Kinetic partitioning between alternative protein-protein interactions controls a transcriptional switch

Biotin protein ligase as you like it: Either extraordinarily specific or promiscuous protein biotinylation

Biotin (vitamin H or B7) is a coenzyme essential for all forms of life. Biotin has biological activity only when covalently attached to a few key metabolic enzyme proteins. Most organisms have only one attachment enzyme, biotin protein ligase (BPL), which attaches biotin to all target proteins. The sequences of these proteins and their substrate proteins are strongly conserved throughout biology. Structures of both the biotin ligase- and biotin-acceptor domains of mammals, plants, several bacterial species, and archaea have been determined. These, together with mutational analyses of ligases and their protein substrates, illustrate the exceptional specificity of this protein modification. For example, the Escherichia coli BPL biotinylates only one of the >4000 cellular proteins. Several bifunctional bacterial biotin ligases transcriptionally regulate biotin synthesis and/or transport in concert with biotinylation. The human BPL has been demonstrated to play an important role in that mutations in the BPL encoding gene cause one form of the disease, biotin-responsive multiple carboxylase deficiency. Promiscuous mutant versions of several BPL enzymes release biotinoyl-AMP, the active intermediate of the ligase reaction, to solvent. The released biotinoyl-AMP acts as a chemical biotinylation reagent that modifies lysine residues of neighboring proteins in vivo. This proximity-dependent biotinylation (called BioID) approach has been heavily utilized in cell biology.

Protein oligomerization as a metabolic control mechanism: Application to apoE

It has been estimated that 30%-50% of proteins self-assemble to form complexes consisting of multiple copies of themselves. If there is a functional difference between different molecular weight forms and if these forms interconvert on a reasonable time scale then oligomerization could be an important metabolic control mechanism. The example given here is of apoE for which the oligomerization process is measured in minutes to hours and the monomer binds lipids while the tetramer does not. Examination of the literature reveals few reports on the rate constants that control the interconversion of different molecular weight forms. Perhaps it is time to collect such data.

A conserved regulatory mechanism in bifunctional biotin protein ligases

Class II bifunctional biotin protein ligases (BirA), which catalyze post-translational biotinylation and repress transcription initiation, are broadly distributed in eubacteria and archaea. However, it is unclear if these proteins all share the same molecular mechanism of transcription regulation. In Escherichia coli the corepressor biotinoyl-5'-AMP (bio-5'-AMP), which is also the intermediate in biotin transfer, promotes operator binding and resulting transcription repression by enhancing BirA dimerization. Like E. coli BirA (EcBirA), Staphylococcus aureus, and Bacillus subtilis BirA (Sa and BsBirA) repress transcription in vivo in a biotin-dependent manner. In this work, sedimentation equilibrium measurements were performed to investigate the molecular basis of this biotin-responsive transcription regulation. The results reveal that, as observed for EcBirA, Sa, and BsBirA dimerization reactions are significantly enhanced by bio-5'-AMP binding. Thus, the molecular mechanism of the Biotin Regulatory System is conserved in the biotin repressors from these three organisms.

Current Experimental Methods for Characterizing Protein-Protein Interactions

Protein molecules often interact with other partner protein molecules in order to execute their vital functions in living organisms. Characterization of protein-protein interactions thus plays a central role in understanding the molecular mechanism of relevant protein molecules, elucidating the cellular processes and pathways relevant to health or disease for drug discovery, and charting large-scale interaction networks in systems biology research. A whole spectrum of methods, based on biophysical, biochemical, or genetic principles, have been developed to detect the time, space, and functional relevance of protein-protein interactions at various degrees of affinity and specificity. This article presents an overview of these experimental methods, outlining the principles, strengths and limitations, and recent developments of each type of method.

Current Experimental Methods for Characterizing Protein-Protein Interactions

Protein molecules often interact with other partner protein molecules in order to execute their vital functions in living organisms. Characterization of protein-protein interactions thus plays a central role in understanding the molecular mechanism of relevant protein molecules, elucidating the cellular processes and pathways relevant to health or disease for drug discovery, and charting large-scale interaction networks in systems biology research. A whole spectrum of methods, based on biophysical, biochemical, or genetic principles, have been developed to detect the time, space, and functional relevance of protein-protein interactions at various degrees of affinity and specificity. This article presents an overview of these experimental methods, outlining the principles, strengths and limitations, and recent developments of each type of method.

