## Workshop 4: Mathematical Challenges in Drug and Protein Design

### Organizers

Eric Cances
CERMICS, Ecole des Ponts and INRIA
Michael Gilson
Skaggs School of Pharmacy and Pharmaceutical Sciences, UC San Diego
Platform Technology and Science, GlaxoSmithKline Pharmaceuticals
Ridgway Scott
Computer Science and Mathematics, University of Chicago

Rational drug design and protein design have a profound impact to human health care. A fundamental goal is to predict whether a given molecule will bind to a biomolecule, such as a protein, so as to activate or inhibit its function, which in turn results in a therapeutic benefit to the patient. Typical drugs are small organic molecules, but biopolymer-based and protein-based drugs are becoming increasingly common. Computer-aided drug design and the design of protein containers for drug delivery have established a proven record of success, not only because of improved understanding of the basic science --- the molecular mechanism of drug and protein interactions, but also because of advances in mathematical models, geometric representations, computational algorithms, optimization procedure, and the availability of massive parallel and GPU computers. Indeed, mathematics plays an essential role in rational drug design and the development of new drug delivery systems, from consensus scoring, geometric analysis, cluster analysis, to global optimization. Moreover, mathematical approaches, such geometric analysis for high throughput drug screening, persistent homology for protein-drug binding detection, reduced manifold representation for discriminating false protein-protein and protein-drug interfaces, and machine learning techniques for protein-drug binding site analysis, have great potentials for drug design and drug discovery. Despite significant accomplishments, drug discovery rates seem to have reached a plateau, due to metabolism instability, side effects, and limitations in the understanding of fundamental drug-target interactions. An ideal drug should be acceptable to the human metabolic system, not to affect any other important off-target" molecules or antitargets that may be similar to the target molecule, and bind to a target sufficiently strongly. In fact, the molecular mechanism of drug design has its roots in another closely related field, the protein design, which tests the fundamental principles of protein-protein and protein-ligand interactions. Both protein-protein and protein-drug binding are subject to a large number of effects, from stereospecificity, polarization, hydrogen bond, electrostatic effect and solvation to allosteric modulation, to mention only a few. The application of molecular mechanism towards entire proteomes, enzyme pathways/families (e.g. catecholamine biosynthesis, botulinum neurotoxins), and high value drug targets, including G-protein coupled receptors (GPCRs) are now starting to emerge. Nano-bio technologies for drug transport and drug delivery have been a hot area of research. To design efficient drugs and functional protein, it takes collaborative efforts from biologists, biophysicists, biochemists, computer scientists and mathematicians to come up with better homology modeling, geometric models, molecular docking algorithms, molecular dynamics, quantum calculation, de novo design and statistical models. This workshop will bring together experts from both academia and industry that have an open mind to cross their line of defense to share their problems. We will create a forum for researchers to jointly find solutions and explore applications to the design of new drugs and delivery systems. This workshop will be of particular benefit to junior mathematicians who are looking for ways of applying their mathematical skills and tools also outside of academia and want to use their skills to make an impact in society via innovations benefiting the health sector. The interaction between mathematicians and pharmaceutical industry will be encouraged in this workshop.

### Accepted Speakers

Cameron Abrams
Chemical and Biological Engineering, Drexel University
Emil Alexov
Computational Biophysics and Bioinformatics, Clemson University
Chris Chipot
Theoretical and Computational Biophysics Group, University of Illinois at Urbana-Champaign
Valeriu Damian-Iordache
Ron Dror
Computer Science, Stanford University
Ron Elber
Chemistry/ICES, University of Texas
Tom Kurtzman
Ph.D. Program in Chemistry, The Graduate Center of the City University of New York
Huan Lei
Tony Lelievre
CERMICS, ' Ecole Nationale des Ponts-et-Chauss'ees (ENPC)
Bo Li
Department of Mathematics, University of California, San Diego
Alex MacKerell
Pharmaceutical Sciences, University of Maryland
David Mobley
Pharmaceutical Sciences & Chemistry, University of California, Irvine
Ruth Nussinov
LEIDOS BIOMEDICAL, National Cancer Institute
Christof Schütte
Mathematics and Computer Science, Freie Universit""at Berlin
Jana Shen
Pharmaceutical Sciences, University of Maryland at Baltimore
Sandor Vajda
Biomedical Engineering, Boston University
Dexuan Xie
Department of Mathematical Sciences, University of Wisconsin
Wei Yang
Chemistry and Biochemistry, Florida State University
Monday, December 7, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM

Welcome, overview, introductions: Marty Golubitsky

09:30 AM
10:00 AM

Introduction by Workshop Organizers

10:00 AM
10:45 AM
Ruth Nussinov - KRAS/Calmodulin/PI3Ka: A Promising New Adenocarcinoma-Specific Drug Target?

