubule, which keeps kinesin walking along the longitudinal direction of microtubule rather than lateral direction. The simulated pathways on N-kinesin, C-kinesin and nanoparticle show that the electrostatic interactions guide the kinesins walking toward their directions.

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Statistical thermodynamics requires having a theory of liquid structure which is accurate. Simulations are an important tool but are not a theory of the liquid state. In order to better understand general effects of the size and energy disparities between macromolecules and solvent molecules in solution, especially for macromolecular constructs self-assembled from smaller molecules, we compare theory and simulation to investigate multicomponent mixtures of fluids. We will compare a structured continuum solvation calculation on proteins with simulations and integral equations to evaluate the electrostatic free energy contribution to the solution thermodynamics. Using several peptide test cases, we compare the use of our theory with free energy simulations and traditional continuum estimates of the electrostatic solvation free energy.

Ions play significant role in all living cells. They are involved in multiple biological processes by maintaining the unique fold of macromolecules; participating in their enzymatic activity; and screening electrostatic interactions. While experimental methods are not always able to assign the exact location of ions, computational methods are in demand. Although the majority of computational methods are successful in predicting the position of ions buried inside macromolecules, they are less effective in deciphering positions of surface bound ions. The new BION algorithm (compbio.clemson.edu/bion_server_pH/) predicts the location of ions of the surface of proteins based on electrostatic and geometrical properties of both ions and proteins. The advanced clustering procedure in combination with pairing rules improves both the efficiency and the accuracy of the method. The webserver allows specifying the pH and the salt concentration in predicting ions positions. The example of BION application is demonstrated in the study of the origin of the Chronic Berillium Disease and functionality of TAR/TSR bacterial chemoreceptors.

Ab initio energy decomposition schemes such as symmetry adapted perturbation theory (SAPT) provide physically meaningful decomposition of intermolecular interaction energy into the electrostatic, polarization, dispersion and repulsion-exchange components. By systematically investigating a large number of molecular clusters using SAPT, we have developed a general and transferable empirical model to capture the short range electrostatic penetration effect. This improvement significantly enhances the accuracy in modeling electrostatic interaction energy from using atomic point multipoles alone. We expect that incorporation of such penetration correction will lead to more balanced and transferable classical potential energy functions for describing molecular binding and assembly in general.

Dipoles are ubiquitous in nature. Many materials are made of dipolar molecules, such as water. Thus it is of interest to know how large collections of dipoles can interact on a macro scale. One measure of this is called the Madelung constant. Materials whose dipoles coordinate on a global scale are called ferro-electric, by analogy with ferro-magnets. Ferro-electric materials can store a permanent charge. We describe how it is possible for water ice to become ferro-electric, and we discuss how to interpret Madelung constants in cases where the corresponding sum of dipoles appears divergent.

In this presentation a molecular Debye-Huckel theory for ionic fluids is developed. Starting from the macroscopic Maxwell equations for bulk systems, the dispersion relation leads to a generalized Debye-Huckel theory which is related to the dressed ion theory in the static case.Due to the multi-pole structure of the dielectric function of ionic fluids, the electric potential around a single solute has a multi-Yukawa form. Given the dielectric function, the multi-Yukawa potential can be determined from our molecular Debye-Huckel theory, hence, the electrostatic contributions to thermodynamic properties of ionic fluids can be obtained. Applications to solutes with arbitrary shapes in model electrolyte solutions demonstrated the accuracy of our approach. In combination with cavity formation energy a variational approach can be used to define the boundary between a solute and its continuum solvent. Thus, our approach provides a simple and efficient path to go beyond the traditional Poisson-Boltzmann model in biophysics.