Mechanisms of biotin-regulated gene expression in microbes

Biotin is an essential micronutrient that acts as a co-factor for biotin-dependent metabolic enzymes. In bacteria, the supply of biotin can be achieved by de novo synthesis or import from exogenous sources. Certain bacteria are able to obtain biotin through both mechanisms while others can only fulfill their biotin requirement through de novo synthesis. Inability to fulfill their cellular demand for biotin can have detrimental consequences on cell viability and virulence. Therefore understanding the transcriptional mechanisms that regulate biotin biosynthesis and transport will extend our knowledge about bacterial survival and metabolic adaptation during pathogenesis when the supply of biotin is limited. The most extensively characterized protein that regulates biotin synthesis and uptake is BirA. In certain bacteria, such as Escherichia coli and Staphylococcus aureus, BirA is a bi-functional protein that serves as a transcriptional repressor to regulate biotin biosynthesis genes, as well as acting as a ligase to catalyze the biotinylation of biotin-dependent enzymes. Recent studies have identified two other proteins that also regulate biotin synthesis and transport, namely BioQ and BioR. This review summarizes the different transcriptional repressors and their mechanism of action. Moreover, the ability to regulate the expression of target genes through the activity of a vitamin, such as biotin, may have biotechnological applications in synthetic biology.

Biotin and Lipoic Acid: Synthesis, Attachment, and Regulation

Two vitamins, biotin and lipoic acid, are essential in all three domains of life. Both coenzymes function only when covalently attached to key metabolic enzymes. There they act as "swinging arms" that shuttle intermediates between two active sites (= covalent substrate channeling) of key metabolic enzymes. Although biotin was discovered over 100 years ago and lipoic acid 60 years ago, it was not known how either coenzyme is made until recently. In Escherichia coli the synthetic pathways for both coenzymes have now been worked out for the first time. The late steps of biotin synthesis, those involved in assembling the fused rings, were well described biochemically years ago, although recent progress has been made on the BioB reaction, the last step of the pathway in which the biotin sulfur moiety is inserted. In contrast, the early steps of biotin synthesis, assembly of the fatty acid-like "arm" of biotin were unknown. It has now been demonstrated that the arm is made by using disguised substrates to gain entry into the fatty acid synthesis pathway followed by removal of the disguise when the proper chain length is attained. The BioC methyltransferase is responsible for introducing the disguise, and the BioH esterase is responsible for its removal. In contrast to biotin, which is attached to its cognate proteins as a finished molecule, lipoic acid is assembled on its cognate proteins. An octanoyl moiety is transferred from the octanoyl acyl carrier protein of fatty acid synthesis to a specific lysine residue of a cognate protein by the LipB octanoyltransferase followed by sulfur insertion at carbons C-6 and C-8 by the LipA lipoyl synthetase. Assembly on the cognate proteins regulates the amount of lipoic acid synthesized, and, thus, there is no transcriptional control of the synthetic genes. In contrast, transcriptional control of the biotin synthetic genes is wielded by a remarkably sophisticated, yet simple, system, exerted through BirA, a dual-function protein that both represses biotin operon transcription and ligates biotin to its cognate proteins.

Fatty acid synthesis in Escherichia coli and its applications towards the production of fatty acid based biofuels

The idea of renewable and regenerative resources has inspired research for more than a hundred years. Ideally, the only spent energy will replenish itself, like plant material, sunlight, thermal energy or wind. Biodiesel or ethanol are examples, since their production relies mainly on plant material. However, it has become apparent that crop derived biofuels will not be sufficient to satisfy future energy demands. Thus, especially in the last decade a lot of research has focused on the production of next generation biofuels. A major subject of these investigations has been the microbial fatty acid biosynthesis with the aim to produce fatty acids or derivatives for substitution of diesel. As an industrially important organism and with the best studied microbial fatty acid biosynthesis, Escherichia coli has been chosen as producer in many of these studies and several reviews have been published in the fields of E. coli fatty acid biosynthesis or biofuels. However, most reviews discuss only one of these topics in detail, despite the fact, that a profound understanding of the involved enzymes and their regulation is necessary for efficient genetic engineering of the entire pathway. The first part of this review aims at summarizing the knowledge about fatty acid biosynthesis of E. coli and its regulation, and it provides the connection towards the production of fatty acids and related biofuels. The second part gives an overview about the achievements by genetic engineering of the fatty acid biosynthesis towards the production of next generation biofuels. Finally, the actual importance and potential of fatty acid-based biofuels will be discussed.