Decades of efforts have yet to yield a safe and effective drug to target lung, pancreatic and colorectal cancers driven by the highly oncogenic K-Ras4B. K-Ras4B’ pocketless surface, cancer tissue/cell heterogeneity, tolerated lipid post-translational modification exchange, as well as drug-elicited toxicity present a daunting challenge. We propose a new adenocarcinoma-specific drug concept (1). Calmodulin binds to K-Ras4B but not to other Ras isoforms. Physiologically, in calcium- and thus calmodulin-rich environments such as ductal tissues, calmodulin (CaM) can sequester K-Ras4B from the membrane; in cancer, CaM/Ca2+ can replace the missing receptor tyrosine kinase (RTK) signal, acting to fully activate PI3Kα. An oncogenic GTP-bound K-Ras/CaM/PI3Kα complex is supported by available experimental and clinical data; therefore, targeting it addresses an unmet therapeutic need in KRas-driven cancer. High resolution electron microscopy (EM) or crystal structure of the tripartite complex would allow orthosteric or allosteric drug discovery to disrupt the CaM/PI3Kα interface thus Akt/mTOR signaling.

10:45 AM
11:00 AM

Break

11:00 AM
11:45 AM
Valeriu Damian-Iordache
11:45 AM
02:00 PM

Lunch Break

02:00 PM
02:45 PM
David Mobley
02:45 PM
03:00 PM

Break

03:00 PM
03:45 PM
Bo Li - Variational Implicit Solvation with Application to Identifying Ligand-Protein Binding Sites

The variational implicit-solvent model (VISM) is an advanced solvation theory and computational approach. It is based on the minimization of a solvation free-energy functional of all possible solute-solvent interfaces, i.e., dielectric boundaries. The free energy includes the volume contribution, interfacial energy with a curvature-corrected surface tension, solute-solvent van der Waals interaction energy, and electrostatic energy. For years, we have developed a robust level-set method to numerically minimize such a functional for arbitrarily shaped biological molecules. Our intensive computational results have demonstrated that this efficient approach can capture the wet and dry states of hydration, and subtle charge effects; and can provide quantitatively good estimates of solvation free energies. In this talk, we review what we have achieved with the level-set VISM, describe some initial work on modeling the solvent dynamics with the VISM dielectric boundary force, and report our recent level-set VISM application to identifying ligand-protein binding pockets that are crucial in rational drug design.

04:00 PM
06:00 PM

Reception and poster session in MBI lounge

06:00 PM

Shuttle pick-up from MBI

Tuesday, December 8, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:45 AM
Tony Lelievre - Adaptive Multilevel Splitting algorithms for rare event simulations

I will present a numerical method that we are currently developping in the NAMD software and which aim at simulation reactive trajectories. Numerical and theoretical results on this technique will be described.

09:45 AM
10:00 AM

Break

10:00 AM
10:45 AM
Alex MacKerell - Grand Canonical Solute Sampling in Combination with the Site Identification by Ligand Competitive Saturation (SILCS) Ligand Design Methodology

Computational functional group affinity mapping of proteins is of utility for ligand design in the context of database screening, fragment-based design and lead compound optimization. The SILCS methodology allows for the generation of functional group affinity maps (FragMaps) of proteins that take into account contributions from protein desolvation, functional group desolvation, protein flexibility as well as direct interactions of the functional groups with the protein. Boltzmann transformation of the maps yields Grid Free Energy (GFE) FragMaps that may be used both qualitatively and quantitatively to direct ligand design. To allow for the application of the SILCS approach to deep and occluded pockets in proteins an oscillating μex Grand Canonical Monte Carlo (GCMC) approach was developed that allows for insertions of small solute molecules in the presence of an explicit aqueous environment. Combining the GCMC method with MD simulations for the inclusion of protein flexibility allows for the determination of GFE Fragmaps in occluded pockets. An overview of the GCMC/MD SILCS methodology along with application of the method to T4-lysozyme pocket mutants, nuclear receptors and GPCRs will be presented.

10:45 AM
11:00 AM

Break

11:00 AM
11:45 AM
Wei Yang - Efficient Sampling of Long-Timescale Structural Responses to Enable Quantitative Protein-Ligand Binding Calculations

Proteins constantly fluctuate in aqueous solution. Any perturbation, either geometrical or chemical, may take very long time for a protein system to respond and relax. Indeed, such timescale issue has been a major bottleneck to the dream of quantitative protein-ligand binding predictions. To tackle this problem, we have developed the orthogonal space sampling theory and algorithms, which can uniquely accelerate response motions specific to perturbation fluctuations. In this talk, the theory, the methods, and the applications on protein-ligand binding calculations will be presented.

