Abstracts of Selected Publications



Electrostatic Complementarity at Ligand Binding Sites: Application to Chorismate Mutase. E. Kangas and B. Tidor. J. Phys. Chem. B 105: 880-888 (2001).

Recently developed electrostatic charge optimization methods allow the calculation of a set of partial atomic charges for one molecule that provide it with a minimum electrostatic free energy contribution for binding its partner molecule. Charge optimization methods were applied here to the binding of the Bacillus subtilis chorismate mutase enzyme by its endo-oxabicyclic transition state analog. In particular, electrostatically optimized templates for the twelve different active sites in the X-ray crystal structure were used to define regions of the transition state analog whose electrostatic properties are particularly non-optimal for binding. Structural variations of the analog that could improve its electrostatic affinity for the enzyme are suggested by changes that more closely mimic the optimal charge distributions. Results indicate that the replacement of one of the analog's carboxyl groups with a nitro group may improve the electrostatic component of the binding free energy by up to about 3.1 kcal/mol. The principal mechanism is a decrease in the desolvation penalty of the ligand without a significant loss in ligand-enzyme interactions. Additional fluorine substitutions have been identified that, together with the nitro, are suggested to improve binding by up to about 3.8 kcal/mol. This work shows that charge optimization techniques are capable of identifying chemically reasonable substitutions to known ligands that produce substantial improvements in computed binding affinity through electrostatic enhancement. In the current case, much of the electrostatic enhancement comes from the removal of a formal charge and might be better termed electrostatic re-balancing. Comparison of the results across twelve crystallographically independent active sites confirms that the approach is not overly sensitive to subtle structural variation. Additionally, results indicate that the mean square residual surface potential correlates well with the improvement in electrostatic binding free energy for all variations examined.


Electrostatic Specificity in Molecular Ligand Design. E. Kangas and B. Tidor. J. Chem. Phys. 112: 9120-9131 (2000).

Designing ligand molecules that bind with high affinity and specificity to a target molecule (or a family of related targets) is a fundamental goal of molecular biophysical research. While it is generally recognized that electrostatic interactions can contribute to binding specificity, it is unclear whether the inclusion of interactions that result in tight binding also necessarily lead to highly specific binding. Here we make use of recently developed charge-optimization techniques to explore the affinity--specificity relation in the context of electrostatic interactions. Using model problems we find that affinity-optimized electrostatic interactions do not necessarily create specificity. Furthermore, we develop several rigorous methods that indicate how best to perturb affinity-optimized ligand-charge distributions to increase specificity with minimal sacrifice in affinity for the target or target set. We provide a theoretical framework for improving specificity against any number of known receptors and/or binding modes and against uncharacterized receptors.


Optimization of Electrostatic Interactions in the Presence of Aqueous Ions. E. Kangas and B. Tidor. (in preparation).


Methods have been developed to design optimal electrostatic interactions for molecular binding for situations in which the charge distribution of one binding partner is fixed, the other is adjustable, and the system can be described by the Poisson equation [L.-P. Lee and B. Tidor, J. Chem. Phys. 106, 8681 (1997)]. In some fields of interest (e.g., rational drug design), the solvent contains mobile ions, and the system is adequately described by the linearized Poisson-Boltzmann equation. Here the analytical framework for electrostatic optimization is extended to such situations. The case of spherical molecular geometries with an ion-excluding Stern layer has been treated in detail. Calculational results are reported for a variety of model receptors and ionic strengths. The effects of increasing the ionic strength up to 1.0 M are relatively modest: the electrostatic component of the optimized electrostatic binding free energy is progressively weaker in the presence of increasing ionic strength but is still favorable. The optimal ligand-charge distributions are relatively insensitive to ionic strength.


Enzyme and Antibody Catalysis of the Claisen Rearrangement of Chorismate: A Theoretical Perspective. E. Kangas and B. Tidor. Protein Science 8, suppl. 1: 78 (1999).

