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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Dynamics and Kinetics in Structural Biology Understand the latest experimental tools in structural biology with this pioneering work Structural biology seeks to understand the chemical mechanisms and functions of biological molecules, such as proteins, based on their atomic structures. Until recently, these structures have been studied only statically, using procedures which deliberately freeze atomic motion. However, freezing eliminates the rapid structural motions so essential to biological activity and function; the molecules are inactive. But with the recent development of X-ray free electron laser (XFEL) sources, efforts to conduct dynamic experiments have expanded using the principles of dynamics and kinetics to capture active biological molecules as they function. Dynamics and Kinetics in Structural Biology promotes the development of these experiments and their successful application. It grounds readers in the foundational principles of dynamics and kinetics; proceeds through extended discussions of experimental procedures and data analysis techniques; and explores experimental frontiers in structural dynamics. The book will aid researchers to gather and interpret cutting-edge data on the dynamic structure of biological molecules, under conditions where they retain their biological functions. Dynamics and Kinetics in Structural Biology offers readers: * Authorship by founding figures in the field * In-depth presentation of time-resolved X-ray crystallography, solution scattering, and more * A pioneering contribution to a rapidly developing field of study Dynamics and Kinetics in Structural Biology is essential reading for graduate students, scientists, researchers and industry professionals engaged in structural studies of biological systems. Industry professionals considering dynamic studies in the development of new product lines will also benefit.
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Dynamics and Kinetics in Structural Biology
Unravelling Function Through Time-Resolved Structural Analysis
Keith Moffat Department of Biochemistry and Molecular Biology The University of Chicago Chicago, IL USA
Eaton E. Lattman Department of Materials Design and Innovation University at Buffalo Buffalo, NY USA
This edition first published 2024
© 2024 John Wiley & Sons Ltd
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.
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A catalogue record for this book is available from the Library of Congress
Paperback ISBN: 9781119696285; ePub ISBN: 9781119696308; ePDF ISBN: 9781119696339; oBook ISBN: 9781119696353
Cover image: Greg Stewart, SLAC National Accelerator Laboratory
Cover design: Wiley
Set in 9.5/12.5pt STIXTwoText by Integra Software Services Pvt. Ltd, Pondicherry, India
This book is dedicated to our wives Anne Simon Moffat and Susan Pfeiffer and to our late colleagues Quentin Gibson and John C. H. Spence