11:45 AM
02:00 PM

Lunch Break

02:00 PM
02:45 PM
Jana Shen - pH-dependent BACE1 activity and inhibition

BACE1, a major therapeutic target for treatment of Alzheimer's disease, functions within a narrow pH range. Despite tremendous effort and progress in the development of BACE1 inhibitors, details of the underlying pH-dependent regulatory mechanism remain unclear. In this talk I will discuss our recent work in exploring the pH-dependent conformational mechanism that regulates BACE1 activity and substrate/inhibitor binding using continuous constant-pH molecular dynamics. The new insights greatly extend the knowledge of BACE1 and have implications for further optimization of inhibitors and understanding potential side effects of targeting BACE1.

02:45 PM
03:00 PM

Break

03:00 PM
03:45 PM
Sandor Vajda - Binding hot spots, druggability, and ligand deconstruction

Binding energy hot spots, smaller regions of binding sites that contribute a disproportionate amount to the free energy of binding any ligand, can be determined computationally from ligand-free structures of protein targets. The hot spot structure of a protein target provides very useful information on binding properties. The first application that will be discussed is predicting druggability, i.e., the ability of a site of binding druglike ligands with sufficient affinity. We applied the method to a large set of proteins. Results showed that, because the method is based on the biophysics of binding rather than on empirical parameterization, meaningful information can be gained about classes of proteins and classes of compounds beyond those resembling validated targets and conventionally druglike ligands. In particular, the method identifies targets that, while not druggable by druglike compounds, may become druggable using compound classes such as macrocycles or other large molecules beyond the rule-of-five limit. Second, we show that the hot spots provide crucial insights into the prospects for successful application of fragment-based drug discovery (FBDD), and whether a fragment hit can be advanced into a high affinity ligand. The key factor is the strength of the top ranking hot spot, and how well a given fragment complements it. We show that published data are sufficient to provide a sophisticated and quantitative understanding of how hot spot strength, number and spatial arrangement govern the potential for a surface site to bind to fragment-sized and larger ligands. This improved understanding provides important guidance for the effective application of FBDD in drug discovery.

03:45 PM
04:00 PM

Break

04:00 PM
05:30 PM

Open discussion of first two days

05:30 PM

Shuttle pick-up from MBI

Wednesday, December 9, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:45 AM
Cameron Abrams - Markovian Milestoning MD Simulations for Computing On- and Off-Rates

Prediction of binding and unbinding kinetics from all-atom molecular simulations could one day be an important component in the toolkit for structure-based drug design. Unfortunately, in contrast to binding affinity prediction, algorithms for estimating on- and off-rates in relatively complicated systems remain relatively undeveloped. Here we demonstrate one approach that has been applied to successfully compute the entry and exit rates of small gas molecules into globular proteins. The method is an application of transition-path theory and involves performing milestoning MD simulations in cells forming a Voronoi tesselation of some chosen state-discriminating collective-variable space. Particular attention is paid to handshaking the simulations with a continuous approximation of the solute flux to a protein target surface as a function of ligand diffusivity and bulk concentration. The method is applicable beyond small gas molecules and extensions involving more complicated molecules will be discussed.

09:45 AM
10:00 AM

Break

10:00 AM
10:45 AM
Chris Chipot - Challenges in rational drug discovery - From drug binding to drug bioavailability

One of the grand challenges of rationale drug design is the prediction of the affinity of potential therapeutic agents for a given protein target. This challenge is in large measure rooted in the considerable changes in configurational entropy that accompanies the binding process, which atomistic simulations cannot easily sample. Two strategies relying upon alchemical transformations, on the one hand, and geometric transformations, notably potential of mean force calculations, on the other hand, are proposed, invoking a series of geometric restraints acting on collecting variables designed to alleviate sampling limitations inherent to classical molecular dynamics simulations. I will show through the example of a protein binding a small substrate, that both strategies, however of clearly different nature, can yield nearly identical standard binding free energies within chemical accuracy. I will further show how the methodology can be seamlessly transposed to protein-protein complexes. I will also outline current strategies to estimate binding entropies from such calculations. Downstream from the prediction of binding affinities is the challenging prediction of bioavailability. To estimate the permeability of the biological membrane to a drug candidate, an approach based upon Bayesian inferences, which reconciles thermodynamics and kinetics in molecular dynamics simulations with time-dependent biases, is put forth. Performance of the method is illustrated with prototypical permeants diffusing in a homogeneous lipid bilayer.

