and sequencing and is likely to play an increasing role in diagnosis. This article reviews, from the point of view of a physicist, the mechanisms responsible for electrophoretic separation of polyelectrolytes. This separation is mainly performed in gels, and a wide variety of migration mechanisms can come into play, depending on the polyelectrolyte’s architecture, on the electric fields applied, and on the properties of the gel. After a brief review of the thermodynamic and electrohydrodynamic principles relating to polyelectrolyte solutions, the author treats the phenomenology of electrophoresis and describes the conceptual and theoretical tools in the field. The reptation mechanisms, by which large flexible polyelectrolytes thread their way through the pores of the gel matrix, play a prominent role. Biased reptation, the extension of this model to electrophoresis, provides a very intuitive framework within which numerous physical ideas can be introduced and discussed. It has been the most popular theory in this domain, and it remains an inspiring concept for current development. There have also been important advances in experimental techniques such as single-molecule viodeomicroscopy and the development of nongel separation media and mechanisms. These, in turn, form the basis for fast-developing and innovative technologies like capillary electrophoresis, electrophoresis on microchips, and molecular ratchets.

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Electrophoresis of DNA and other polyelectrolytes: Physical mechanisms

1. Introduction: Overview of CA as a Model
Carbonic anhydrase (CA, EC 4.2.1.1) is a protein that is especially well-suited to serve as a model in many types of studies in biophysics, bioanalysis, the physical-organic chemistry of inhibitor design, and medicinal chemistry. In vivo, this enzyme catalyzes the hydration of CO2 and the dehydration of bicarbonate (eq 1).


CO2+H2O⇌HCO3−+H+

(1)


The active site of α-CAs comprises a catalytic ZnII ion coordinated by three imidazole groups of histidines and by one hydroxide ion (or water molecule), all in a distorted tetrahedral geometry. This grouping is located at the base of a cone-shaped amphiphilic depression, one wall of which is dominated by hydrophobic residues and the other of which is dominated by hydrophilic residues.1 Unless otherwise stated, “CA” in this review refers to (i) various isozymes of α-CAs or (ii) the specific α-CAs human carbonic anhydrases I and II (HCA I and HCA II) and bovine carbonic anhydrase II (BCA II); “HCA” refers to HCA I and HCA II; and “CA II” refers to HCA II and BCA II.

CA is particularly attractive for biophysical studies of protein–ligand binding for many reasons. (i) CA is a monomeric, single-chain protein of intermediate molecular weight (~30 kDa), and it has no pendant sugar or phosphate groups and no disulfide bonds. (ii) It is inexpensive and widely available. (iii) It is relatively easy to handle and purify, due in large part to its excellent stability under standard laboratory conditions. (iv) Amino acid sequences are available for most of its known isozymes. (v) The structure of CA, and of its active site, has been defined in detail by X-ray diffraction, and the mechanism of its catalytic activity is well-understood. (vi) As an enzyme, CA behaves not only as a hydratase/anhydrase with a high turnover number but also as an esterase (a reaction that is easy to follow experimentally). (vii) The mechanism of inhibition of CA by ligands that bind to the ZnII ion is fairly simple and well-characterized; it is, therefore, easy to screen inhibitors and to examine designed inhibitors that test theories of protein–ligand interactions. (viii) It is possible to prepare and study the metal-free apoenzyme and the numerous variants of CA in which the ZnII ion is replaced by other divalent ions. (ix) Charge ladders of CA II—sets of derivatives in which acylation of lysine amino groups (−NH3+ → −NHAc) changes the net charge of the protein—allow the influence of charge on properties to be examined by capillary electrophoresis. Some disadvantages of using CA include the following: (i) the presence of the ZnII cofactor, which can complicate biophysical and physical-organic analyses; (ii) a structure that is more stable than a representative globular protein and, thus, slightly suspect as a model system for certain studies of stability; (iii) a function—interconversion of carbon dioxide and carbonate—that does not involve the types of enzyme/substrate interactions that are most interesting in design of drugs; (iv) a catalytic reaction that is, in a sense, too simple (determining the mechanism of a reaction is, in practice, usually made easier if the reactants and products have an intermediate level of complexity); and (v) the absence of a solution structure of CA (by NMR spectroscopy). The ample X-ray data, however, paint an excellent picture of the changes (which are generally small) in the structure of CA that occur on binding ligands or introducing mutations.