Contents
Cover
Title Page
Copyright Page
Dedication
List of Figures
Acknowledgments
Acronyms/Abbreviations
Units
1 Introduction: Principles of Kinetics and Dynamics
1.1 Structure, Function, and Mechanism
1.2 Activity in the Crystal
1.3 Other Structure-informing Techniques
1.4 Dynamics, Kinetics, Movies, Pathways, and Functional Trajectories
1.5 The Time-resolved Experiment: An Overview
1.5.1 Proof and Disproof of Mechanisms in Structurally-based Chemical Kinetics
1.5.2 Spatial Resolution
1.5.3 Temporal Resolution
1.5.4 Reaction Initiation
1.5.5 Conclusion
References
2 Physical Chemistry of Reactions
2.1 Introduction
2.2 Thermodynamics: States and Equilibria
2.3 Kinetics, Rates, and Rate Coefficients
2.4 Enzyme Kinetics
2.4.1 Steady-State and Pre-Steady-State Kinetics
2.4.2 Relaxation Kinetics
2.4.3 Conclusions
2.5 Transition State Theory and Energy Landscapes
2.5.1 Transition State Theory
2.5.2 Energy Landscapes
2.6 Trapping of Intermediates
References
3 The Experiment
3.1 Introduction
3.2 Signal and Noise
3.2.1 Signal, Accuracy, and Systematic Errors
3.2.2 Difference Experiments
3.2.3 Experimental Design
3.3 Reaction Initiation
3.3.1 Principles
3.3.2 Experimental Approaches
3.3.2.1 Mixing: Chemical Initiation
3.3.2.2 Relaxation: Physical Initiation
3.3.2.3 Light
3.3.2.3.1 Principles of light absorption
3.3.2.3.2 Practical considerations
References
4 The Sample
4.1 Crystal and Solution Samples
4.2 Introduction of the Sample to the X-ray Beam: Injection and Fixed Targets
4.3 Radiation Damage
4.3.1 Introduction
4.3.2 Generation of Primary and Secondary Radiation Damage
4.3.3 Diffraction before Destruction
4.3.4 Quantitative Studies of Radiation Damage
4.4 Optogenetics and Photopharmacology
References
5 Time-resolved Crystallography, Solution Scattering, and Molecular Dynamics
5.1 Time-resolved Crystallography
5.1.1 Time-resolved Monochromatic Diffraction
5.1.2 Time-resolved Laue Diffraction
5.1.3 Time-dependent Substitutional Disorder and Loss of Crystal Symmetry
5.1.4 Are My Crystals Active? What Time Points Should Be Collected?
5.2 Time-resolved X-ray Solution Scattering
5.2.1 Basics of the Experiment
5.2.2 The I(q) Curve
5.2.2.1 Calculation of I(q)
5.2.2.2 Pair Distance Distribution Function
5.2.2.3 Invariants
5.2.3 Dynamic Applications of TR SAXS/WAXS
5.2.3.1 Introduction
5.2.3.2 Example 1: Protein Quake
5.2.3.3 Example 2: Folding of Cytochrome C from Heterogeneous Unfolded States
5.2.3.4 Example 3: Modulation of HIV Protease Flexibility
5.2.3.5 Example 4: XSS as a Probe with Stopped-Flow Kinetics
5.2.3.6 XSS and RNA Dynamics
5.3 Molecular Dynamics Simulations
5.3.1 The MD Algorithm
5.3.2 The Range of MD Simulations
5.3.3 Simulation of Structures Not at Equilibrium
5.3.4 Example: The Role of Lipids in Rhodopsin Function
References
6 X-ray Sources, Detectors, and Beamlines
6.1 Introduction
6.2 Sources of Synchrotron Radiation
6.2.1 Introduction
6.2.2 Generation and Properties of Synchrotron Radiation
6.2.3 Third Generation Storage Ring Sources
6.2.4 Fourth Generation Storage Ring Sources
6.3 X-ray Free Electron Lasers
6.4 Detectors
6.4.1 Introduction
6.4.2 The Adaptive Gain Integrating Pixel Detector: AGIPD
6.4.3 The JUNGFRAU Detector
6.5 Beamlines and Experimental Stations
6.5.1 Introduction
6.5.2 Beamline Example: The Coherent X-ray Imaging Facility
6.5.2.1 Beam Monitoring and Use
References
7 Data Analysis and Interpretation
7.1 Introduction
7.2 General Constraints on Analysis and Interpretation
7.3 Difference Electron Density Maps
7.3.1 Hidden Advantages
7.3.2 Phase Improvement
7.3.3 Partial Occupancy
7.3.4 Timing Uncertainty
7.4 Singular Value Decomposition (SVD)
7.5 Features Commonly Found in DED Maps
7.6 Refinement of Intermediate Structures
7.7 Example: The Photosynthetic Reaction Center
7.8 Making a Molecular Movie
7.9 Does the Mechanism in the Crystal Represent the Mechanism in Solution?
References
8 Other Structural Biology Techniques
8.1 Introduction
8.2 Single-Particle Cryo-Electron Microscopy
8.2.1 Dizzying Progress
8.2.2 Outline of the Experiment
8.2.3 Reconstruction of Structure from Single Particles
8.2.4 Time-resolved Studies
8.3 Energy Landscape Analysis
8.3.1 Landscapes
8.3.2 Energy Landscapes Derived from Structural Fluctuations
8.3.3 Generation of the Energy Landscape: Details
8.4 X-ray Spectroscopy
8.4.1 Introduction: Spectroscopy of Transition Metals
8.4.2 X-ray Absorption Spectroscopy
8.4.3 XANES and EXAFS Spectroscopies
8.4.4 Experimental Approaches to XAS
8.4.4.1 Simultaneous Observation of XAS and Diffraction
8.4.5 X-ray Emission Spectroscopy (XES)
8.4.5.1 Photosystem II: An Example
8.4.5.2 XES Studies on PS-II
8.5 Nuclear Magnetic Resonance: Joseph Sachleben (University of Chicago)
8.5.1 Principles
8.5.2 Dynamic Information
8.5.2.1 Example: Zinc Finger Dynamics
8.6 Hydrogen–Deuterium Exchange
References
9 Looking Forward
9.1 Overview: Unraveling Function and Mechanism
9.2 Single Particle Imaging, Energy Landscape Analysis, and Functional Trajectories
9.3 Artificial Intelligence and Machine Learning
9.3.1 AI/ML and Physical Chemistry Approaches to Folding and Structure
9.3.2 AI/ML and Structural Dynamics
9.3.3 AI/ML and De Novo Protein Design
9.4 Experimental Approaches
9.4.1 Time-resolved Electron Microscopy of Active Samples
9.4.2 The Compact X-ray Free Electron Laser Source
9.4.3 Weak fs Pulses
9.4.4 Temporal Noise and Chirped X-ray Pulses
9.4.5 New Light-dependent Systems
9.4.6 Advantage in Dynamic Crystallography of Multiple Copies in the Asymmetric Unit
9.4.7 Exploiting Correlations in DED Maps
9.5 Evolutionary Relevance of Trajectories
References
Appendix A Review of Crystallography
Index
End User License Agreement
List of Tables
CHAPTER 06
Table 6.1 Operating characteristics of...
CHAPTER 08
Table 8.1 NMR time constants.
List of Illustrations
CHAPTER 01
Figure 1.1 Photolysis and recombination...
Figure 1.2 The gait of...
Figure 1.3 Some simple chemical...
Figure 1.4 Time scales of...
CHAPTER 02
Figure 2.1 Interconversion of X...
Figure 2.2 Formation of the...
Figure 2.3 Dependence of free...
CHAPTER 03
Figure 3.1 DED maps of...
Figure 3.2 Chromophores of sensory...
Figure 3.3 Spectroscopic and schematic...
Figure 3.4 Comparison of time...
CHAPTER 04
Figure 4.1 Dependence of scattering...
Figure 4.2 Domain diversity of...
CHAPTER 05
Figure 5.1 Ewald construction for...
Figure 5.2 Ewald construction for...
Figure 5.3 Ewald construction for...
Figure 5.4 Ewald construction for...
Figure 5.5 The kinetics of...
Figure 5.6 Plane polarized absorption...
Figure 5.7 The time dependence...
Figure 5.8 SAXS experimental setup...
Figure 5.9 I(q) plot...
Figure 5.10 The averaging process...
Figure 5.11 Kratky plot. Kratky...
Figure 5.12 Protein quake studied...
Figure 5.13 Cytochrome c folding...
CHAPTER 06
Figure 6.1 Peak brightness. Comparison...
Figure 6.2a Cartoon of storage...
Figure 6.2b Plan of the...
Figure 6.3 Formation of electron...
Figure 6.4 Energy spectrum of...
Figure 6.5 Timing structure of...
Figure 6.6 JUNGFRAU detector. Left...
Figure 6.7 Layout of the...
Figure 6.8 Main components of...
CHAPTER 07
Figure 7.1 Flow chart of...
Figure 7.2 Structure factor diagram...
Figure 7.3 Block diagram of...
Figure 7.4 TRX study of...
Figure 7.5 Electron-transfer steps...
Figure 7.6 Light-induced electron...
CHAPTER 08
Figure 8.1 Schematic representation of...
Figure 8.2 Three views of...
Figure 8.3 Flowchart representation of...
Figure 8.4 Analysis of data...
Figure 8.5 Allosteric behavior of...
Figure 8.6 Processes triggered when...
Figure 8.7 X-ray absorption...
Figure 8.8 Experimental setup for...
Figure 8.9 Schematic illustration of...
Figure 8.10 Mn Kβ...
Figure 8.11 Nuclear spin. Panel...
