Biomolecular Kinetics

A Step-by-Step Guide

Clive R. Bagshaw

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781351646666
• Edition: 1
• Topic: Medicina
• Subtopic: Bioquímica en medicina

"a gem of a textbook which manages to produce a genuinely fresh, concise yet comprehensive guide"
–Mark Leake, University of York

"destined to become a standard reference…. Not just a 'how to' handbook but also an accessible primer in the essentials of kinetic theory and practice."
–Michael Geeves, University of Kent

"covers the entire spectrum of approaches, from the traditional steady state methods to a thorough account of transient kinetics and rapid reaction techniques, and then on to the new single molecule techniques"
–Stephen Halford, University of Bristol

This illustrated treatment explains the methods used for measuring how much a reaction gets speeded up, as well as the framework for solving problems such as ligand binding and macromolecular folding, using the step-by-step approach of numerical integration. It is a thoroughly modern text, reflecting the recent ability to observe reactions at the single-molecule level, as well as advances in microfluidics which have given rise to femtoscale studies. Kinetics is more important now than ever, and this book is a vibrant and approachable entry for anyone who wants to understand mechanism using transient or single molecule kinetics without getting bogged down in advanced mathematics.

Clive R. Bagshaw is Emeritus Professor at the University of Leicester, U.K., and Research Associate at the University of California at Santa Cruz, U.S.A.

1Introduction

1.1What Can We Learn from Kinetics?

Kinetics concerns the measurement and analysis of phenomena as a function of time. Chemical kinetics investigates the rates of interconversion of molecular species during chemical reactions. The focus of this book is on biomolecular kinetics and covers reactions in which at least one reacting species is a biopolymer, such as a protein or nucleic acid. The ultimate aim of many kinetic measurements is to understand mechanism, i.e., the sequence and timing of chemical and structural events during a reaction. The concepts used in biomolecular kinetics are based on those derived for “simple” chemical reactions. The Holy Grail of these studies is to account for the observed reaction rates from ab initio calculations using fundamental physical laws and quantum mechanics. This has been effectively achieved for simple reactions such as D + H2

HD + H in the gas phase [6]. In solution, the reactant molecules exchange energy with solvent, which may promote or hinder the chemical reaction. Calculations in the condensed phase require approximations for their computation and the agreement between experiment and theory is less good [7]. Furthermore, when the reactions involve macromolecules, further approximations are required, and even then, current computing power is rarely sufficient to model reactions over their full time course with atomic resolution.

Somewhat surprisingly, biomolecular reactions often appear to follow the relatively simple rate laws that were derived for reactions involving just a few atoms, although the parameters abstracted (e.g., rate constants) are empirical and are not easily related to the fundamental vibrational processes of atoms and small molecules. This has both “good” and “bad” consequences. The observation of simple kinetics means that the myriad of conformational states of macromolecules that must exist can be effectively lumped into one or a few ensemble states that have some kind of weighted-average properties. In this way, we can attempt to relate the few ensemble states to those observed by structural methods and make meaningful progress in understanding mechanism, albeit at a much coarser level than for small molecules in a gas phase reaction. The less good news is that the characterization of processes within the ensemble requires further investigation, as this information cannot be extracted from the observed kinetics when the latter can be explained, to within experimental precision, by simple rate laws. This brings us to the meaning of the term “elementary reaction,” which varies depending on context. A physical chemist may be concerned with reactions limited by the time scale of molecular vibrations on the time scale of 10−12 s, while a biochemist may consider the domain motion of a protein in the time scale of 10−6 s as being a single elementary step. At the other extreme, a biologist modeling reactions within a cell might consider protein synthesis as a single step. The number of elementary steps in a kinetic mechanism is therefore liable to expansion or contraction depending on the context, with the simplest model that is sufficient to account for the data under consideration being selected.

Kinetics is the core technique of enzymology, the study of Nature’s catalysts. It both defines the magnitude of the problem under study (i.e., the degree to which a reaction is speeded up over the noncatalyzed reaction) as well as provides a framework for its solution (i.e., the characterization of the alternative pathway(s) taken [8]). Every general biochemistry textbook devotes a section to the fundamentals of enzyme kinetics and describes how such measurements led to the concept of an enzyme–substrate Michaelis complex [9,10], long before detailed structural information became available. Identification of intermediates and measurement of their lifetimes remains the primary goal of kinetic assays. To this end, kinetic measurements are usually interpreted in conjunction with structural data to help define the mechanism in chemical terms. However, kinetic methods are used to study processes other than catalysis, with ligand binding and macromolecular folding being among other topics that are addressed here.