10:45 AM
11:00 AM

Break

11:00 AM
11:45 AM
Martin Goethe - Correcting Free Energy Expressions for Thermal Motion

Minimizing a suitable free energy expression is arguably the most common approach in (ab initio) protein structure prediction. The achieved accuracy depends crucially on the quality of the free energy expression in use. Here, we present corrections to existing free energy expressions which arise from the thermal motion of the protein. We (i) devise a term accounting for the vibrational entropy of the protein, and (ii) correct existing potentials for the "thermal smoothing effect".

(i) Vibrational entropy is almost always neglected in free energy expressions as its consideration is difficult. This practice, however, may lead to incorrect output because distinct conformations of a protein can contain very different amount of vibrational entropy, as we show for the chicken villin headpiece explicitly [1]. For considering vibrational entropy, we suggest a knowledge based approach where typical fluctuation and correlation patterns are extracted from known proteins and then applied to new targets.

(ii) At ambient conditions, time-averaged potentials of proteins are considerably smoother when expressed in terms of the average atom coordinates than the Hamiltonian. This effect caused by thermal motion is referred to as the thermal smoothing effect. The strength of the effect varies strongly between atoms. This allows to increase the accuracy of free energy expressions significantly by subdividing atom species regarding their typical fluctuation behavior inside proteins and assigning time-averaged potentials for the new sub-species independently [2].

[1] M. Goethe, I. Fita, and J.M. Rubi, Vibrational Entropy of a Protein: Large Differences between Distinct Conformations, J. Chem. Theory Comput. 11, 351 (2015).
[2] M. Goethe, I. Fita, and J.M. Rubi, Thermal Motion in Proteins: Large Effects on the Time-Averaged Interaction Energies, in revision.

11:45 AM
02:00 PM

Lunch Break

02:00 PM
02:45 PM
Tom Kurtzman - Exploiting Active-site Solvation Structure and Thermodynamics for Drug Discovery and Design

Despite recent advances in methodologies that better characterize local water structure and thermodynamics, the simply- stated question of whether it would be beneficial or detrimental, in a free-energetic sense, to displace water from a region of a protein with a suitably complementary ligand continues to be a conundrum. Solvation thermodynamic mapping techniques have provided valuable insight into the role of displacing water in molecular recognition however solvation thermodynamics alone is not predictive of displaceability and tightly binding ligands regularly displace water from both regions that are characterized as having favorable solvation and regions that are characterized as having unfavorable solvation. Part of the difficulty of assessing the thermodynamics of water displacement is due to the large number of often counteracting contributions and the consequent lack of a simplifying conceptual framework. We will discuss the key insights which have been gained from solvation thermodynamic mapping and how we are incorporating them into drug discovery and design methodologies. We will also discuss remaining issues on predicting favorability of water displacement and suggest how they might be tackled.

02:45 PM
03:00 PM

Break

03:00 PM
03:45 PM
Christof Schütte
03:45 PM
04:00 PM

Break

04:00 PM
05:30 PM

Open discussion

05:30 PM

Shuttle pick-up from MBI

Thursday, December 10, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:45 AM
Dexuan Xie - New Advances in Local and Nonlocal Electrostatic Modeling and Calculation for Ionic Solvated Biomolecules

Calculation of electrostatics for a biomolecule (or a complex of a protein with a drug molecule) in an ionic solvent is a fundamental task in the fields of structural biology, computational biochemistry, biophysics, and mathematical biology. The Poisson-Boltzmann equation (PBE) is one commonly used dielectric model for predicting electrostatics of ionic solvated biomolecules. It has played important roles in rational drug design and protein design as well as other bioengineering applications. However, it is known not to work properly near a highly charged biomolecular surface, since it does not reflect any polarization correlation among water molecules and ionic size effects.

To improve the quality of PBE in the calculation of electrostatic solvation and binding free energies, we made many progresses recently on the study of nonlocal dielectric models, and developed several fast nonlocal model solvers. Meanwhile, we developed new numerical algorithms for solving PBE and one size modified PBE by using finite element, finite difference, solution decomposition, domain decomposition, and multigrid methods.