Figure 8.12 The pulsed NMR...
Figure 8.13 NMR relaxation. NMR...
Guide
Cover
Title Page
Copyright Page
Dedication
Table of Contents
List of Figures
Acknowledgments
Acronyms/Abbreviations
Units
Begin Reading
Appendix A Review of Crystallography
Index
End User License Agreement
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List of Figures
1.1 Photolysis and recombination of CO with crystalline horse hemoglobin after flash photolysis.
1.2 The gait of a horse.
1.3 Some simple chemical kinetic mechanisms.
1.4 Time scales of structural processes and experimental techniques.
2.1 Interconversion of X and Y state.
2.2 Formation of the pre-steady state and buildup of the steady state.
2.3 Dependence of free energy on the reaction coordinate in a schematic reaction.
3.1 DED maps of the entire PYP molecule.
3.2 Representative chromophores and their photochemistry.
3.3 Spectroscopic and schematic electronic transitions in photoactive yellow protein.
3.4 Comparison of time-resolved DED maps of the chromophore of PYP and its pocket, obtained at the LCLS/XFEL and BioCARS/APS.
4.1 Dependence of scattering processes on X-ray energy.
4.2 Domain diversity of proteins containing a LOV domain.
5.1 Ewald construction for monochromatic diffraction with crystal rotation.
5.2 Ewald construction for Laue diffraction: stationary crystal, wide bandwidth.
5.3 Ewald construction for Laue diffraction: stationary crystal, narrow bandwidth.
5.4 Ewald construction for Laue diffraction: volume stimulated.
5.5 The kinetics of time dependence in a simple chemical kinetic mechanism.
5.6 Plane polarized absorption spectra of a single PYP crystal.
5.7 The time dependence of the photocycle of wild type PYP.
5.8 SAXS experimental setup.
5.9 I(q) plot with resolution ranges.
5.10 The averaging process in XSS.
5.11 Kratky plot.
5.12 Protein quake studied by solution scattering.
5.13 Cytochrome c folding dynamics landscape.
6.1 Peak brightness.
6.2a Cartoon of storage ring, insertion devices, and beamlines.
6.2b Plan of the European Synchrotron Radiation Facility.
6.3 Formation of electron microbunches.
6.4 Energy spectrum of a SASE pulse.
6.5 Timing structure of X-ray pulses at the European XFEL.
6.6 JUNGFRAU detector.
6.7 Layout of the CXI instrument.
6.8 Main components of the CXI instrument.
7.1 Flow chart of steps in the improvement and analysis of DED maps.
7.2 Structure factor diagram for DED map coefficients F.
7.3 Block diagram of matrices involved in SVD.
7.4 TRX study of the photocycle of PYP as a function of temperature.
7.5 Electron-transfer steps of the photosynthetic reaction center of B. viridis.
7.6 Light-induced electron density changes in BvRC at the site of photo-oxidation.
8.1 Schematic representation of the standard free-energy landscape for the catalytic network of an enzyme reaction.
8.2 Three views of a cryo-EM map of the 80S ribosome from yeast.
8.3 Flowchart representation of the overall computational approach.
8.4 Analysis of data falling into a single projection direction by manifold embedding.
8.5 Allosteric behavior of the ryanodine receptor type 1 (RyR1) in the absence and presence of key ligands.
8.6 Processes triggered when an X-ray beam is incident on a sample.
8.7 X-ray absorption spectroscopy.
8.8 Experimental setup for femtosecond X-ray emission spectroscopy.
8.9 Schematic illustration of simultaneous XRD and XES measurements.
8.10 Mn Kβ X-ray emission spectra of PS-II.
8.11 Nuclear spin.
8.12 The pulsed NMR experiment.
8.13 NMR relaxation.
A.1 Bragg planes.
A.2 Bragg construction.
A.3 Crystal and reciprocal lattice.
A.4 Ewald construction.
Acknowledgments
A book such as this could not have been completed without the advice and good counsel of many scientists. We’re deeply indebted to colleagues – still friends – who supplied constructive comments on drafts ranging from single chapters to the (nearly) complete text: Andy Aquila, Sean Crosson, Tom Grant, Andreas Moeglich, Abbas Ourmazd, George Phillips Jr., Joseph Piccirilli, Phoebe Rice, Marius Schmidt, Peter Schwander, Tobin Sosnick, Vukica Srajer, Emina Stojkovic, and Minglei Zhao. In particular, we acknowledge Joseph Sachleben (University of Chicago), who rewrote and reillustrated Chapter 8.5 on nuclear magnetic resonance. We incorporated nearly all their suggestions. We also thank Caitlin Cash who competently prepared many of the figures, and Andreas Moeglich for Figure 3.4. All responsibility for remaining inaccuracies and clumsy wording of course rests with us. Perfection is impossible – but “damn good” is an attainable goal.
Scientists often reflect their mentors. Both authors are old enough that unfortunately, our formal mentors Max Perutz, Quentin Gibson (Moffat), and Warner Love, Carolyn Cohen, Don Caspar (Lattman) are no longer with us. Happily, Lattman’s postdoctoral advisor Robert Huber is alive and well as this is being written.
Our own research has been driven by the enthusiasm they displayed which has infected us; we hope they would approve. That research in turn has been motivated and carried forward by generations of students, postdocs, and scientific colleagues, in our own labs and X-ray facilities worldwide. In addition to those listed above, Keith Moffat notes Marian Szebenyi, Don Bilderback, Michael Wulff, Dominique Bourgeois, Wilfried Schildkamp, Xiaojing Yang, Zhong Ren, Sudar Rajagopal, Ben Perman, and Spencer Anderson, together with generations of users such as Michael Rossmann, Jack Johnson, and Ada Yonath at MacCHESS/CHESS and BioCARS/APS. He’s very conscious that many more names could be added to the list of users, all of whom contribute to the ongoing success of these facilities.
Eaton Lattman is also indebted to most of those named above. He has also had many invaluable collaborators and trainees whose work and creativity allowed his laboratory to flourish. Among these are Patrick Loll, Apostolos Gittis, Wayne Hendrickson, Lisa Keefe, George Rose, Mario Amzel, and Bertrand Garcia-Moreno. Many more names could readily be added.