The study of enzyme kinetics has a long history primarily because small amounts of enzyme are required for an assay. When the activity of an enzyme is measured via the appearance of the product, the catalytic enhancement amplifies the signal many thousands of times, a crucial factor for many detection methods. Enzymes also demonstrate specificity for the reactions they catalyze, allowing a single enzyme type to be assayed in crude cell extracts. During the purification procedure, the catalytic activity per milligram of protein (i.e., the specific activity) increases as contaminant proteins are removed. When a constant maximum value of the specific activity is reached, it is assumed that the enzyme is pure. This aspect of kinetics is often taken for granted, but its importance is quickly rediscovered when attempts are made to purify native nonenzymic proteins where no such convenient assay exists. Nowadays, the problem is usually side-tracked by expressing a protein with a tag, such as a sequence of six to eight histidine residues, to identify and aid isolation of the required protein. However, comparison of tagged-expressed protein with tissue-extracted wild-type protein is desirable, so the use of specific activity has not become redundant.

Once purified, the usual next goal is to understand the mechanism of an enzyme. In the early days, this was normally achieved using steady-state kinetics to identify the order of binding of substrates and release of products and the rate-limiting step. Subsequently, structural information became available, which allowed a more detailed mechanism to be proposed. Following the tremendous advances in molecular biology and recombinant technology, this order is now often reversed. A protein may be expressed and crystallized before any catalytic, or other functional, activity is identified. Consequently, kinetic analysis may be the “final” procedure to be employed. Either way, an important message is that mechanism cannot be determined from structure alone. For example, a protein may be crystallized in an open conformation in the absence of substrate and a closed conformation in its presence. This might imply that the substrate induces a conformation change on binding: the so-called induced-fit mechanism. However, it is also possible that the enzyme undergoes the conformational change spontaneously and the substrate binds to the closed conformation: the conformational-selection mechanism. Distinguishing these alternatives requires kinetic analysis and is not always trivial (see Section 10.3). As with other areas of science, a mechanism may only be ruled out by the data and the “accepted” model is the simplest one that can account for the data. Often, competing models cannot be distinguished by the data but may suggest further experiments that may do so. This raises a related point. Kineticists like to argue and often they do not agree on the reaction scheme for a specific system under study. These discrepancies are frequently experimental and depend on the preparation used. Sometimes, arguments between researchers come down to the significance placed on a small deviation of experimental records from a specific model or the weight placed on circumstantial evidence. Occasionally, discrepancies come down to blatant errors in the method of analysis. Throughout this book, some common pitfalls are highlighted, such as failing to check for internal thermodynamic balance (Section 2.9) or wrongly assuming that the total concentration of a reactant is an adequate approximation for its free concentration in a kinetic or equilibrium calculations (Section 6.3.1).

Enzyme kinetics is frequently used to obtain empirical data to compare the effectiveness of different substrates and inhibitors. This approach is widely used in the characterization of drugs, which often act by activating or inhibiting a specific enzyme. Similarly, different enzymes may be compared quantitatively, whether they are natural isoforms or engineered variants. The latter approach allows the role of individual amino acids in binding and catalysis to be determined. Knowing the overall kinetic properties of an enzyme is also useful in understanding how they couple to other enzymes and control the flux through a metabolic pathway [11,12].

Nonenzymic systems are also widely studied by kinetic methods. These often concern the interaction between a macromolecule with a small molecule or another macromolecule and invariably involve a binding step early in the pathway. As binding is the first step in enzyme catalysis, many of the methods and concepts are common to both situations. While binding can be characterized at equilibrium to determine thermodynamic parameters, there is much to be gained by measuring the kinetics. Indeed, some consideration of kinetics has to be included in every measurement, even if it is only to show the system has reached equilibrium. Kinetic methods allow an independent assessment of the equilibrium parameters (equilibrium constant = ratio of forward and reverse rate constants). Equilibrium constants cannot be used to determine the pathway of a reaction, because the Laws of Thermodynamics require that the energetics of alternate pathways are the same. Furthermore, living systems do not operate at equilibrium and so consideration of kinetics is required to understand all aspects of biochemistry.

Kinetic measurements may help understand the biological role of a process. In vitro assays have been developed to characterize the coupling between a chemical ...