Workshop 4: Mathematical Challenges in Drug and Protein Design

(December 7,2015 - December 11,2015 )


Eric Cances
CERMICS, Ecole des Ponts and INRIA
Michael Gilson
Skaggs School of Pharmacy and Pharmaceutical Sciences, UC San Diego
Martha (Marti) Head
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
Nathan Baker
Computational and Statistical Analytics Division, Pacific Northwest National Laboratory
Chris Chipot
Valeriu Damian-Iordache
Ron Dror
Ron Elber
Tom Kurtzman
Ph.D. Program in Chemistry, The Graduate Center of the City University of New York
Christopher Langmead
Tony Lelievre
CERMICS, ' Ecole Nationale des Ponts-et-Chauss'ees (ENPC)
Alex MacKerell
Pharmaceutical Sciences, University of Maryland
Stephen Mayo
David Mobley
Ruth Nussinov
Pengyu Ren
Biomedical Engineering, The University of Texas at Austin
Robert Rizzo
Tamar Schlick
Bio/Chem/Bio math, New York University
Christof Schütte
Jana Shen
Sandor Vajda
Dexuan Xie
Department of Mathematical Sciences, University of Wisconsin
Wei Yang
Chemistry and Biochemistry, Florida State University
Monday, December 7, 2015
Time Session
Tuesday, December 8, 2015
Time Session
Wednesday, December 9, 2015
Time Session
Thursday, December 10, 2015
Time Session
Friday, December 11, 2015
Time Session
Name Email Affiliation
Abrams, Cameron
Baker, Nathan Computational and Statistical Analytics Division, Pacific Northwest National Laboratory
Cances, Eric CERMICS, Ecole des Ponts and INRIA
Cao, Yin Mathematics, Michigan State University
Chipot, Chris
Damian-Iordache, Valeriu
Dror, Ron
Elber, Ron
Fenley, Marcia Biophysics, Florida State University
Gilson, Michael Skaggs School of Pharmacy and Pharmaceutical Sciences, UC San Diego
Goethe, Martin Fisica Fonamental (Fundamental Physics), University of Barcelona
Kravtsova, Natalia Statistics, Ohio State University
Kurtzman, Tom Ph.D. Program in Chemistry, The Graduate Center of the City University of New York
Langmead, Christopher
Lasisi, Nurudeen Mathematiss Units, Federal Polytechnic, kaura Namoda
Lelievre, Tony CERMICS, ' Ecole Nationale des Ponts-et-Chauss'ees (ENPC)
MacKerell, Alex Pharmaceutical Sciences, University of Maryland
Madrasi, Kumpal Pharmacy Practice, Mercer University
Matthews, Charles
Mayo, Stephen
Mobley, David
Mohlenkamp, Martin
Nussinov, Ruth
Ren, Pengyu Biomedical Engineering, The University of Texas at Austin
Rizzo, Robert
Sch�tte, Christof
Schlick, Tamar Bio/Chem/Bio math, New York University
Scott, Ridgway Computer Science and Mathematics, University of Chicago
Shen, Jana
Soliman, Omar Chemistry - Nanotechnology, American University in Cairo
Vajda, Sandor
Van Koten, Brian Statistics, University of Chicago
Wang, Bao Department of Mathematics, Michigan State University
Xie, Dexuan Department of Mathematical Sciences, University of Wisconsin
Yang, Wei Chemistry and Biochemistry, Florida State University
Yang, Sichun School of Medicine, Case Western Reserve University
Zhao, Shan Department of Mathematics,
Zhao, Zhixiong Maths, Michigan State University
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.

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.

Long time dynamics from short time simulations: two algorithms

I will present two numerical techniques to efficiently sample metastable trajectories: the parallel replica method, which has been proposed by A.F. Voter in 1998 and the adaptive multilevel splitting techniques, which has been introduced by F. Cérou and A. Guyader in 2007. The first algorithm has already been extensively used for various applications, and we will concentrate and the mathematical foundations of the algorithm. The second algorithm is more recent, and we will present some numerical results which have been recently obtained on simple systems.

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.

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).

Orthogonal Space Sampling for Free Energy Simulation of Protein Ligand Recognition

Free energy perturbation calculations have long suffered from inadequate sampling of long timescale configurational responses to applied chemical responses. Such a bottleneck issue has greatly limited the usability of free energy simulation methods in drug discovery. Recently, we developed the orthogonal space sampling scheme, which allows selective acceleration of necessary configurational responses. In this talk, the theory, the methods, and applications in the context of protein ligand recognition will be presented.