Professor Anastassia Alexandrova and Professor Mark Eberhart
(Prof. A.A.) UCLA, USA; (Prof. M.E.) Colorado School of Mines, USA
Enzymes host active sites inside protein macromolecules, which have diverse, often incredibly complex structures. It is an outstanding question as to the role played by this atom-expensive scaffolding in mediating enzymatic function. One theory, known as electrostatic preorganization, posits that the scaffolding’s polar groups are specifically arranged to preorganize the active site electric field in a manner that facilitates the charge redistribution associated with the catalytic reaction and thereby lowers its activation barrier. Dynamics and protein vibrations promoting the reaction barrier crossing is also a leading theory. The two are strongly physically linked. Enabling the deep understanding of the protein’s role in natural enzymes, and, importantly, making use of the insights in the design of proficient artificial enzymes are among the key goals of modern enzymology. In this lecture, we will discuss new theoretical tools for this purpose, based on global electric fields, and on the geometry of electron density.
While it is common to probe electric fields via vibrational Stark spectroscopy, effectively measuring a field at a specific bond, we firstly note that electric fields in enzyme active sites are complicated heterogenous 3-D vector fields, produced by all atoms in the protein. We will show that this global view on the field is in fact critical for the description of the protein’s role in catalysis. The field will be analyzed with the tools from fluid dynamics and machine learning. We will also offer an alternative perspective, based on the active site’s electron density– a scalar field. The two perspectives are both common in chemistry, each chosen as a matter of convenience. For example, the properties of polar and ionic molecules derive from their electric fields, whereas organic reaction mechanisms may be represented with electron pushing arrows depicting the evolution of the charge density through a reaction. A molecule’s electric field fixes its charge density, and inversely the charge density determines its electric field. Importantly, these are global relationships, changes to the field/density at one point will alter the density/field throughout the molecule. A needed addition to the chemist’s tool kit is a conceptual bridge linking the electric field and charge density perspectives. Using this bridge, it would then be possible to predict how changes to the electric field at one point alter the charge density at some distant point. This conceptual bridge is particularly useful for enzymology, for describing the effect of distant groups on enzymatic catalysis.
We will show that changes to the electric field produce predictable, in fact, mathematically required changes to the geometry of the electron density. Toward this end we extend Quantum Theory of Atoms in Molecules (QTAIM) beyond its topological foundations to include a geometric representation of the charge density in terms of its nested isosurfaces. We show how this geometry can be analyzed, linked to the enzyme-catalyzed reaction barriers, and associated with the intramolecular electric fields in enzymes. We demonstrate these tools in the investigation of electrostatic preorganization in several representative enzyme classes, both natural and artificial and highlight the forward-looking aspects of the approach.
Keywords: Electrostatic preorganization in enzymes, electric fields, Quantum Theory of Atoms in Molecules (QTAIM), Bond bundles, enzyme
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