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Introduction:Principles of Kinetics and Dynamics

1.1 Structure, Function, and Mechanism

Why study structure in biology? The imaging of structure has long been of interest, where structures range in length scale from an entire ecosystem to the gross anatomy of the human body, to cellular, molecular, and atomic structure. Here, we concentrate on structure at the molecular and atomic level and on the essential, dynamic variations in structure with time. Determining biological structure at this level is undeniably powerful, as evidenced by the library of more than 160,000 experimental and increasingly, computational structures in the Protein Data Bank (PDB). An arguably more interesting reason is broader: structure at the molecular and atomic level provides a powerful avenue into understanding both function and mechanism.

The three words understanding, function, and mechanism are critical to our arguments. Understanding means different things to biologists, chemists, and biophysicists. For example, a biologist seeks to understand gene transcription by identifying transcription factors, the specific DNA sequences to which they bind, the role of the RNA polymerase enzyme that catalyzes transcription, and the genes whose expression they control. A biochemist or biophysicist is certainly interested in those aspects, but also wishes, for example, to determine the atomic structures of the molecules involved, the chemical interactions that confer specificity between a transcription factor and its binding site, the intermediate structures involved in the binding of RNA polymerase and its catalytic processes, and how a particular step confers specificity or limits the overall rate of transcription. With our goal of understanding dynamic processes, we largely adopt the viewpoint of the biochemist and biophysicist. Function and mechanism are related but not identical. To most biochemists and biophysicists (and to us), function labels what the biological system does, and mechanism labels how it does it. Put less formally, mechanism denotes how the system works. Studies of structure and, as we shall see, of structural dynamics thus directly seek to identify mechanism. The scientific discipline now labeled structural biology explores the relationship between chemical, biochemical, and biophysical processes and three-dimensional (3D) structure at the atomic and molecular level, and thus underpins mechanism. The linkages between structure, mechanism, and function are strong at the atomic and molecular level: structure indeed directly determines mechanism and somewhat less directly, function. For example, hemoglobin molecules from species as diverse as humans, horses, and lampreys have the same overall fold. They are practically identical in their 3D structures and in fluctuations about those structures. The molecules are also closely similar in how that structure changes as hemoglobin carries out its function of transporting oxygen and carbon dioxide between the lungs and the tissues. At this level, structure, mechanism, and function are tightly conserved.

Conservation of structure holds over the length scale of a few nm, characteristic of individual protein molecules such as hemoglobin, up to a few tens of nm, characteristic of large complexes and molecular machines assembled from many proteins and nucleic acids such as a ribosome, transcriptional complexes, or an icosahedral virus. However, the linkage between structure and function weakens at longer length scales characteristic of subcellular organelles and cells. Function is largely conserved, but structure begins to exhibit a wider range. For example, organelles such as mitochondria from a given cell type all have a closely similar function, but their structures vary between individual cells of that type. Although variation is definitely present, it is not extensive enough to prevent confident identification of mitochondria in structural images obtained by electron microscopy.

We restrict ourselves for the moment to the length scale from individual molecules up to large macromolecular complexes and pose a critical question. Is structure both necessary and sufficient to fully understand mechanism and function? The fundamental thrust of our argument is that the answer to this question is: necessary, yes; but sufficient, no. The phrase "Structure determines function" is too limiting; the dynamics of structural changes must also be included. We assert that a more accurate phrase is "Structural dynamics determines function." This assertion underlies all aspects of our argument here. We recognize that the extent of structural dynamics varies from system to system. For example, in proteins whose principal function is scaffolding, dynamics generally plays a lesser role except during their assembly, disassembly, and modulation by ligand binding. The dynamics of sequence-dependent, structural changes in DNA plays a substantial role during replication and transcription.

Whatever form the experimental sample takes when exploring structural dynamics, the molecules comprising the sample should be demonstrably active. That form could be, for example, a crystal, dilute solution, within an intact cell or on a cryo-electron microscopy (cryo-EM) grid. That is, the molecules must display mechanism; they must work in the form used for determination of their structure. If they do not work or work only in aberrant fashion, elaborate experiments in structural dynamics will be seriously misdirected.

Consider structure determination by X-ray crystallography. A large majority of the structures in the PDB were determined by applying crystallographic techniques using synchrotron radiation emitted by storage ring (SR) X-ray sources (Chapters 5.1 and 6.2). Most crystals were frozen to around 100 K to mitigate radiation damage to the structure arising from X-ray absorption (Chapter 4.3.4). Freezing exposes three problems. First, at 100 K molecules have lost their normal function. Atomic motion is abolished, literally frozen. The molecules are inert, devoid of biological activity, unable to work (Rasmussen et al. 1992). Atomic motion and the resultant, time-dependent changes in structure - structural dynamics - are inescapably linked to mechanism and function, not merely in biology but also in chemistry and physics. "If it doesn't wriggle, it's not biology!" is a trenchant statement attributed to the British physiologist A.V. Hill in conversation with John Kendrew in the late 1940s. Kendrew was at the time a beginning research student in Max Perutz's Medical Research Council Unit in Cambridge, England, at the dawn of protein X-ray crystallography. Hill's statement remains valid today: the absence of "wriggling" at 100 K accounts for the lack of function. Second, raw experimental data in crystallography arise from a space average over all the very large number of molecules in the crystal and a time average over the X-ray exposure time. For almost all systems, refinement against these data ultimately generates a single set of atomic coordinates to represent the structure. If the data were acquired at near-physiological temperature, refinement represents any atomic motion by the fuzziness of individual atoms, the so-called temperature factors. The atomic coordinates and temperature factors defined by refinement are both time-independent. That is, the structure is static, independent of time, and lacks any wriggling. Third, structures and more importantly, their energetics differ in detail between 100 K and more physiological temperatures (Halle 2004; Bock and Grubmüller 2022) where wriggling and function are retained (Chapter 2.6). Some of these energetic and structural differences are critical for mechanism.

Decades of crystallographers have studied structure as an essential determinant of mechanism related to function. Even when a crystal structure is determined at near-physiological temperatures where wriggling and function are retained, that structure is time-independent and does not yield the range of structures - the structural changes - inherent in mechanism and function. Although it's possible to trap the structures of normally short-lived intermediates in an overall reaction by chemical means rather than by the physical means of freezing, these static structures are limited in what they can reveal about mechanism (Chapter 2.6).

1.2 Activity in the Crystal

Since structural changes and the dynamic, time dependence of these changes are inherent in mechanism at the molecular level, a full understanding of mechanism and biological function must extend beyond inert, static structures to active, dynamic structures. This requires the ability to generate and determine short-lived, intermediate structures whose populations vary with time as the biological reaction proceeds. Going even further, it is becoming possible to determine the functional trajectories by which molecules pass from one intermediate structure to the next (Chapter 9.2). As we shall see, structures of intermediates can be determined experimentally by, for example, time-resolved crystallography under conditions where the molecules in the crystal can indeed wriggle. Another potential problem appears: the structural changes essential to activity may be affected by the 3D packing of molecules into a crystal, or by the solvents from which crystals were grown that occupy their intermolecular channels. Unusual, nonphysiological properties of the solvent such as extremes of pH, high ionic strength, or the absence of a key cation may substantially alter or...