Sedimentation Equilibrium Data Research Articles

Mutation of Active Site Residues of Insulin-degrading Enzyme Alters Allosteric Interactions

The active site glutamate (Glu(111)) and the active site histidine (His(112)) of insulin-degrading enzyme (IDE) were mutated. These mutant enzymes exhibit, in addition to a large decrease in catalytic activity, a change in the substrate-velocity response from a sigmoidal one seen with the native enzyme (Hill coefficient > 2), to a hyperbolic response. With 2-aminobenzoyl-GGFLRKHGQ-N-(2,4-dinitrophenyl)ethylenediamine as substrate, ATP and triphosphate increase the reaction rate of the wild type enzyme some 50-80-fold. This effect is dampened with glutamate mutants to no effect or less than a 3-fold increase in activity and changed to inhibition with the histidine mutants. Sedimentation equilibrium shows the IDE mutants exhibit a similar oligomeric distribution as the wild type enzyme, being predominantly monomeric, with triphosphate having little if any effect on the oligomeric state. Triphosphate did induce aggregation of many of the IDE mutants. Thus, the oligomeric state of IDE does not correlate with kinetic properties. The His(112) mutants were shown to bind zinc, but with a lower affinity than the wild type enzyme. The glutamate mutants displayed an altered cleavage profile for the peptide beta-endorphin. Wild type IDE cleaved beta-endorphin at Leu(17)-Phe(18) and Phe(18)-Lys(19), whereas the glutamate mutants cleaved at these sites, but in addition at Lys(19)-Asn(20) and at Met(5)-Thr(6). Thus, active site mutations of IDE are suggested to not only reduce catalytic activity but also cause local conformational changes that affect the allosteric properties of the enzyme.

The hydrophobic domain 26 of human tropoelastin is unstructured in solution

Elastin is the protein responsible for the elastic properties of vertebrate tissue. Very little is currently known about the structure of elastin or of its soluble precursor tropoelastin. We have used high-resolution solution NMR methods to probe the conformational preferences of a conserved hydrophobic region in tropoelastin, domain 26 (D26). Using a combination of homonuclear, 15N-separated and triple resonance experiments, we have obtained essentially full chemical shift assignments for D26 at 278 K. An analysis of secondary chemical shift changes, as well as NOE and 15N relaxation data, leads us to conclude that this domain is essentially unstructured in solution and does not interact with intact tropoelastin. D26 does not display exposed hydrophobic clusters, as expected for a fully unfolded protein and commensurate with an absence of flexible structural motifs, as identified by lack of binding of the fluorescent probe 4,4′-dianilino-1,1′-binaphthyl-5,5′-disulfonic acid. Sedimentation equilibrium data establish that this domain is strictly monomeric in solution. NMR spectra recorded at 278 and 308 K indicate that no significant structural changes occur for this domain over the temperature range 278–308 K, in contrast to the characteristic coacervation behavior that is observed for the full-length protein.

Decrypting the Biochemical Function of an Essential Gene from Streptococcus pneumoniae Using ThermoFluor® Technology

The protein product of an essential gene of unknown function from Streptococcus pneumoniae was expressed and purified for screening in the ThermoFluor affinity screening assay. This assay can detect ligand binding to proteins of unknown function. The recombinant protein was found to be in a dimeric, native-like folded state and to unfold cooperatively. ThermoFluor was used to screen the protein against a library of 3000 compounds that were specifically selected to provide information about possible biological functions. The results of this screen identified pyridoxal phosphate and pyridoxamine phosphate as equilibrium binding ligands (K(d) approximately 50 pM, K(d) approximately 2.5 microM, respectively), consistent with an enzymatic cofactor function. Several nucleotides and nucleotide sugars were also identified as ligands of this protein. Sequence comparison with two enzymes of known structure but relatively low overall sequence homology established that several key residues directly involved in pyridoxal phosphate binding were strictly conserved. Screening a collection of generic drugs and natural products identified the antifungal compound canescin A as an irreversible covalent modifier of the enzyme. Our investigation of this protein indicates that its probable biological role is that of a nucleoside diphospho-keto-sugar aminotransferase, although the preferred keto-sugar substrate remains unknown. These experiments demonstrate the utility of a generic affinity-based ligand binding technology in decrypting possible biological functions of a protein, an approach that is both independent of and complementary to existing genomic and proteomic technologies.