Lattman also wants to offer special thanks to his coauthor Keith Moffat who introduced him to the delights and frustrations of SR data collection in the early days of MacCHESS. The user consortium BioXFEL, which he directed and whose Advisory Committee Moffat once chaired, played a dominant role in informing their interest and knowledge of XFELs.
Sarah Higginbotham was the persuasive Acquisitions Editor at John Wiley and Sons who, starting with a cold call, persuaded us that we both should and could undertake this book on a novel topic, seeking to expand decades of powerful – but of necessity limited – static structure determination into dynamics and kinetics. Advice while we considered whether to proceed and if so how, was offered by two friends very experienced in publishing: John McMurry (Cornell, author of numerous textbooks in chemistry) and Garrett Kiely (Director of the University of Chicago Press). Stefanie Volk and latterly, Richa John expertly guided our efforts into print, aided behind the scenes by the copyediting and production teams at Integra. We thank them all. We particularly thank the artist Greg Stewart and the Media Manager Manuel Gnida at the Stanford Linear Accelerator Center for the spectacular cover art and permission to use it, and Tanya Domeier at Wiley who expertly coordinated the cover design.
Last but certainly not least, we owe a large debt to our wives Anne Simon Moffat and Susan Pfeiffer. They inspired our efforts, gently criticized run-on sentences and jargon, and got us back on track when writers’ block struck. At a more practical but equally important level, Anne announced “lunch is ready!” when Keith became immersed - all too frequently - in the text.
Acronyms/Abbreviations
ADE
Acoustic droplet ejection
ADP, ATP
Adenosine diphosphate, adenosine triphosphate
AGIPD
Adaptive gain individual pixel detector
AI
Artificial intelligence
AMD
Accelerated molecular dynamics
APS
Advanced Photon Source at Argonne National Laboratory
ASIC
Application-specific integrated circuit
c
Velocity of light
CAT
Collaborative Access Team at the Advanced Photon Source, Argonne National Laboratory
CD
Circular dichroism
CESR
Cornell Electron Storage Ring
CEST
Chemical exchange magnetization transfer
CHESS
Cornell High Energy Synchrotron Source
C
p
, C
v
Specific heat at constant pressure or constant volume
CPMG
Carr-Purcell-Meiboom-Gill
Cryo
Cryogenic
Cryo-EM
Cryoelectron microscopy
CTF
Contrast transfer function
DED
Difference electron density
D
max
Maximum particle dimension in solution scattering
E
Energy of an X-ray photon or an electron beam in a storage ring
ε
Emittance of an electron beam
ELA
Energy landscape analysis
ESRF
European Synchrotron Radiation Facility, Grenoble, France
EuXFEL
European X-ray Free Electron Laser, Hamburg, Germany
EXAFS
Extended X-ray absorption fine structure
F
Larmor frequency of a radiofrequency pulse in NMR
FAD
Flavin adenine nucleotide
FMN
Flavin mononucleotide
FT
Fourier Transform
FWHM
Full width half maximum
G
Gibbs free energy
GDVN
Gas dynamic virtual nozzle
GPCR
G-protein-coupled receptor
H
Enthalpy
HDX
Hydrogen-deuterium exchange
HIV
Human immunodeficiency virus
hkl
Coordinates of a point in the reciprocal lattice
HSQC
Heteronuclear single quantum coherence
IR
Infrared
ITC
Isothermal calorimetry
k
Denotes a rate coefficient
κ
Transmission coefficient across an energy barrier
KB
Kirkpatrick-Baez focusing mirror pair
k
B
Boltzmann constant
K
M
Michaelis constant
λ
X-ray wavelength
LCLS
Linac Coherent Light Source, at the Stanford Linear Accelerator Center
LCP
Lipidic cubic phase
LOV
Light-oxygen-voltage
MBA
Multiple bend achromat
MD
Molecular dynamics
MFX
Macromolecular femtosecond crystallography beamline at the Linac Coherent Light Source
MS
Mass spectrometry
MT
Magnetization transfer
NAD, NADH, NADH
2
Nicotinamide adenine dinucleotide
NBD
Nucleotide binding domain
NMR
Nuclear magnetic resonance
NOESY
Nuclear Overhauser Effect Spectroscopy
NSLS
National Synchrotron Light Source, Brookhaven National Laboratory
OYE
Old Yellow Enzyme
PAS
Per-ARNT-Sim domain
PD
Projection direction
PDB
Protein Data Bank
PF
Photon Factory, Tsukuba, Japan
PRC
Photosynthetic reaction center
PS-II
Photosystem II
PYP
Photoactive yellow protein
Q
Quantum yield
R
Gas constant
RDC
Residual Dipolar Coupling
RF
Radiofrequency
R
g
Radius of gyration
RLP
Reciprocal lattice point
Rms
Root mean square; rmsd Root mean square displacement
RNA
Ribonucleic acid
S
Entropy
S
Svedberg (unit of sedimentation in a centrifuge)
σ
Sigma; the rms value of the difference electron density across the asymmetric unit
SAD, MAD
Single (Multiple) wavelength anomalous dispersion
SASE
Self-amplified spontaneous emission
SAXS
Small angle X-ray scattering
SFX
Serial femtosecond crystallography
SP
Special pair
SPB
Single particles, clusters and biomolecules beamline at the EuXFEL
SPEAR
Stanford Positron Electron Accelerator Ring
SPI
Single particle imaging
SR
Storage ring
SSC
Serial sample chamber
SSX
Serial synchrotron crystallography
SV
Singular vector; rSV right singular vector; lSV left singular vector
SVD
Singular value decomposition
SX
Serial crystallography
τ
Relaxation time
T
1
Longitudinal relaxation time, in NMR
T
2
Transverse relaxation time, in NMR
TR
Time-resolved
TRX
Time-resolved crystallography
TT
Timing tool at the LCLS
U
Potential energy function or force field
UV
Ultraviolet
WAXS
Wide angle X-ray scattering
WT
Wild type
XANES
X-ray absorption near edge spectroscopy
XAS
X-ray absorption spectroscopy
XES
X-ray emission spectroscopy
XFEL
X-ray free electron laser
XSS
X-ray solution scattering
1D, 2D, 3D
One-, two-, or three-dimensional
Units
Length, Time, Concentration
m cm mm µm nm
meter, centimeter, millimeter, micrometer, nanometer
s ms µs ns ps fs as
second, millisecond, microsecond, nanosecond, picosecond, femtosecond, attosecond
M, mM, µM, nM, pM
molar, millimolar, micromolar, nanomolar, picomolar
Miscellaneous
s
–1
Per second (first order rate coefficient)
M
–1
s
–1
Per molar per second (second order rate coefficient)
kV
Kilovolt (voltage)
KeV
Kiloelectronvolt (energy of a photon or electron)
GeV
Gigaelectronvolt (energy of an electron)
J, kJ
Joule, kilojoule (energy)
kJ/mol
kiloJoule per mole (energy in molar units)
kcal
Kilocalorie (energy)
kcal/mol
Kilocalorie per mole (energy in molar units)
Da, kDa
Dalton, kilodalton (molecular mass)
Hz, kHz
Hertz, kilohertz (frequency)
K
Kelvin (temperature)
C
Celsius (temperature)
mA
milliamp (current)
GW
GigaWatt (power)
Gy GGy
Gray, GigaGray (radiation dose)
mrad
milliradian (angle)
1 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 even abolish activity and mechanism in the crystal. For time-resolved crystallography to be physiologically useful, we must confirm that mechanism in the crystal is similar to mechanism and function in the authentic, physiological environment.