The most important class of inhibitors of CA, the aryl-sulfonamides, has several characteristics that also make it particularly suitable for physical-organic studies of inhibitor binding and in drug design: (i) arylsulfonamides are easily synthesized; (ii) they bind with high affinity to CA (1 μM to sub-nM); (iii) they share one common structural feature; and (iv) they share a common, narrowly defined geometry of binding that exposes a part of the ligand that can be easily modified synthetically. There are also many non-sulfonamide, organic inhibitors of CA, as well as anionic, inorganic inhibitors.

We divide this review into five parts, all with the goal of using CA as a model system for biophysical studies: (I) an overview of the enzymatic activity and medical relevance of CA; (II) the structure and structure–function relationships of CA and its engineered mutants; (III) the thermodynamics and kinetics of the binding of ligands to CA; (IV) the effect of electrostatics on the binding of ligands to and the denaturation of CA; and (V) what makes CA a good model for studying protein–ligand binding and protein stability.



1.1. Value of Models 
CA serves as a good model system for the study of enzymes. That is, it is a protein having some characteristics representative of enzymes as a class, but with other characteristics that make it especially easy to study. It is a moderately important target in current medicinal chemistry: its inhibition is important in the treatment of glaucoma, altitude sickness, and obesity; its overexpression has recently been implicated in tumor growth; and its inhibition in pathogenic organisms might lead to further interesting drugs.2,3 More than its medical relevance, its tractability and simplicity are what make CA a particularly attractive model enzyme.

The importance of models in science is often underestimated. Models represent more complex classes of related systems and contribute to the study of those classes by focusing research on particular, tractable problems. The development of useful, widely accepted models is a critical function of scientific research: many of the techniques (both experimental and analytical) and concepts of science are developed in terms of models; they are thoroughly engrained in our system of research and analysis.

Examples of models abound in successful areas of science: in biology, E. coli, S. cerevisiae, Drosophila mela-nogaster, C. elegans, Brachydanio rerio (zebrafish), and the mouse; in chemistry, the hydrogen atom, octanol as a hydrophobic medium, benzene as an aromatic molecule, the 2-norbornyl carbocation as a nonclassical ion, substituted cyclohexanes for the study of steric effects, p-substituted benzoic acids for the study of electronic effects, cyclodextrins for ligand–receptor interactions; in physics, a vibrating string as an oscillator and a particle in a box as a model for electrons in orbitals.

Science needs models for many reasons:


Focus: Models allow a community of researchers to study a common subject. Solving any significant problem in science requires a substantial effort, with contributions from many individuals and techniques. Models are often the systems chosen to make this productive, cooperative focus possible.


Research Overhead: Development of a system to the point where many details are scientifically tractable is the product of a range of contributions: for enzymes, these contributions are protocols for preparations, development of assays, determination of structures, preparation of mutants, definition of substrate specificity, study of rates, and development of mechanistic models. In a well-developed model system, the accumulation of this information makes it relatively easy to carry out research, since before new experiments begin, much of the background work–the fundamental research in a new system–has already been carried out.


Recruiting and Interdisciplinarity: The availability of good model systems makes it relatively easy for a neophyte to enter an area of research and to test ideas efficiently. This ease of entry recruits new research groups, who use, augment, and improve the model system. It is especially important to have model systems to encourage participation by researchers in other disciplines, for whom even the elementary technical procedures in a new field may appear daunting.


Comparability: A well-established model allows researchers in different laboratories to calibrate their experiments, by reproducing well-characterized experiments.


Community: The most important end result of a good model system is often the generation of a scientific community–that is, a group of researchers examining a common problem from different perspectives and pooling information relevant to common objectives.



One of the goals of this review is to summarize many experimental and theoretical studies of CA that have established it as a model protein. We hope that this summary will make it easier for others to use this protein to study fundamentals of two of the most important questions in current chemistry: (i) Why do a protein and ligand associate selectively? (ii) How can one design an inhibitor to bind to a protein selectively and tightly? We believe that the summary of studies of folding and stability of CA will be useful to biophysicists who study protein folding. In addition, we hope that the compilation of data relevant to CA in one review will ease the search for information for those who are beginning to work with this protein.

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Carbonic Anhydrase as a Model for Biophysical and Physical-Organic Studies of Proteins and Protein–Ligand Binding

High performance capillary electrophoresis is expected to be the fastest-growing analytical technique since HPLC. The method has already shown its utility in a variety of applications.

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High-performance capillary electrophoresis

Structural investigations of glycoconjugates at high sensitivity.