Modeling protein association mechanisms and kinetics

Substantial advances have been made in modeling protein association mechanisms and in calculating association rate constants (ka). We now have a clear understanding of the physical factors underlying the wide range of experimental ka values. Half of the association problem, where ka is limited by diffusion, is perhaps solved, and for the other half, where conformational changes become rate-limiting, a number of promising methods are being developed for ka calculations. Notably, the binding kinetics of disordered proteins are receiving growing attention, with 'dock-and-coalesce' emerging as a general mechanism. Progress too has been made in the modeling of protein association kinetics under conditions mimicking the heterogeneous, crowded environments of cells, an endeavor that should ultimately lead to a better understanding of cellular functions.

A large solvent isotope effect on protein association thermodynamics

Solvent reorganization can contribute significantly to the energetics of protein-protein interactions. However, our knowledge of the magnitude of the energetic contribution is limited, in part, by a dearth of quantitative experimental measurements. The biotin repressor forms a homodimer as a prerequisite to DNA binding to repress transcription initiation. At 20 °C, the dimerization reaction, which is thermodynamically coupled to binding of a small ligand, bio-5'-AMP, is characterized by a Gibbs free energy of -7 kcal/mol. This modest net dimerization free energy reflects underlying, very large opposing enthalpic and entropic driving forces of 41 ± 3 and -48 ± 3 kcal/mol, respectively. The thermodynamics have been interpreted as indicating coupling of solvent release to dimerization. In this work, this interpretation has been investigated by measuring the effect of replacing H2O with D2O on the dimerization thermodynamics. Sedimentation equilibrium measurements performed at 20 °C reveal a solvent isotope effect of -1.5 kcal/mol on the Gibbs free energy of dimerization. Analysis of the temperature dependence of the reaction in D2O indicates enthalpic and entropic contributions of 28 and -37 kcal/mol, respectively, considerably smaller than the values measured in H2O. These large solvent isotope perturbations to the thermodynamics are consistent with a significant contribution of solvent release to the dimerization reaction.

Protein:protein interactions in control of a transcriptional switch

Protein partner exchange plays a key role in regulating many biological switches. Although widespread, the mechanisms dictating protein partner identity and, therefore, the outcome of a switch have been determined for a limited number of systems. The Escherichia coli protein BirA undergoes a switch between posttranslational biotin attachment and transcription repression in response to cellular biotin demand. Moreover, the functional switch reflects formation of alternative mutually exclusive protein:protein interactions by BirA. Previous studies provided a set of alanine-substituted BirA variants with altered kinetic and equilibrium parameters of forming these interactions. In this work, DNase I footprinting measurements were employed to investigate the consequences of these altered properties for the outcome of the BirA functional switch. The results support a mechanism in which BirA availability for DNA binding and, therefore, transcription repression is controlled by the rate of the competing protein:protein interaction. However, occupancy of the transcriptional regulatory site on DNA by BirA is exquisitely tuned by the equilibrium constant governing its homodimerization.

The detection and quantitation of protein oligomerization

There are many different techniques available to biologists and biochemists that can be used to detect and characterize the self-association of proteins. Each technique has strengths and weaknesses and it is often useful to combine several approaches to maximize the former and minimize the latter. Here we review a range of methodologies that identify protein self-association and/or allow the stoichiometry and affinity of the interaction to be determined, placing an emphasis on what type of information can be obtained and outlining the advantages and disadvantages involved. In general, in vitro biophysical techniques, such as size exclusion chromatography, analytical ultracentrifugation, scattering techniques, NMR spectroscopy, isothermal titration calorimetry, fluorescence anisotropy and mass spectrometry, provide information on stoichiometry and/or binding affinities. Other approaches such as cross-linking, fluorescence methods (e.g., fluorescence correlation spectroscopy, FCS; Förster resonance energy transfer, FRET; fluorescence recovery after photobleaching, FRAP; and proximity imaging, PRIM) and complementation approaches (e.g., yeast two hybrid assays and bimolecular fluorescence complementation, BiFC) can be used to detect protein self-association in a cellular context.