This is by no means a new problem. In the earliest days of protein crystallography, a fundamental question arose: are the molecules in the crystal biologically active? The very first, near-atomic resolution structure of any protein was determined by John Kendrew and colleagues in 1960, that of myoglobin, a simpler, single subunit relative of hemoglobin (Kendrew et al. 1960). The relevance of the crystal structure of myoglobin to its physiology was at once questioned. As an oxygen storage protein, myoglobin has the relatively simple physiological function of binding and release of molecular oxygen. The crystal structure showed that the iron atom at the center of the heme group to which molecular oxygen binds was buried in the interior of myoglobin. This raised the possibility that the protein surrounding the heme might hinder access to the iron by molecules of the dimensions of oxygen.
The biophysicist Britton Chance and colleagues therefore sought to test “…the possibility that the structures of crystalline and dissolved [myoglobin] are not identical” (Chance et al. 1966). Hence, their functions might differ quantitatively or worse yet, qualitatively. Chance was the first to measure biological activity in any protein crystal and compare it directly with solution. As a pioneer in stopped-flow kinetic techniques based on rapid mixing (Chapter 3.3.2.1), he had designed the necessary mixing apparatus to fit in an elegant, fully portable leather briefcase. (Expensive apparatus and world-class competition were no barriers. Better off than most scientists, he had won a gold medal in yachting at the Olympic Games in 1952.)
Kendrew’s initial crystals contained the oxidized form of myoglobin known as metmyoglobin whose ferric iron can bind and release small, oxygen-sized molecules such as cyanide and azide. Access of cyanide or azide to the ferric heme iron closely resembles that of oxygen to the ferrous heme iron in the authentic, physiological reaction. Chance applied his rapid mixing, stopped-flow kinetic techniques to initiate the reaction of metmyoglobin in a slurry of tiny crystals and in solution. He monitored progress of the reaction with ms time resolution, through the substantial change in optical absorbance that accompanies binding of azide. The relatively simple function of azide binding was indeed qualitatively retained in crystals but occurred with a reaction rate that was quantitatively different, some 20-fold lower in crystals of 5–10 μm dimensions than in solution. The reaction rate might have been lowered by hindered diffusion of azide through the solvent channels between the myoglobin molecules in the crystals, or by restriction of rate-contributing structural changes in the myoglobin molecule itself. Although it was unlikely that the structural changes in the molecule were large-scale, it was a realistic possibility that they were small-scale. For example, these changes could arise from the necessity to displace a sulfate ion derived from the crystallization solvent that was non-covalently bound to the distal histidine side chain. This histidine lies on the likely binding path of azide from the solvent to the heme. In a prescient observation, Chance concluded that “…transitional conformation changes are restricted in the crystalline state and diminish the reactivity with azide…” and went on to note that “…the problem can ultimately be explored by rapid methods for investigating protein structure in the transition [sic] state” (Chance et al. 1966). Just so! We give a modern view of the fleeting nature of the transition state that lies between two short-lived, transient intermediates in Chapter 2.5.
The determination of high-resolution crystal structures of other proteins such as hemoglobin and the enzymes lysozyme, α-chymotrypsin, and ribonuclease-S in the middle to late 1960s made discussion of possible differences in structure and reactivity between crystals and solution both more general and more urgent. In seminal research (Parkhurst and Gibson 1967) directly attacked the question of the physiological relevance of crystal structures and purified solutions, once more using heme proteins. They compared the reaction of CO with the ferrous form of horse hemoglobin under three very different conditions: in the authentic physiological environment of the erythrocyte, in the biochemical environment of a dilute solution of purified hemoglobin, and in the crystallographic environment of a polycrystalline slurry. Similar reaction properties under these three conditions would support the physiological relevance of results on purified solutions and crystals. Conversely, very different reaction properties would suggest that purification and crystallization were modifying hemoglobin, perhaps to the point of physiological irrelevance of the crystal structure. This reaction offers several experimental advantages. The CO-bound form of heme proteins such as hemoglobin and myoglobin is light-sensitive, which enables the covalent bond between CO and the ferrous heme iron to be readily broken by a light pulse in the visible region of the spectrum. The photo-dissociated CO diffuses briskly away from the heme and rebinds in the dark after the light pulse has terminated. Reaction initiation by a light pulse avoids the need for rapid mixing and the ensuing, slower diffusion processes of CO or azide into crystals (Chapter 3.3.2), both of which might influence the overall reaction course. The time resolution can be improved from the ms range characteristic of mixing reactions to the μs range by using a short light pulse, which also takes advantage of the high quantum yield of the photodissociation reaction. As with azide binding to myoglobin, the progress of the CO rebinding reaction to hemoglobin can readily be measured optically (Figure 1.1).
