## 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
Nathan Baker
Computational and Statistical Analytics Division, Pacific Northwest National Laboratory
Chris Chipot
Valeriu Damian-Iordache
Ron Dror
Ron Elber
Tom Kurtzman
Tony Lelievre
Alex MacKerell
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
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 cameron.f.abrams@drexel.edu
Baker, Nathan nathan.baker@pnl.gov Computational and Statistical Analytics Division, Pacific Northwest National Laboratory
Cances, Eric cances@cermics.enpc.fr CERMICS, Ecole des Ponts and INRIA
Chipot, Chris chipot@ks.uiuc.edu
Damian-Iordache, Valeriu Valeriu.2.Damian-Iordache@gsk.com
Dror, Ron ron.dror@stanford.edu
Elber, Ron ron@ices.utexas.edu
Gilson, Michael mgilson@ucsd.edu Skaggs School of Pharmacy and Pharmaceutical Sciences, UC San Diego
Kurtzman, Tom
Lelievre, Tony lelievre@cermics.enpc.fr
MacKerell, Alex alex@outerbanks.umaryland.edu
Mayo, Stephen steve@mayo.caltech.edu
Mobley, David dmobley@mobleylab.org
Nussinov, Ruth ruthnu@helix.nih.gov
Ren, Pengyu pren@mail.utexas.edu Biomedical Engineering, The University of Texas at Austin
Rizzo, Robert rizzorc@gmail.com
Sch�tte, Christof schuette@mi.fu-berlin.de
Schlick, Tamar Schlick@nyu.edu Bio/Chem/Bio math, New York University
Scott, Ridgway ridg@uchicago.edu Computer Science and Mathematics, University of Chicago
Shen, Jana jshen@rx.umaryland.edu
Vajda, Sandor vajda@bu.edu
Xie, Dexuan dxie@uwm.edu Department of Mathematical Sciences, University of Wisconsin
Yang, Wei
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.

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.

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.