Mapping the Deltex-binding surface on the notch ankyrin domain using analytical ultracentrifugation

The Notch signal transduction pathway controls cell fate determination during metazoan development. The Notch gene encodes a transmembrane receptor that is cleaved upon activation, liberating the Notch intracellular domain, which enters the nucleus and assembles transcriptional activation complexes that drive expression of Notch-responsive genes. The most conserved region of the Notch intracellular domain is an ankyrin domain (Nank), which binds directly to the cytosolic effector protein Deltex (Dx), controlling intracellular Notch activity. However, the structural and energetic basis for this interaction remains unknown. Here, we analyze the thermodynamics and hydrodynamics of the Nank:Dx heteroassociation, as well as a weaker Nank self-association, using sedimentation velocity analytical ultracentrifugation. By comparing g(s*) and c(s) distributions, and by direct fitting of sedimentation boundaries with thermodynamic association models, we were able to characterize the Nank:Dx heterodimer, measure its affinity, and map the interaction on the surface on Nank. N- and C-terminal deletions of whole ankyrin units implicate repeats 3 and 4 as key for mediating heteroassociation. An alanine scan across the interaction loops of Nank identifies a conserved hot spot in repeats 3 and 4, centered at R127, as critical for Dx binding. In addition, we were able to detect weak but reproducible Nank homodimerization (K(d) in the millimolar range). This association is disrupted by substitution of a conserved arginine (R107) with alanine, a residue previously implicated in a functionally relevant mode of interaction within dimeric transcription complexes. The distinct binding surfaces on Nank for homotypic versus Dx interaction appear to be compatible with teterameric Notch(2):Dx(2) assembly.

In vivo tests of thermodynamic models of transcription repressor function

One emphasis of the Gibbs Conference on Biothermodynamics is the value of thermodynamic measurements for understanding behaviors of biological systems. In this study, the correlation between thermodynamic measurements of in vitro DNA binding affinity with in vivo transcription repression was investigated for two transcription repressors. In the first system, which comprised an engineered LacI/GalR homolog, mutational changes altered the equilibrium constant for binding DNA. Changes correlated with altered repression, but estimates of in vivo repressor concentration suggest a ≥25-fold discrepancy with in vitro conditions. In the second system, changes in ligand binding to BirA altered dimerization and subsequent DNA occupancy. Again, these changes correlate with altered in vivo repression, but comparison with in vitro measurements reveals a ~10-fold discrepancy. Further analysis of each system suggests that the observed discrepancies between in vitro and in vivo results reflect the contributions of additional equilibria to the transcription repression process.

The use of analytical sedimentation velocity to extract thermodynamic linkage

For 25 years, the Gibbs Conference on Biothermodynamics has focused on the use of thermodynamics to extract information about the mechanism and regulation of biological processes. This includes the determination of equilibrium constants for macromolecular interactions by high precision physical measurements. These approaches further reveal thermodynamic linkages to ligand binding events. Analytical ultracentrifugation has been a fundamental technique in the determination of macromolecular reaction stoichiometry and energetics for 85 years. This approach is highly amenable to the extraction of thermodynamic couplings to small molecule binding in the overall reaction pathway. In the 1980s this approach was extended to the use of sedimentation velocity techniques, primarily by the analysis of tubulin-drug interactions by Na and Timasheff. This transport method necessarily incorporates the complexity of both hydrodynamic and thermodynamic nonideality. The advent of modern computational methods in the last 20 years has subsequently made the analysis of sedimentation velocity data for interacting systems more robust and rigorous. Here we review three examples where sedimentation velocity has been useful at extracting thermodynamic information about reaction stoichiometry and energetics. Approaches to extract linkage to small molecule binding and the influence of hydrodynamic nonideality are emphasized. These methods are shown to also apply to the collection of fluorescence data with the new Aviv FDS.

Biotinylation, a post-translational modification controlled by the rate of protein-protein association

Biotin protein ligases catalyze specific covalent linkage of the coenzyme biotin to biotin-dependent carboxylases. The reaction proceeds in two steps, including synthesis of an adenylated intermediate followed by biotin transfer to the carboxylase substrate. In this work specificity in the transfer reaction was investigated using single turnover stopped-flow and quench-flow assays. Cognate and noncognate reactions were measured using the enzymes and minimal biotin acceptor substrates from Escherichia coli, Pyrococcus horikoshii, and Homo sapiens. The kinetic analysis demonstrates that for all enzyme-substrate pairs the bimolecular rate of association of enzyme with substrate limits post-translational biotinylation. In addition, in noncognate reactions the three enzymes displayed a range of selectivities. These results highlight the importance of protein-protein binding kinetics for specific biotin addition to carboxylases and provide one mechanism for determining biotin distribution in metabolism.