The enzyme chorismate mutase catalyzes the conversion of chorismate to prephenate (formally a Claisen rearrangement), which is the committed step in the synthesis of tyrosine and phenylalanine in microorganisms and higher plants. The enzyme differs structurally among a variety of microorganisms. In addition, at least two catalytic antibodies have been isolated that carry out the same reaction (1F7 and 11F1-2E9). Thus, this is an excellent system in which to examine the commonality and diversity of features necessary for efficient catalysis. We have utilized novel continuum electrostatic theoretical modeling approaches to compute the relative complementarity of the catalyst for substrate, model transition-state, and product for the enzyme from B. subtilis and for the 1F7 catalytic antibody. Analysis of the relative affinity and specificity of each catalyst provides some insight into what is being optimized in enzyme evolution. Binding properties of transition-state analogs (used as haptens in the generation of catalytic antibodies) are discussed with the aim of assisting the design of second-generation haptens that may elicit more active catalytic antibodies.


Electrostatic Optimization in Ligand Complementarity and Design. E. Kangas and B. Tidor. Nonconvex Optimization and Its Applications (series). Optimization in Computational Chemistry and Molecular Biology : Local and Global Approaches 40: 231-242 (2000).

Analytic and numerical methods now allow optimization of the electrostatic contribution to the free energy of association of two molecules in solution. Using a continuum electrostatic approximation based on the linearized Poisson-Boltzmann equation, the electrostatic free energy of rigid bimolecular association becomes a quadratic function of the reactant-charge distributions. By optimizing the charge distribution of one reactant, we find that the electrostatic free energy can be minimized, and made favorable in many cases. Furthermore, a rigorous method for visualizing the extent of electrostatic complementarity between two molecules has been developed. In this paper we review the framework and progress of charge optimization and discuss some of the implications emerging to date.


Charge Optimization Leads to Favorable Electrostatic Binding Free Energy. E. Kangas and B. Tidor. Phys. Rev. E 59: 5958-5961 (1999).

Variational optimization of molecular electrostatic charge distributions is a tool for the study of association reactions of molecules in solution. In principle, this method can be used in drug design and protein folding to analyze and improve molecular interactions and to provide electrostatic templates for molecular design. This optimization problem reduces to an inverse source problem in classical electrostatics, where the sources are determined by a combination of external and self-polarization potentials. In this Letter, we show that the electrostatic portion of the free energy of association for electrostatically optimized molecules has an upper bound of zero in many situations of physical interest. That is, variational optimization provides a ligand charge distribution that contributes favorably to the energetics of binding (even in a strongly polar medium), stabilizing association reactions contrary to the usual role of electrostatics in aqueous complexes (in which desolvation effects generally dominate). We also show the existence and non-uniqueness of the variational solution and make a connection to the electrostatic image charge problem.


Optimizing Electrostatic Affinity in Ligand-Receptor Binding: Theory, Computation, and Ligand Properties. E. Kangas and B. Tidor. J. Chem. Phys. 109: 7522-7545 (1998).

The design of tight-binding molecular ligands involves a trade off between an unfavorable electrostatic desolvation penalty incurred when the ligand binds a receptor in aqueous solution and the generally favorable intermolecular interactions made in the bound state. Using continuum electrostatic models we have developed a theoretical framework for analyzing this problem and shown that the ligand-charge distribution can be optimized to produce the most favorable balance of these opposing free energy contributions [L.-P. Lee and B. Tidor, J. Chem. Phys. 106, 8681 (1997)]. Herein the theoretical framework is extended and calculations are performed for a wide range of model receptors. We examine methods for computing optimal ligands (including cases where there is conformational change) and the resulting properties of optimized ligands. In particular, indicators are developed to aid in the determination of the deficiencies in a specific ligand or basis. A connection is established between the optimization problem here and a generalized image problem, from which an inverse-image basis set can be defined; this basis is shown to perform very well in optimization calculations. Furthermore, the optimized ligands are shown to have favorable electrostatic binding free energies (in contrast to many natural ligands), there is a strong correlation between the receptor desolvation penalty and the optimized binding free energy for fixed geometry, and the ligand and receptor can not generally be mutually optimal. Additionally, we introduce the display of complementary desolvation and interaction potentials and the deviation of their relationship from ideal as a useful tool for judging effective complementarity. Scripts for computing and displaying these potentials with GRASP are available at http://web.mit.edu/tidor/www/


Specificity in Ligand-Receptor Binding. E. Kangas and B. Tidor. Protein Science 6, suppl. 2: 91 (1997).