Figure 1.1 Photolysis and recombination of CO with crystalline horse hemoglobin after flash photolysis. The kinetics of recombination of CO from a thin film of polycrystalline slurry were followed optically. The ordinate shows the % of deoxyhemoglobin (Hb). Solid lines calculated, dashed lines observed; flash energies of 2025, 1500, and 900 J. Parkhurst and Gibson 1967/ELSEVIER/Licensed under CC BY 4.0.
However, hemoglobin is considerably more complicated than myoglobin in its structure, function, and the structural changes that accompany oxygen or CO binding and release. Myoglobin is monomeric with a single polypeptide chain, but hemoglobin is tetrameric with four globin chains of two types denoted α and β, each of which contains a heme that binds and releases oxygen or CO. The amino acid sequences of the chains – their primary structures – are closely related to each other and to that of the single chain of myoglobin. Correspondingly, the overall folds – their tertiary structures – of the individual chains and of myoglobin are similar. The crystal structures of deoxyhemoglobin with no oxygen or CO bound, and that of methemoglobin (a proxy for the oxygen- and CO-bound forms) differ slightly in the tertiary structure of each chain but substantially in the quaternary structure of the molecule. That is, the structures of deoxy- and CO-hemoglobin differ in the spatial disposition of the four chains with respect to each other and the nature of the interfaces between the chains (Muirhead et al. 1967). Aspects of the function of hemoglobin such as the binding reactions of oxygen and CO also differ substantially from those of myoglobin.
In the erythrocyte and dilute solution, Gibson found that photodissociation of CO from the hemes was followed by two bimolecular rates of CO rebinding denoted fast and slow. In the crystal only one bimolecular fast rate was observed; the slow rate was absent. The fast rates are closely similar in magnitude in the erythrocytes, dilute solution, and crystals (see Table 1.1 of Parkhurst and Gibson 1967). Whatever structures give rise to this rate, they are for practical purposes identical under these three very different experimental conditions.
The first important conclusion is that hemoglobin in erythrocytes, solution, and crystals quantitatively retains the function represented by this fast reaction. Thus, the results confirm the physiological relevance of the crystal structure of the reactant, CO-bound form, and of the immediate photoproduct. The second conclusion follows from the absence of the slow reaction in the crystal. We now attribute the fast reaction to hemoglobin in the quaternary structure of the reactant, CO-bound form, and the slow reaction to the quite different quaternary structure of the ultimate photoproduct, the deoxy form. The transition in quaternary structure and from the fast to the slow rebinding forms in hemoglobin underlies its unusual cooperativity in oxygen and CO binding, a distinguishing, functional property not found in myoglobin. The change in quaternary structure from the fast to the slow form is unconstrained in the erythrocyte and dilute solution and occurs more rapidly than CO rebinding. However, the change is apparently constrained by the intermolecular contacts in this crystal form. That is, a functionally critical reaction of hemoglobin, namely the change in quaternary structure from the CO-bound form to the deoxy form, is qualitatively altered in this crystal.
However, many protein systems are highly polymorphic. The same protein or the homologous protein from other species can be crystallized under a range of solvent conditions in many different space groups, each with a different crystal lattice, intermolecular interfaces, spatial constraints, and sensitivity to large structural changes. It is often possible to discover a crystal space group compatible with whatever large structural changes the system exhibits. This is indeed the case with hemoglobin. One of the best pieces of evidence that crystallization does not interfere with tertiary and quaternary structure comes from the many cases in which a given molecule – such as hemoglobin – shows the same overall structure, though crystallized under very different conditions.
All is not lost but the cautionary tale remains. Activity and mechanism in the crystal, or indeed in solution, on a cryo-EM grid or in other forms, may be altered from the physiological state.
1.3 Other Structure-informing Techniques
These classical experiments emphasize the strong desirability of preceding or at least, paralleling dynamic structural studies by optical, spectroscopic studies in solution and in polycrystalline slurries of tiny single crystals, in relevant space groups. Exploring a variety of sample conditions and techniques enables crystals to be selected in which the molecules clearly retain the desired reactivities. Selection may also identify a time range when spectroscopically interesting changes do NOT occur. In such a time range only a single intermediate structure may be present, which simplifies determination of the crystal structure of that intermediate (Chapter 5.1.4).
A more general conclusion is that for dynamic studies to be most relevant, the sample and experimental conditions must permit the desired reaction to proceed with minimum constraints. This conclusion applies to all techniques and does not depend on the structural technique actually used. In principle, any static structural technique can be extended to the time domain, thus adding a dynamic aspect. This emphasizes the desirability of dynamic studies that offer the near-atomic structural resolution of crystallography but do not require such non-biological aspects as unusual solvents, high vacuum, dehydration, or crystallization. In addition to time-resolved X-ray crystallography, we therefore consider in more detail a number other structure-based, experimental techniques and their application to dynamic studies: time-resolved solution X-ray scattering (Chapter 5.2), nuclear magnetic resonance (Chapter 8.5), single particle imaging by cryo-EM (Chapter 8.2), X-ray spectroscopies (Chapter 8.4), and hydrogen-deuterium exchange (Chapter 8.6). The last can identify flexible, solvent-accessible regions. In a powerful combination of experiment and computation, interpretation of today’s successful experimental approaches to dynamics by structure and spectroscopy can also be aided by recently-developed theoretical and computational approaches such as energy landscape analysis (Chapter 8.3). Extension of powerful, artificial intelligence-based predictions of static protein structures (Jumper et al. 2021) to dynamic structures offers a new challenge (Chapter 9).