In this talk, I will first review our nonlocal dielectric theory. I then will present a new nonlocal PBE and its finite element solver. I will also describe our new numerical algorithms for solving PBE and one size modified PBE. A collection of these new solvers has led to a new software tool, called SDPBS (Solution Decomposition Poisson-Boltzmann Solvers), which is available online for free through our web server. Finally, application examples for chemical molecules, proteins, protein-drug, and peptide-RNA will be given to demonstrate the high performance and numerical stability of SDPBE in the calculation of salvation and binding free energies. This project is a joined work with Prof. L. Ridgway Scott at the University of Chicago under the support by NSF grants (DMS-0921004, DMS-1226259, and DMS-1226019).

09:45 AM
10:00 AM

Break

10:00 AM
10:45 AM
Tamar Schlick
10:45 AM
11:00 AM

Break

11:00 AM
11:45 AM
Ron Dror
11:45 AM
02:00 PM

Lunch Break

02:00 PM
02:45 PM
Ron Elber - The design of protein switches

We focus on special protein pairs that can switch their fold following a single point mutation. These proteins are of special interest since they offer a way to dramatically affect protein function. They also offer pathways for the evolution of protein structures. Special algorithms are required to explore the exponentially large space of protein sequences (in the sequence length) that may lead to a switch. I will describe the algorithms, detailed examination of a protein switch that was investigated experimentally, and the construction of a network of protein switches. Join work with Leonid Meyerguz, Jon Kleinberg, BaoQiang Cao, and Serena Chen.

02:45 PM
03:00 PM

Break

03:00 PM
04:30 PM

Open discussion

04:30 PM

Shuttle pick-up from MBI

06:30 PM
07:00 PM

Cash bar

07:00 PM
09:00 PM

Banquet in the Fusion Room @ Crowne Plaza Hotel

Friday, December 11, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:45 AM
09:45 AM
10:00 AM

Break

10:00 AM
10:45 AM
Huan Lei
10:45 AM
11:00 AM

Break

11:00 AM
11:45 AM
Emil Alexov
11:45 AM
12:00 PM

Open discussion

12:00 PM

Shuttle pick-up from MBI (One to airport and one back to hotel)

Name Email Affiliation
Abrams, Cameron cameron.f.abrams@drexel.edu Chemical and Biological Engineering, Drexel University
Alexov, Emil ealexov@clemson.edu Computational Biophysics and Bioinformatics, Clemson University
Cances, Eric cances@cermics.enpc.fr CERMICS, Ecole des Ponts and INRIA
Cao, Yin caoyin@msu.edu Mathematics, Michigan State University
Chipot, Chris chipot@ks.uiuc.edu Theoretical and Computational Biophysics Group, University of Illinois at Urbana-Champaign
Damian-Iordache, Valeriu Valeriu.2.Damian-Iordache@gsk.com
Dror, Ron ron.dror@stanford.edu Computer Science, Stanford University
Elber, Ron ron@ices.utexas.edu Chemistry/ICES, University of Texas
Fenley, Marcia mfenley@sb.fsu.edu Biophysics, Florida State University
Gilson, Michael mgilson@ucsd.edu Skaggs School of Pharmacy and Pharmaceutical Sciences, UC San Diego
Goethe, Martin martingoethe@ub.edu Fisica Fonamental (Fundamental Physics), University of Barcelona
Kravtsova, Natalia kravtsova.2@osu.edu Statistics, Ohio State University
Kurtzman, Tom thomas.kurtzman@lehman.cuny.edu Ph.D. Program in Chemistry, The Graduate Center of the City University of New York
Lasisi, Nurudeen nurudeenlasisi2009@yahoo.com Mathematiss Units, Federal Polytechnic, kaura Namoda
Lei, Huan Huan.Lei@pnnl.gov
Lelievre, Tony lelievre@cermics.enpc.fr CERMICS, ' Ecole Nationale des Ponts-et-Chauss'ees (ENPC)
Li, Bo bli@math.ucsd.edu Department of Mathematics, University of California, San Diego
Li, Chenglong li.728@osu.edu Medicinal Chemistry, The Ohio State University
MacKerell, Alex alex@outerbanks.umaryland.edu Pharmaceutical Sciences, University of Maryland
Matthews, Charles c.matthews@galton.uchicago.edu Statistics, The University of Chicago
Mobley, David dmobley@mobleylab.org Pharmaceutical Sciences & Chemistry, University of California, Irvine
Mohlenkamp, Martin mohlenka@ohio.edu Mathematics, Ohio University
Nussinov, Ruth ruthnu@helix.nih.gov LEIDOS BIOMEDICAL, National Cancer Institute
Sch�tte, Christof schuette@mi.fu-berlin.de Mathematics and Computer Science, Freie Universit""at Berlin
Scott, Ridgway ridg@uchicago.edu Computer Science and Mathematics, University of Chicago
Shen, Jana jshen@rx.umaryland.edu Pharmaceutical Sciences, University of Maryland at Baltimore
Soliman, Omar omarabdo@cu.edu.eg Chemistry - Nanotechnology, American University in Cairo
Vajda, Sandor vajda@bu.edu Biomedical Engineering, Boston University
Van Koten, Brian vankoten@galton.uchicago.edu Statistics, University of Chicago
Wang, Bao wangbao@msu.edu Department of Mathematics, Michigan State University
Wong, Chung wongch@umsl.edu Chemistry and Biochemistry, University of Missouri-St. Louis
Xie, Dexuan dxie@uwm.edu Department of Mathematical Sciences, University of Wisconsin
Yang, Wei yang@sb.fsu.edu Chemistry and Biochemistry, Florida State University
Yang, Sichun sichun.yang@case.edu School of Medicine, Case Western Reserve University
Zhao, Zhixiong zhaozx@msu.edu Maths, Michigan State University
Markovian Milestoning MD Simulations for Computing On- and Off-Rates