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Ions are essential in physical chemistry, colloidal science, electrochemistry, biology and many other areas of science and engineering. While their role is commonly described in terms of screening and translational entropy, many phenomena, ranging from some classical experimental observations made many decades ago to some new systems of current interest, cannot be explained, even qualitatively, by these concepts. A key effect that is often ignored or inadequately treated in the main literature on electrolytes and polyelectrolytes is the self-energy of the ions. In this talk, I will discuss several self-energy effects in macromolecular and interfacial systems. First, we show that the preferential solvation energy of the ions provides a significant driving force for phase separation. This concept is used to develop a theory to explain the dramatic shift in the order-disorder transition temperature in PEO-PS diblock copolymers upon the addition of salt. Second, we show that the dielectric contrast between the polymer backbone and the solvent significantly affects the conformation and charge condensation in dilute polyelectrolyte solutions. Third, we show that the image force has qualitative effects on the double layer structure and forces, such as like charge attraction and charge inversion. Finally we present a simple model for understanding the specific ion effects in the interfacial activity for air/water and oil/water interfaces.

SecY constitutes the core of the highly conserved SecYEG translocon complex that governs the translocation or integration of proteins across or into cytoplasmic membranes. Besides its role of guiding nascent membrane protein chains into the lipid bilayer, it also plays an important role in determining transmembrane topology via the so-called positive-inside rule. Site-directed mutations of translocons are known to modify the topology of nascent α-helical segments [1]. We performed molecular dynamics simulations of SecYE from *Pyrococcus furiosus* [2] embedded in a POPC bilayer. SecY in the *P. furiosus* structure is in a partially open ‘primed’ state. It conveniently remained open over the course of a 450 nsec simulation due to the presence of lipids wedged between helices TM2B and TM7 (the lateral gate), thus allowing close examination of the electrostatics within the translocon. Within the channel, water dipoles exhibit a preferred orientation, which affects the electrostatic (ES) potential. Time-averaged ES maps reveal a largely positive potential relative to the bulk aqueous phase within the channel except for a strong negative peak at the N-terminus of TM2b. This has implications for the entry of signal sequences into the translocon channel. Research supported by NIH grants RO1 GM74637 and PO1 GM86685.

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Water and ions are an integral part of biological systems. In this talk, I will use several medically important enzymes to illustrate versatile roles of water and ions in enzyme function. Our computational approaches center on Born-Oppenheimer ab initio QM/MM molecular dynamics simulation (aiQM/MM-MD) with umbrella sampling. Under the guidance of our elucidated insights, we have discovered a novel time-dependent HDAC2-selective inhibitor. In addition, I will briefly describe AlphaSpace – fragment centric topographical mapping to target protein-protein interaction (PPI) interfaces. The resulting high-resolution map of underutilized, targetable pocket space can be used to guide the rational design and optimization of synthetic PPI modulators.

Water is a universal lubricant in life and plays a critical role in biomolecular structure, dynamics and function. Here, we report the systematic characterization of water motions around protein surfaces and protein-DNA interfaces in real time. Hydration water is found to strongly slave protein fluctuations. A series of correlations between the dynamics and protein properties was observed. These results revealed the wide range of heterogeneous water dynamics on the picosecond time scales but are well correlated with the protein structures, dynamics and even function. Such water dynamics could be general at any other nanointerfaces.

Amino acids with ionizable side chains, e.g., Asp, Glu, His, Lys, and Arg, impart important properties to proteins. Modulation of the charges on these amino acids, e.g., by pH, may result in significant changes such as protein unfolding. Charged residues can play critical roles in regulating protein assembly, as illustrated by the Glu6 ? Val mutation in the *β* chains of sickle-cell hemoglobin. Nucleic acids and cell membranes have surface charges, thus proteins that bind to these targets may well utilize electrostatic interactions. Charges also have profound effects in processes such as conduction of ions through transmembrane channels, binding of metals (e.g., Ca2+ and Zn2+) or charged ligands to specific sites in proteins, and phosphorylation-dephosphorylation of Ser, Thr, and Tyr. This talk aims to present a unifying theme among the various effects of protein charges and electrostatic interactions. Basic ideas of electrostatic interactions in proteins will be introduced through simple models. These ideas will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, and assembly, and related biological functions.