Given a target receptor molecule, and a set of other competing receptors, R, one seeks to choose a ligand out of a set L that binds to the target receptor most specifically. In other words, not only is the free energy of binding very favorable, but as few as possible receptors in R also bind well to the ligand. A mathematical definition of specificity in this context has been developed in terms of the binding energy function and the distribution of ligands and receptors in binding-energy space. This definition is then specialized to the case of rigid binding where the only variation within the set of receptors or ligands is their electrostatic charge distribution. For several specific ligand and receptor shapes and binding configurations, the binding specificity can be optimized analytically yielding a specific ligand charge distribution. Application to physical systems is discussed.



Dynamics of Helix Deformation in a Chiral Smectic C* Liquid Crystal: Optical Experiments and Modeling. E. Kangas, J.-F. Li and C. Rosenblatt. Phys. Rev. E 53: 696-700 (1996).

Measurements are reported for the optical response in the classical electroclinic geometry of a chiral smectic C* liquid crystal. The sample was subjected to a weak a.c. electric field applied perpendicular to the helical axis. The response was found to be linear in field for E much smaller than the critical field associated with complete unwinding, and nearly independent of sample thickness, falling off approximately as f-1 in the frequency range 200 < f < 20 000 Hz. The behavior is modeled by a time-dependent Landau-Ginzburg model in which both the local polarization and dielectric anisotropy are coupled to the electric field.


Solitary Waves in an Antiferroelectric Liquid Crystal. J.-F. Li, X.Y. Wang, E. Kangas, C. Rosenblatt, Y. Suzuki, and P.E. Cladis. Mol. Cryst. Liq. Cryst. 228: 73-82 (1996).

Propagating finger-like solitary waves are observed in an antiferroelectric liquid crystal on application of an electric field greater than a characteristic threshold field Eth. On reducing the field below Eth the fingers recede, also as solitary waves. The velocity of the waves, which to our knowledge is the fastest observed for a liquid crystal, scales approximately as E - Eth for E near Eth. A simple model, which includes a layer-layer coupling term, is presented which describes much of the observed behavior.


Reversible Propagating Fingers in an Anti-Ferroelectric Liquid Crystal. J.-F. Li, X.Y. Wang, E. Kangas, C. Rosenblatt, Y. Suzuki, and P.E. Cladis. Phys. Rev. B 52: R13075-R13078 (1995).

Propagating finger-like solitary waves are observed in an antiferroelectric liquid crystal on application of an electric field above a threshold field Eth. On reducing the field below Eth the fingers recede, also as solitary waves. The velocity of the waves, which to our knowledge is the fastest observed for a liquid crystal, scales approximately as E - Eth for E near Eth. A simple model, which includes a layer-layer coupling term, is presented which describes much of the observed behavior.



Analysis of Charged-Particle-Photon Correlations in Hadronic Multiparticle Production. T. C. Brooks, et al. Phys. Rev. D 55: 5667-5680 (1997).

In order to analyze data on joint charged-particle/photon distributions from an experimental search (T-864, MiniMax) for disoriented chiral condensate (DCC) at the Fermilab Tevatron Collider, we have identified robust observables, ratios of normalized bivariate factorial moments, with many desirable properties. These include insensitivity to many efficiency corrections and the details of the modeling of the primary pion production, and sensitivity to the production of DCC, as opposed to the generic, binomial-distribution partition of pions into charged and neutral species. The relevant formalism is developed and tested in Monte-Carlo simulations of the MiniMax experimental conditions.


Studying the Structure of the Vacuum. E. Kangas. Proceedings of Ohio Space Grant Consortium Research Project Symposium, NASA Lewis Research Center (April 15, 1994).

Fermilab experiment T864 is ultimately a search for areas of "disoriented vacuum" produced in high energy hadronic collisions. To date, little experimental work has been done with high-multiplicity events in the far forward direction though there is much physics besides the search for "disoriented chiral condensates" (dcc) than can only be seen in such events. Detailed Monte-Carlo simulation and actual data have led to an understanding of the difficulties involved in track reconstruction based upon data from a multiple wire proportional chamber "telescope." Typical combinatorial particle trackers are very slow and have a sharp upper bound on how many tracks they can find in the presence of a small signal-to-noise ratio. A novel method for finding tracks using an adaptive Hough transform algorithm has been developed. This algorithm has proven much faster and in some ways more efficient then traditional combinatorial methods. More importantly, the Hough transform enables accurate tracking of particles in high multiplicity events while finding remarkably few spurious tracks. Beam-beam and beam-gas events are currently being analyzed to perfect our methodology and increase the signal-to-noise ratio.