Dissociation of Human Copper-Zinc Superoxide Dismutase Dimers Using Chaotrope and Reductant: INSIGHTS INTO THE MOLECULAR BASIS FOR DIMER STABILITY

The dissociation of apo- and metal-bound human copper-zinc superoxide dismutase (SOD1) dimers induced by the chaotrope guanidine hydrochloride (GdnHCl) or the reductant Tris(2-carboxyethyl)phosphine (TCEP) has been analyzed using analytical ultracentrifugation. Global fitting of sedimentation equilibrium data under native solution conditions (without GdnHCl or TCEP) demonstrate that both the apo- and metal-bound forms of SOD1 are stable dimers. Sedimentation velocity experiments show that apo-SOD1 dimers dissociate cooperatively over the range 0.5-1.0 M GdnHCl. In contrast, metal-bound SOD1 dimers possess a more compact shape and dissociate at significantly higher GdnHCl concentrations (2.0-3.0 M). Reduction of the intrasubunit disulfide bond within each SOD1 subunit by 5-10 mM TCEP promotes dissociation of apo-SOD1 dimers, whereas the metal-bound enzyme remains a stable dimer under these conditions. The Cys-57 --> Ser mutant of SOD1, a protein incapable of forming the intrasubunit disulfide bond, sediments as a monomer in the absence of metal ions and as a dimer when metals are bound. Taken together, these data indicate that the stability imparted to the human SOD1 dimer by metal binding and the formation of the intrasubunit disulfide bond are mediated by independent molecular mechanisms. By combining the sedimentation data with previous crystallographic results, a molecular explanation is provided for the existence of different SOD1 macromolecular shapes and multiple SOD1 dimeric species with different stabilities.

PH-Dependent Dimerization of the Carboxyl Terminal Domain of Cx43

Previous studies have demonstrated that the carboxyl terminus of the gap junction protein Cx43 (Cx43CT) can act as an independent, regulatory domain that modulates intercellular communication in response to appropriate chemical stimuli. Here, we have used NMR, chemical cross-linking, and analytical ultracentrifugation to further characterize the biochemical and biophysical properties of the Connexin43 carboxyl terminal domain (S255-I382). NMR-diffusion experiments at pH 5.8 suggested that the Connexin43 carboxyl terminus (CX43CT) may have a molecular weight greater than that of a monomer. Sedimentation equilibrium and cross-linking data demonstrated a predominantly dimeric state for the Cx43CT at pH 5.8 and 6.5, with limited dimer formation at a more neutral pH. NMR-filtered nuclear Overhauser effect studies confirmed these observations and identified specific areas of parallel orientation within Cx43CT, likely corresponding to dimerization domains. These regions included a portion of the SH3 binding domain, as well as two fragments previously found to organize in α-helical structures. Together, these data show that acidification causes Cx43CT dimer formation in vitro. Whether dimer formation is an important structural component of the regulation of Connexin43 channels remains to be determined. Dimerization may alter the affinity of Cx43CT regions for specific molecular partners, thus modifying the regulation of gap junction channels.