Insight into protein-protein interactions from analytical ultracentrifugation

Analytical ultracentrifugation is a free solution technique with no supplementary immobilization, columns or membranes required, and can be used to study self-association and hetero-interactions, stoichiometry, reversibility and interaction strength across a very large dynamic range (dissociation constants from 10(-12) M to 10(-1) M). In the present paper, we review some of the advances that have been made in the two different types of sedimentation experiment--sedimentation equilibrium and sedimentation velocity--for the analysis of protein-protein interactions and indicate how major complications such as thermodynamic and hydrodynamic non-ideality can be dealt with.

Biochemical properties and biological function of a monofunctional microbial biotin protein ligase

Biotin protein ligases constitute a family of enzymes that catalyze the linkage of biotin to biotin-dependent carboxylases. In bacteria, these enzymes are functionally divided into two classes: the monofunctional enzymes that catalyze only biotin addition and the bifunctional enzymes that also bind to DNA to regulate transcription initiation. Biochemical and biophysical studies of the bifunctional Escherichia coli ligase suggest that several properties of the enzyme have evolved to support its additional regulatory role. Included among these properties are the order of substrate binding and linkage between the oligomeric state and ligand binding. To test this hypothesized relationship between functionality and biochemical properties in ligases, we have conducted studies of the monofunctional ligase from Pyrococcus horikoshii. Sedimentation equilibrium measurements to determine the effect of ligand binding on oligomerization indicate that the enzyme exists as a dimer regardless of liganded state. Measurements performed using isothermal titration calorimetry and fluorescence spectroscopy indicate that, in contrast to the bifunctional E. coli enzyme, substrate binding does not occur by an obligatorily ordered mechanism. Finally, thermodynamic signatures of ligand binding to the monofunctional enzyme differ significantly from those measured for the bifunctional enzyme. These results indicate a correlation between the functional complexity of biotin protein ligases and their detailed biochemical characteristics.

The switch regulating transcription of the Escherichia coli biotin operon does not require extensive protein-protein interactions

Transcription of the Escherichia coli biotin (bio) operon is regulated by BirA, a protein that is not only the repressor that regulates bio operon expression by DNA binding but also the enzyme that covalently attaches biotin to its cognate acceptor proteins. Binding of BirA to the bio operator requires dimerization of the protein that is triggered by BirA-catalyzed synthesis of biotinoyl-adenylate (bio-AMP), the obligatory intermediate of the attachment reaction. The current model postulates that the unmodified acceptor protein binds the monomeric BirA:bio-AMP complex and thereby blocks assembly (dimerization) of the form of BirA that binds DNA. We report that expression of fusion proteins that carry synthetic biotin-accepting peptide sequences was as effective as the natural acceptor protein in derepression of bio operon transcription. These peptide sequences have sequences that are remarkably dissimilar to that of the natural acceptor protein, and our data thus argue that the regulatory switch does not require the extensive protein-protein interactions postulated in the current model.

Effect of kinetics on sedimentation velocity profiles and the role of intermediates

We have previously presented a tutorial on direct boundary fitting of sedimentation velocity data for kinetically mediated monomer-dimer systems [Correia and Stafford, 2009]. We emphasized the ability of Sedanal to fit for the k(off) values and measure their uncertainty at the 95% confidence interval. We concluded for a monomer-dimer system the range of well-determined k(off) values is limited to 0.005-10(-5) s(-1) corresponding to relaxation times of approximately 70 to approximately 33,000 s. More complicated reaction schemes introduce the potential complexity of low concentrations of an intermediate that may also influence the kinetic behavior during sedimentation. This can be seen in a cooperative ABCD system (A+B --> C; B+C --> D) where C, the 1:1 complex, is sparsely populated (K(1)=10(4) M(-1), K(2)=10(8) M(-1)). Under these conditions a k(1,off)<0.01 s(-1) produces slow kinetic features. The low concentration of species C contributes to this effect while still allowing the accurate estimation of k(1,off) (although k(2,off) can readily compensate and contribute to the kinetics). More complex reactions involving concerted assembly or cooperative ring formation with low concentrations of intermediate species also display kinetic effects due to a slow flux of material through the sparsely populated intermediate states. This produces a kinetically limited reaction boundary that produces partial resolution of individual species during sedimentation. Cooperativity of ring formation drives the reaction and thus separation of these two effects, kinetics and energetics, can be challenging. This situation is experimentally exhibited by systems that form large oligomers or rings and may especially contribute to formation of micelles and various protein aggregation diseases including formation of beta-amyloid and tau aggregates. Simulations, quantitative parameter estimation by direct boundary fitting and diagnostic features for these systems are presented with an emphasis on the features available in Sedanal to simulate and analyze kinetically mediated systems.