Prediction of binding and unbinding kinetics from all-atom molecular simulations could one day be an important component in the toolkit for structure-based drug design. Unfortunately, in contrast to binding affinity prediction, algorithms for estimating on- and off-rates in relatively complicated systems remain relatively undeveloped. Here we demonstrate one approach that has been applied to successfully compute the entry and exit rates of small gas molecules into globular proteins. The method is an application of transition-path theory and involves performing milestoning MD simulations in cells forming a Voronoi tesselation of some chosen state-discriminating collective-variable space. Particular attention is paid to handshaking the simulations with a continuous approximation of the solute flux to a protein target surface as a function of ligand diffusivity and bulk concentration. The method is applicable beyond small gas molecules and extensions involving more complicated molecules will be discussed.

Challenges in rational drug discovery - From drug binding to drug bioavailability

One of the grand challenges of rationale drug design is the prediction of the affinity of potential therapeutic agents for a given protein target. This challenge is in large measure rooted in the considerable changes in configurational entropy that accompanies the binding process, which atomistic simulations cannot easily sample. Two strategies relying upon alchemical transformations, on the one hand, and geometric transformations, notably potential of mean force calculations, on the other hand, are proposed, invoking a series of geometric restraints acting on collecting variables designed to alleviate sampling limitations inherent to classical molecular dynamics simulations. I will show through the example of a protein binding a small substrate, that both strategies, however of clearly different nature, can yield nearly identical standard binding free energies within chemical accuracy. I will further show how the methodology can be seamlessly transposed to protein-protein complexes. I will also outline current strategies to estimate binding entropies from such calculations. Downstream from the prediction of binding affinities is the challenging prediction of bioavailability. To estimate the permeability of the biological membrane to a drug candidate, an approach based upon Bayesian inferences, which reconciles thermodynamics and kinetics in molecular dynamics simulations with time-dependent biases, is put forth. Performance of the method is illustrated with prototypical permeants diffusing in a homogeneous lipid bilayer.

The design of protein switches

We focus on special protein pairs that can switch their fold following a single point mutation. These proteins are of special interest since they offer a way to dramatically affect protein function. They also offer pathways for the evolution of protein structures. Special algorithms are required to explore the exponentially large space of protein sequences (in the sequence length) that may lead to a switch. I will describe the algorithms, detailed examination of a protein switch that was investigated experimentally, and the construction of a network of protein switches. Join work with Leonid Meyerguz, Jon Kleinberg, BaoQiang Cao, and Serena Chen.

Correcting Free Energy Expressions for Thermal Motion

Minimizing a suitable free energy expression is arguably the most common approach in (ab initio) protein structure prediction. The achieved accuracy depends crucially on the quality of the free energy expression in use. Here, we present corrections to existing free energy expressions which arise from the thermal motion of the protein. We (i) devise a term accounting for the vibrational entropy of the protein, and (ii) correct existing potentials for the "thermal smoothing effect".

(i) Vibrational entropy is almost always neglected in free energy expressions as its consideration is difficult. This practice, however, may lead to incorrect output because distinct conformations of a protein can contain very different amount of vibrational entropy, as we show for the chicken villin headpiece explicitly [1]. For considering vibrational entropy, we suggest a knowledge based approach where typical fluctuation and correlation patterns are extracted from known proteins and then applied to new targets.

(ii) At ambient conditions, time-averaged potentials of proteins are considerably smoother when expressed in terms of the average atom coordinates than the Hamiltonian. This effect caused by thermal motion is referred to as the thermal smoothing effect. The strength of the effect varies strongly between atoms. This allows to increase the accuracy of free energy expressions significantly by subdividing atom species regarding their typical fluctuation behavior inside proteins and assigning time-averaged potentials for the new sub-species independently [2].