Poly(vinyl alcohols) (PVA) of a molecular weight of about 50 000 were applied to the modification of fused silica surfaces for the separation of large charged molecules such as proteins. Basic and acidic proteins could be separated in PVA-modified capillaries at highly optimized and analytically suitable performance with regard to efficiency, zone symmetry, and resolution. PVA can be used in the dynamic mode as an additive to the buffer medium or as a water-insoluble permanent coating on the fused silica surfaces which can be achieved by a simple procedure of thermal immobilization

Capillary Zone Electrophoresis Separations of Basic and Acidic Proteins Using Poly(vinyl alcohol) Coatings in Fused Silica Capillaries

The application of free solution capillary electrophoresis (FSCE) to the separation of protein and peptide mixtures is presented. Both qualitative and quantitative aspects of FSCE separations are considered. In addition, a brief introduction describing the separation principle behind FSCE separations and a discussion of electrophoretic mobility are included. The applications were chosen in order to highlight the selectivity of FSCE separations and to demonstrate applications of potential practical interest to the bioanalytical chemist. Comparison of FSCE relative to traditional analytical separation alternatives is stressed throughout. The examples are presented in three broad categories: protein separations, peptide separations, and the application of both to the analysis of recombinant protein products. In the first section, FSCE separations of peptide mixtures are presented which demonstrate the suitability of FSCE for the analysis of the purity of peptide samples, the homogeneity of peptide samples prior to sequencing, the identity of peptides by using electrophoretic mobility values, and the reduction of an intrachain disulfide bridge. In the second section, protein separations are presented that show the resolution of glycoproteins having the same primary structure and the separation of immune complexes from free unreacted antibody and antigen. In the final section, highly purified and well-characterized samples of biosynthetic human insulin (BHI), biosynthetic human growth hormone (hGH), and their derivatives were used to evaluate FSCE as a complement and/or alternative to conventional analytical separation techniques for the determination of purity and identity of biosynthetic human proteins. In addition, the quantitative aspects of FSCE analysis such as linearity of response, precision, and limit of detection were examined.

Application of free-solution capillary electrophoresis to the analytical scale separation of proteins and peptides.

Factors affecting the performance of capillary electophoresis separations - joule heating, electroosmosis, and zone dispersion, PD Grossman detection methods in capillary electrophoresis, TM Olefirowicz and AG Ewing quantitative aspects of capillary electrophoresis analysis, SE Moring modes of capillary - free-solution capillary electrophoresis, PD Grossman capillary gel electrophoresis, RS Dubrow fundamentals of micellar electrolinetic capillary chromatography, MJ Sepaniak, et al iso-electric focusing in capillaries, S Hjerten capillary electrophoresis in entangled polymer solutions, PD Grossman applications of capillary electrophoresis - capillary electrophoresis separations of peptides - practical aspects and applications, JC Colburn protein analysis by capillary electrophoresis, JE Wiktorowicz and JC Colburn separation of small molecules by high-performance capillary electrophoresis, CW Demarest, et al Appendix - trouble-shooting guide to capillary electrophoresis operations, JC Colburn and PD Grossman chapter references

Capillary electrophoresis : theory & practice

A semiempirical model for the electrophoretic mobilities of peptides in free-solution capillary electrophoresis.

Analysis of proteins by capillary electrophoresis requires strategies which minimize coulombic interactions with the capillary surface. Thus buffers with pH's above the isoelectric points (pI) of proteins, or near the pI of silanol are required for efficient separation. Covalent modification of the capillary surface is also effective; however, this strategy is technically difficult, abolishes endosmotic flow and suffers from the inherent lability of the siloxane bond. Finally, "dynamic coating" agents, which interact weakly with the capillary surface and therefore, must be included in the separation buffer, suffer from the potential interaction of coating agent with analytes, altering the selectivity of the system. In the following paper, we describe another approach which overcomes all of these difficulties, and demonstrate the ease of use, nondenaturing property, stability and selectivity of the coating strategy with several model protein systems.

Joel C. Colburn

Papers

Application of free-solution capillary electrophoresis to the analytical scale separation of proteins and peptides.

Capillary electrophoresis : theory & practice

A semiempirical model for the electrophoretic mobilities of peptides in free-solution capillary electrophoresis.

Separ of cationic proteins via charge reversal in capillary electrophoresis

The use of capillary electrophoresis in a micropreparative mode: methods and applications.