Monomeric Cu,Zn-superoxide Dismutase Is a Common Misfolding Intermediate in the Oxidation Models of Sporadic and Familial Amyotrophic Lateral Sclerosis

Proteinacious intracellular aggregates in motor neurons are a key feature of both sporadic and familial amyotrophic lateral sclerosis (ALS). These inclusion bodies are often immunoreactive for Cu,Zn-superoxide dismutase (SOD1) and are implicated in the pathology of ALS. On the basis of this and a similar clinical presentation of symptoms in the familial (fALS) and sporadic forms of ALS, we sought to investigate the possibility that there exists a common disease-related aggregation pathway for fALS-associated mutant SODs and wild type SOD1. We have previously shown that oxidation of fALS-associated mutant SODs produces aggregates that have the same morphological, structural, and tinctorial features as those found in SOD1 inclusion bodies in ALS. Here, we show that oxidative damage of wild type SOD at physiological concentrations ( approximately 40 microm) results in destabilization and aggregation in vitro. Oxidation of either mutant or wild type SOD1 causes the enzyme to dissociate to monomers prior to aggregation. Only small changes in secondary and tertiary structure are associated with monomer formation. These results indicate a common aggregation prone monomeric intermediate for wild type and fALS-associated mutant SODs and provides a link between sporadic and familial ALS.

Hydrodynamic bead modelling of the 2:1 p50–IκBγ complex

NFκB is an important and ubiquitous transcription factor formed by various homo- and heterodimers of the NFκB family. The active transcription factor regulates genes involved in immune, inflammatory and survival responses. Specificity in gene regulation is achieved, at least in part, by the distinct DNA binding preferences of the various homo- and heterodimers and by the complex pathways that lead to signal-induced degradation of the IκB inhibitors. Analytical ultracentrifugation and hydrodynamic bead modelling were used to model the solution structures of the NFκB family member p50, its inhibitor IκBγ and their complex. Sedimentation equilibrium (SE) and sedimentation velocity (SV) data show that p50 is a dimer in solution with a sedimentation coefficient consistent with a conformation intermediate between the closed conformation observed in the crystal structure of the p50 (N-terminal domain)–p65 heterodimer complexed with IκBα and the open conformation adopted by p50 when bound to DNA. SE and SV data show that IκBγ is a monomer in solution and is prone to aggregation over time. p50 forms a 2:1 stoichiometric complex with IκBγ in solution with a sedimentation coefficient consistent with a closed conformation for the p50 dimer.

The cochlear F-box protein OCP1 associates with OCP2 and connexin 26

OCP1 and OCP2 are the most abundant proteins in the organ of Corti. Their distributions map identically to the epithelial gap-junction system, which unites the supporting cell population. Sequence data imply that OCP1 and OCP2 are subunits of an SCF E3 ubiquitin ligase. Consistent with that hypothesis, electrophoretic mobility-shift assays and pull-down assays with immobilized OCP1 demonstrate the formation of an OCP1–OCP2 complex. Sedimentation equilibrium data indicate that the complex is heterodimeric. The coincidence of the OCP1–OCP2 distribution and the epithelial gap-junction system suggests that one or more connexin isoforms may be targets of an SCF OCP1 complex. Significantly, immobilized OCP1 binds 35S-labeled connexin 26 (Cx26) produced by in vitro transcription–translation. Moreover, Cx26 can be co-immunoprecipitated from extracts of the organ of Corti by immobilized anti-OCP1, implying that OCP1 and Cx26 may associate in vivo. Given that lesions in the Cx26 gene ( GJB2) are the most common cause of hereditary deafness, the OCP1–Cx26 interaction has substantial biomedical relevance.

Re-examining the oligomerization state of macrophage migration inhibitory factor (MIF) in solution