Quasi-structural techniques such as spectroscopies complement these directly structure-based techniques. Optical spectroscopic studies are based on electronic or vibrational transitions in a naturally occurring chromophore such as flavin mononucleotide (FMN) or heme that absorbs or fluoresces in the visible region of the spectrum; or of an aromatic side chain such as the indole of tryptophan that absorbs in the near-ultraviolet (UV) region. They may probe a general spectral property such as absorbance in the infrared (IR) region (Chapter 3.3.2.3). Since heme and flavin are near-planar and optically anisotropic, their orientation in the crystal may be determined by illumination with plane-polarized light. Circular dichroism (CD) probes the overall secondary structure of a protein; fluorescence spectroscopies probe the immediate environment of the fluorophore, which may for example be an indole side chain or an added dye; fluorescence resonance energy transfer reveals the distance between donor and acceptor dyes; and vibrational spectroscopies in the IR offer wider scales of structure and span many atoms whose chemical nature and even their identity in the primary structure may be established. Electron paramagnetic resonance spectroscopy of an added paramagnetic species – a spin label – can directly reveal its extent of dynamic motion and relate that motion to structure (Moffat 1971).
Almost all static, quasi-structural spectroscopic techniques are speedy to apply, at least by the standards of crystallography. They don’t require crystals, and directly detect the rates of change in the structural property and sometimes their extent. The limitations of quasi-structural techniques usually do not lie in experimental detection of the change, but in their structural interpretation. If the technique can also be applied to a polycrystalline slurry or even to a single larger crystal or a single cell, so much the better. Recapitulation of the Parkhurst and Gibson experiment remains powerful. For example, single crystal optical studies can be conducted by absorption spectroscopy in the near-IR (say, 700 – 1000 nm) where the extinction coefficient and hence the crystal absorbance is low despite the protein concentrations, often as high as 1–50 mM, found in crystals.
Structural and quasi-structural techniques may also be classed into those which reveal global information about an entire protein such as X-ray scattering, CD and vibrational IR spectroscopies; and those which provide local information about the environment of a specific component, such as optical absorption spectroscopy of a flavin, tryptophan fluorescence, or electron paramagnetic resonance spectroscopy of a spin label. This introduces a note of caution. The dynamics of the observables in a local technique may not exactly parallel those in a global, directly structure-based technique. The techniques probe quite different scales of structure. For example, the different protein structures of the reaction intermediates of a flavin-containing enzyme may all exhibit closely identical optical absorption spectra of the flavin, a local property that depends very largely on its redox state.
1.4 Dynamics, Kinetics, Movies, Pathways, and Functional Trajectories
Much depends on the consistent use of terminology in structural dynamics, as in many scientific areas. We expand here on our usage of key words and phrases, their meaning and applicability.
The most general scientific usage of dynamic means varying with time or time-dependent. The exact meaning depends on the discipline. For example, in mathematics a system in which a function describes the motion of a point in space is denoted a dynamical system. In the fundamentals of X-ray crystallography (Rupp 2010), dynamical diffraction characterizes in detail the repeated, multiple scattering of an electromagnetic X-ray wave by the electrons associated with spatially separated atoms. This approach contrasts with kinematic diffraction, a treatment of simpler, single scattering by crystals which is nevertheless adequate to describe the position of diffraction spots in reciprocal space and the intensity of each spot. Single scattering in kinematic diffraction underlies most crystallography as we know it and all of static and dynamic structure determination in chemistry and biology. Despite the adjectives dynamical or kinematic, atomic motion is not explicitly considered in either treatment of diffraction (!). The X-ray wave is moving, not the atoms and their electrons in the lattice. Time-resolved X-ray scattering or more specifically, time-resolved crystallography is based on a straightforward extension of kinematic diffraction to incorporate atomic motion (Chapter 5.1).
The distinction between dynamics and kinetics is critical and extends beyond terminology to the fundamentals of experimental approaches. An experiment in dynamics probes the variation with time of a property of a single molecule or entity such as the famous Muybridge horse (Figure 1.2). In contrast, an experiment in kinetics probes the variation with time of a property measured as an average over a statistically large population of molecules. A single molecule or entity exhibits dynamic behavior; a statistically large population of molecules exhibits kinetic behavior. Kinetic behavior is of course based on the underlying – but not directly observable – dynamic behavior of the individual molecules that make up the population. For example, molecular dynamics refers to the time-dependent variations in structure within a single molecule, which may be followed experimentally or more usually, by computation (Chapter 8.2). Chemical kinetics refers to the time-dependent changes in the populations of each of the states (for example, reactants, intermediates, and products) that comprise a chemical or biochemical mechanism (Chapter 2.3). (We consider an explicit thermodynamic definition of state in Chapter 2.2.) However, only the average value can be observed experimentally of a property that depends on a statistically large number of molecules in the sample. Both 3D structure and optical absorbance are examples of such a property. Each state within the sample also contains a statistically large number of molecules. Although the average structure of each state is time-independent, that average differs detectably from state to state. Hence as the reaction proceeds from the reactant via intermediate states to the product, the experimentally measurable quantity of the average structure over all molecules in the sample is time-dependent.
Figure 1.2 The gait of a horse. Photograph by Edward Muybridge; reproduced with permission from the US library of Congress.
In more specific terms, consider a reaction which proceeds via a set of states S1, S2, S3…Sj… . Let Pj be the time-independent structure of molecules in state Sj and fj(t) the population of molecules in that state, at a time t after a reaction is initiated. Then the average structure PAV(t) of all molecules in the sample is
where the summations are taken over all states SJ. The structure Pj in each state is likely to be chemically sensible (though it may be strained; Chapter 7.6). However, the average structure PAV(t) over all molecules and states need not be chemically sensible. As Equation 1.1 shows, PAV (t) is a time-dependent mixture of the time-independent structures in the individual states. This time-dependent mixture affects the total X-ray scattering by the sample (Chapter 5.1).
The raw data of experiments in crystallography, solution scattering or ultrafast spectroscopies thus arise from the simultaneous observation of the properties of a statistically large number of molecules in the sample, averaged over all molecules. A quite large protein complex may have a volume of 500 nm3. Even a tiny nanocrystal of 50 × 100 × 200 nm will thus contain around 2000 molecules of this complex, a statistically large number. It follows that all such time-dependent experiments explore chemical kinetics, not dynamics.