[1] M. Goethe, I. Fita, and J.M. Rubi, Vibrational Entropy of a Protein: Large Differences between Distinct Conformations, J. Chem. Theory Comput. 11, 351 (2015).
[2] M. Goethe, I. Fita, and J.M. Rubi, Thermal Motion in Proteins: Large Effects on the Time-Averaged Interaction Energies, in revision.

Exploiting Active-site Solvation Structure and Thermodynamics for Drug Discovery and Design

Despite recent advances in methodologies that better characterize local water structure and thermodynamics, the simply- stated question of whether it would be beneficial or detrimental, in a free-energetic sense, to displace water from a region of a protein with a suitably complementary ligand continues to be a conundrum. Solvation thermodynamic mapping techniques have provided valuable insight into the role of displacing water in molecular recognition however solvation thermodynamics alone is not predictive of displaceability and tightly binding ligands regularly displace water from both regions that are characterized as having favorable solvation and regions that are characterized as having unfavorable solvation. Part of the difficulty of assessing the thermodynamics of water displacement is due to the large number of often counteracting contributions and the consequent lack of a simplifying conceptual framework. We will discuss the key insights which have been gained from solvation thermodynamic mapping and how we are incorporating them into drug discovery and design methodologies. We will also discuss remaining issues on predicting favorability of water displacement and suggest how they might be tackled.

Adaptive Multilevel Splitting algorithms for rare event simulations

I will present a numerical method that we are currently developping in the NAMD software and which aim at simulation reactive trajectories. Numerical and theoretical results on this technique will be described.

Variational Implicit Solvation with Application to Identifying Ligand-Protein Binding Sites

The variational implicit-solvent model (VISM) is an advanced solvation theory and computational approach. It is based on the minimization of a solvation free-energy functional of all possible solute-solvent interfaces, i.e., dielectric boundaries. The free energy includes the volume contribution, interfacial energy with a curvature-corrected surface tension, solute-solvent van der Waals interaction energy, and electrostatic energy. For years, we have developed a robust level-set method to numerically minimize such a functional for arbitrarily shaped biological molecules. Our intensive computational results have demonstrated that this efficient approach can capture the wet and dry states of hydration, and subtle charge effects; and can provide quantitatively good estimates of solvation free energies. In this talk, we review what we have achieved with the level-set VISM, describe some initial work on modeling the solvent dynamics with the VISM dielectric boundary force, and report our recent level-set VISM application to identifying ligand-protein binding pockets that are crucial in rational drug design.

Grand Canonical Solute Sampling in Combination with the Site Identification by Ligand Competitive Saturation (SILCS) Ligand Design Methodology

Computational functional group affinity mapping of proteins is of utility for ligand design in the context of database screening, fragment-based design and lead compound optimization. The SILCS methodology allows for the generation of functional group affinity maps (FragMaps) of proteins that take into account contributions from protein desolvation, functional group desolvation, protein flexibility as well as direct interactions of the functional groups with the protein. Boltzmann transformation of the maps yields Grid Free Energy (GFE) FragMaps that may be used both qualitatively and quantitatively to direct ligand design. To allow for the application of the SILCS approach to deep and occluded pockets in proteins an oscillating μex Grand Canonical Monte Carlo (GCMC) approach was developed that allows for insertions of small solute molecules in the presence of an explicit aqueous environment. Combining the GCMC method with MD simulations for the inclusion of protein flexibility allows for the determination of GFE Fragmaps in occluded pockets. An overview of the GCMC/MD SILCS methodology along with application of the method to T4-lysozyme pocket mutants, nuclear receptors and GPCRs will be presented.

KRAS/Calmodulin/PI3Ka: A Promising New Adenocarcinoma-Specific Drug Target?

Decades of efforts have yet to yield a safe and effective drug to target lung, pancreatic and colorectal cancers driven by the highly oncogenic K-Ras4B. K-Ras4B’ pocketless surface, cancer tissue/cell heterogeneity, tolerated lipid post-translational modification exchange, as well as drug-elicited toxicity present a daunting challenge. We propose a new adenocarcinoma-specific drug concept (1). Calmodulin binds to K-Ras4B but not to other Ras isoforms. Physiologically, in calcium- and thus calmodulin-rich environments such as ductal tissues, calmodulin (CaM) can sequester K-Ras4B from the membrane; in cancer, CaM/Ca2+ can replace the missing receptor tyrosine kinase (RTK) signal, acting to fully activate PI3Kα. An oncogenic GTP-bound K-Ras/CaM/PI3Kα complex is supported by available experimental and clinical data; therefore, targeting it addresses an unmet therapeutic need in KRas-driven cancer. High resolution electron microscopy (EM) or crystal structure of the tripartite complex would allow orthosteric or allosteric drug discovery to disrupt the CaM/PI3Kα interface thus Akt/mTOR signaling.