Kinetics of association and dissociation of HIV-1 reverse transcriptase subunits

The biologically active form of HIV-1 reverse transcriptase (RT) is the p66/p51 heterodimer. The process of maturation of the heterodimer from precursor proteins is poorly understood. Previous studies indicated that association of p66 and p51 is very slow. Three techniques, a pre-steady-state activity assay, intrinsic tryptophan fluorescence, and a FRET assay, were used to monitor the dimerization kinetics of RT. Kinetic experiments were conducted with purified p66 and p51 proteins in aqueous buffer. All three techniques gave essentially the same results. The dissociation kinetics of p66/p51 were first-order with rate constants (k(diss)) of approximately 4 x 10(-6) s(-1) (t(1/2) = 48 h). The association kinetics of p66 and p51 were concentration-dependent with second-order rate constants (k(ass)) of approximately 1.7 M(-1) s(-1) for the simple bimolecular association reaction. The implications of slow dimerization of p66/p51 for the maturation process are discussed. A reaction-controlled model invoking conformational selection is proposed to explain the slow protein-protein association kinetics.

Thermodynamic and structural investigation of bispecificity in protein-protein interactions

The ability of a single protein to interact with multiple protein partners is central to many biological processes. However, the physical-chemical and structural basis of the multispecificity is not understood. In Escherichia coli, the protein BirA can self-associate to a homodimer or form a heterodimer with the biotin carboxyl carrier protein of the biotin-dependent carboxylase, acetyl coenzyme A carboxylase. The first interaction results in binding of BirA to the biotin operator sequence to repress transcription initiation at the biotin biosynthetic operon and the second is a prerequisite to posttranslational biotin addition to the carrier protein for use in metabolism. A single surface on BirA is used for both interactions and previous studies indicate that, despite the structural differences between the alternative partners, the two dimerization reactions are isoenergetic. In this work, the underlying thermodynamic driving forces and the sequence determinants of the two interactions were investigated in order to elucidate the energetic and structural underpinnings of the dual specificity. Combined measurements of the temperature and salt dependencies of heterodimerization indicate a modest unfavorable enthalpy and no dependence on salt concentration. By contrast, homodimerization is characterized by a very large unfavorable enthalpy and a modest dependence on salt concentration. Measurements of the function of BirA variants with single amino acid replacements in the alternative dimerization reactions indicate that although considerable overlap in structural determinants for both interactions exists, hotspots specific for one but not the other were detected.

Biotin sensing at the molecular level

Biotin influences transcription in organisms from bacteria to humans. The enzyme, biotin protein ligase, which catalyzes post-transcriptional biotin addition to biotin-dependent carboxylases, plays a central roll in transmitting the demand for biotin to gene expression. The molecular mechanism of this communication in bacteria is well understood and involves competing protein:protein interactions. Biochemical measurements indicate that this competition is kinetically controlled. In humans, the biochemistry of biotin sensing at the transcriptional level is not well characterized. However, the biotin holoenzyme ligase (holocarboxylase synthetase) is proposed to both catalyze biotin addition to carboxylases and to histones in its metabolic and transcriptional roles, respectively. Control of human holocarboxylase synthetase function is, however, considerably more complex than the simple competitive protein protein interactions observed in bacterial systems.

Extracting equilibrium constants from kinetically limited reacting systems

It has been known for some time that slow kinetics will distort the shape of a reversible reaction boundary. Here we present a tutorial on direct boundary fitting of sedimentation velocity data for a monomer-dimer system that exhibits kinetic effects. Previous analysis of a monomer-dimer system suggested that rapid reaction behavior will persist until the relaxation time of the system exceeds 100 s (reviewed in Kegeles and Cann, 1978). Utilizing a kinetic integrator feature in Sedanal (Stafford and Sherwood, 2004), we can now fit for the k(off) values and measure the uncertainty at the 95% confidence interval. For the monomer-dimer system the range of well determined k(off) values is limited to 0.005 to 10(-5) s(-1) corresponding to relaxation times (at a loading concentration of the Kd) of approximately 70 to approximately 33,000 s. For shorter relaxation times the system is fast and only the equilibrium constant K but not k(off) can be uniquely determined. For longer relaxation times the system is irreversibly slow, and assuming the system was at initial equilibrium before the start of the run, only the equilibrium constant K but not k(off) can be uniquely determined.