To reemphasize: in chemical kinetics the overall time dependence arises from the variation with time of the populations of individual states, in which each individual state has its own time-independent, average structure. An experiment in chemical kinetics thus observes the formation and decay of states. A chemical kinetic mechanism consists of a definite number of states (e.g. reactant(s), a set of intermediates, and product(s)) connected by reactions describing the formation and decay of each state. Each reaction has an associated forward (formation) and reverse (decay) rate coefficient (Chapter 2). That is, a chemical kinetic mechanism describes states and how they are connected. Figure 1.3 illustrates some simple mechanisms with four states A, B, C, and D.
Figure 1.3 Some simple chemical kinetic mechanisms. Each mechanism has four states A, B, C, and D. Conversion between states is shown by arrows.
The overall goal of structural experiments in chemical kinetics is to decide which mechanism(s) are compatible with the data, to characterize the structure of each of the states in the mechanism(s), and to determine how those states are connected and the rates with which they interconvert.
An experiment in dynamics is distinctly different. Here, the overall time dependence arises from the variation with time of the structure or spectroscopic properties of an individual molecule (more precisely, of a statistically small number of molecules). Dynamics indeed deals with states and more broadly, with pathways between states that can be directly probed by structural or spectroscopic experiments. Kinetic experiments can establish that two states are connected and the magnitudes of the forward and reverse rate coefficients. Dynamic experiments further establish the structural (or spectroscopic) pathways by which this connection occurs.
Use of the terminology movie to describe the results from chemical kinetics is tempting but scientifically misleading. (We acknowledge being tempted; (Moffat 1989).) Movies conjure up visions of motion, of time-dependence. However, the essence of chemical kinetics lies in the time-independent structures of the states that constitute a chemical kinetic mechanism. Authentic movies can however be appropriately presented. For example, the time-dependent X-ray intensity over a range of scattering angles or a time-dependent electron density map both arise from an average over all molecules present in the sample, in all states. Both vary continuously with time as the populations of the constituent states and the average X-ray scattering or electron density associated with each state rises and falls. Movies can also be made by computer-based morphing between the structures of each state. Such movies may guide the eye and help in appreciating the structural differences between states. Unfortunately, they do not contain any structural information beyond that in the time-independent structures themselves. In contrast, molecular dynamics simulations do provide new information and generate genuine movies that illustrate the continuous structural variation of a single molecule.
If it were possible to examine experimentally the structure of an individual molecule as it executed its biochemical reaction e.g. of an enzyme as it bound a substrate, catalyzed its conversion to product, and released the product, the time-varying, dynamic structure of the molecule could be continuously detected by structural or spectroscopic approaches. The more formal terminology functional trajectory denotes a pathway by which a single molecule passes from one state to the next. The functional trajectory (or more likely, the set of functional trajectories followed by many molecules) could in principle be visualized and depicted for each individual molecule as an authentic movie of structural dynamics. We could title this movie the functional trajectory of the biochemical reaction, or the pathway. This highly desirable result has not yet been achieved for an enzyme (but see a functional trajectory for the ribosome; Chapter 8.3.2). In marked contrast to experiments in chemical kinetics, authentic movies directly result from a molecular dynamics calculation. When this calculation is repeated over many individual molecules, it explicitly represents the candidate functional trajectories – with a deliberate use of the plural – between states.
However, it is becoming feasible to obtain raw experimental data on the structure of an individual molecule (or at least at present, of a larger complex) at a single point on the pathway. By repeating the experiment on each of many individual molecules and identifying the point on the reaction coordinate (Chapter 2.5) or more generally, on the high-dimensional energy landscape (Chapter 8.3) associated with each structure, the structures of the various states and the functional trajectories between them could in principle be identified (Ourmazd 2019). We consider experimental approaches to the structures of single molecules and complexes by cryo-EM (Wang et al. 2016) and X-ray scattering in Chapters 8.2, 9.2, and 9.4.
We end in Chapter 9.5 with the interesting and still open question: what is the evolutionary relevance of functional trajectories, mechanisms, and states?
1.5 The Time-resolved Experiment: An Overview
We introduce here several of the general concepts of the time-resolved experiment in structural dynamics, expand on their experimental details in Chapters 3, 4, and 5, and on their analysis and interpretation in Chapter 7. Chapter 6 considers synchrotron radiation and its production in storage ring and free electron laser X-ray sources. Chapter 8 considers non-X-ray-based structural approaches, and Chapter 9 suggests promising undersolved (or unsolved) problems in dynamics and kinetics.
1.5.1 Proof and Disproof of Mechanisms in Structurally-based Chemical Kinetics
A comprehensive structural experiment in chemical kinetics will span the complete time range of the reaction. When the data are of high quality, careful data analysis by, for example, singular value decomposition (SVD) can identify the number of distinct, orthonormal structures and the relaxation times between them (Chapter 7.4). However, each orthonormal structure is a linear combination of the structures of the authentic reactants, intermediates, and products. The coefficients that describe this linear combination are not identified by SVD itself but by the specific chemical kinetic mechanism. The mechanism depends on the linkage between the orthonormal structures, the number of states, relaxation times, and the rate coefficients for the formation and decay of each state, where each state represents a reactant, intermediate, or products. That is, the mechanism depends on how the states are connected (Figure 1.3).
All experiments in chemical kinetics have a fundamental limitation which makes identification of the specific mechanism nontrivial. Although the experiments can disprove candidate mechanisms by demonstrating that they are incompatible with the time-resolved data, they cannot prove that a particular chemical kinetic mechanism holds. Proof of that mechanism demands that all other candidate mechanisms with the observed number of orthonormal structures can be disproved. Since there are many distinct mechanisms with 4, 5, or more states, disproving all but one is a challenging task which has rarely, if ever, been achieved.
Nevertheless, two powerful routes to disproving candidate mechanisms are available. First, a candidate mechanism compatible with the orthonormal structures and associated rate coefficients (Chapter 7