pH-dependent BACE1 activity and inhibition

BACE1, a major therapeutic target for treatment of Alzheimer's disease, functions within a narrow pH range. Despite tremendous effort and progress in the development of BACE1 inhibitors, details of the underlying pH-dependent regulatory mechanism remain unclear. In this talk I will discuss our recent work in exploring the pH-dependent conformational mechanism that regulates BACE1 activity and substrate/inhibitor binding using continuous constant-pH molecular dynamics. The new insights greatly extend the knowledge of BACE1 and have implications for further optimization of inhibitors and understanding potential side effects of targeting BACE1.

Binding hot spots, druggability, and ligand deconstruction

Binding energy hot spots, smaller regions of binding sites that contribute a disproportionate amount to the free energy of binding any ligand, can be determined computationally from ligand-free structures of protein targets. The hot spot structure of a protein target provides very useful information on binding properties. The first application that will be discussed is predicting druggability, i.e., the ability of a site of binding druglike ligands with sufficient affinity. We applied the method to a large set of proteins. Results showed that, because the method is based on the biophysics of binding rather than on empirical parameterization, meaningful information can be gained about classes of proteins and classes of compounds beyond those resembling validated targets and conventionally druglike ligands. In particular, the method identifies targets that, while not druggable by druglike compounds, may become druggable using compound classes such as macrocycles or other large molecules beyond the rule-of-five limit. Second, we show that the hot spots provide crucial insights into the prospects for successful application of fragment-based drug discovery (FBDD), and whether a fragment hit can be advanced into a high affinity ligand. The key factor is the strength of the top ranking hot spot, and how well a given fragment complements it. We show that published data are sufficient to provide a sophisticated and quantitative understanding of how hot spot strength, number and spatial arrangement govern the potential for a surface site to bind to fragment-sized and larger ligands. This improved understanding provides important guidance for the effective application of FBDD in drug discovery.

New Advances in Local and Nonlocal Electrostatic Modeling and Calculation for Ionic Solvated Biomolecules

Calculation of electrostatics for a biomolecule (or a complex of a protein with a drug molecule) in an ionic solvent is a fundamental task in the fields of structural biology, computational biochemistry, biophysics, and mathematical biology. The Poisson-Boltzmann equation (PBE) is one commonly used dielectric model for predicting electrostatics of ionic solvated biomolecules. It has played important roles in rational drug design and protein design as well as other bioengineering applications. However, it is known not to work properly near a highly charged biomolecular surface, since it does not reflect any polarization correlation among water molecules and ionic size effects.

To improve the quality of PBE in the calculation of electrostatic solvation and binding free energies, we made many progresses recently on the study of nonlocal dielectric models, and developed several fast nonlocal model solvers. Meanwhile, we developed new numerical algorithms for solving PBE and one size modified PBE by using finite element, finite difference, solution decomposition, domain decomposition, and multigrid methods.

In this talk, I will first review our nonlocal dielectric theory. I then will present a new nonlocal PBE and its finite element solver. I will also describe our new numerical algorithms for solving PBE and one size modified PBE. A collection of these new solvers has led to a new software tool, called SDPBS (Solution Decomposition Poisson-Boltzmann Solvers), which is available online for free through our web server. Finally, application examples for chemical molecules, proteins, protein-drug, and peptide-RNA will be given to demonstrate the high performance and numerical stability of SDPBE in the calculation of salvation and binding free energies. This project is a joined work with Prof. L. Ridgway Scott at the University of Chicago under the support by NSF grants (DMS-0921004, DMS-1226259, and DMS-1226019).

Efficient Sampling of Long-Timescale Structural Responses to Enable Quantitative Protein-Ligand Binding Calculations

Proteins constantly fluctuate in aqueous solution. Any perturbation, either geometrical or chemical, may take very long time for a protein system to respond and relax. Indeed, such timescale issue has been a major bottleneck to the dream of quantitative protein-ligand binding predictions. To tackle this problem, we have developed the orthogonal space sampling theory and algorithms, which can uniquely accelerate response motions specific to perturbation fluctuations. In this talk, the theory, the methods, and the applications on protein-ligand binding calculations will be presented.

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