The state of oligomerization of macrophage migration inhibitory factor (MIF, also known as glycosylation inhibiting factor, GIF) in solution has been variously reported as monomer, dimer, trimer, or mixtures of all three. Several crystal structures show MIF to be a trimer. Sedimentation velocity shows a recombinant human MIF sample is quite homogeneous, with 98% as a species with s 20, w =3.07 S and D 20, w =8.29×10 −7 cm 2/s. Using the partial specific volume calculated from the amino acid composition these values imply a mass of 33.56 kDa, well above that of dimer, but also 9% below the trimer mass of 37.035 kDa. Sedimentation equilibrium data at loading concentrations from 0.01 to 1 mg/ml show unequivocally that the self-association is extremely tight. However, the apparent mass is 33.53 kDa [95% confidence 33.25–33.82], again 9% below that expected for 100% trimer. To examine the possibility this protein has an unusual partial specific volume, sedimentation equilibrium was also done in H 2O/D 2O mixtures, giving 0.765±0.017 ml/g rather than the calculated 0.735 ml/g. With this revised partial specific volume, the equilibrium and velocity data each give M=37.9±2.8 kDa, fully consistent with a strongly-associated trimeric quaternary structure.

Global analysis of non-specific protein–nucleic interactions by sedimentation equilibrium

Protein–nucleic acid interactions govern a variety of processes, including replication, transcription, recombination and repair. These interactions take place in both sequence-specific and non-specific modes, and the latter occur in many biologically significant contexts. Analytical ultracentrifugation is a useful method for the detailed characterization of the stoichiometry and affinity of macromolecular interactions in free solution. There has been a resurgence of interest in the application of sedimentation equilibrium methods to protein–nucleic acid interactions. However, these studies have been generally focused on sequence–specific interactions. Here we describe an approach to analyze non-specific interactions using sedimentation equilibrium. We have adapted an existing model for non-specific interaction of proteins with finite, one-dimensional nucleic acid lattices for global fitting of multiwavelength sedimentation equilibrium data. The model is extended to accommodate protein binding to multiple faces of the nucleic acid, resulting in overlap of consecutive ligands along the sequence of the RNA or DNA. The approach is illustrated in a sedimentation equilibrium analysis of the interaction of the double-stranded RNA binding motif of protein kinase R with a 20-basepair RNA construct.

Quaternary solution structures of galectins-1, -3, and -7.

Galectins are a growing family of animal lectins with functions in growth regulation and cell adhesion that bind beta-Gal residues in oligosaccharides. Evidence indicates that some of the biological properties of galectins are due to their cross-linking activities with multivalent glycoconjugate receptors. Therefore determination of the quaternary solution structures of these proteins is important in understanding their structure-function properties. The present study reports analytical sedimentation velocity and equilibrium data for galectins-1, -3, and -7 in the absence and presence of bound LacNAc, the natural ligand epitope. Galectin-1 from bovine heart and recombinant human galectin-7 were found to be stable dimers by both methods. In contrast, recombinant murine galectin-3, as well as its proteolytical derived C-terminal domain, are predominantly monomeric. The presence of LacNAc at concentrations sufficient to fully saturate the proteins had no significant effect on either the weight average molecular weight determined by sedimentation equilibrium or the hydrodynamic properties determined from sedimentation velocity experiments. These results show that binding of a monovalent ligand does not affect oligomerization of these galectins.

Measuring Osmotic Pressure of Poly(ethylene glycol) Solutions by Sedimentation Equilibrium Ultracentrifugation

The osmotic pressure of aqueous poly(ethylene glycol) (PEG) solutions (400 and 8000 g/mol) was measured by sedimentation equilibrium (SE) ultracentrifugation over a concentration range of 0−50 wt % and over a temperature range of 10−40 °C. We have developed a procedure to cover a large polymer concentration range by performing a series of ultracentrifugation experiments at different loading concentrations. The SE data agreed well with previous measurements made using a vapor pressure osmometer. To facilitate conversion from concentration to osmotic pressure, the data were fitted to multivariable polynomial expressions as a function of the PEG-to-water ratio G and temperature T. The osmotic pressure of PEG solutions decreases with increasing temperature. We attribute this behavior to the release of structured water associated with the PEG chains which compared to bulk water has a lower entropy.

Quaternary structure of the neuronal protein NAP-22 in aqueous solution

NAP-22, a myristoylated, anionic protein, is a major protein component of the detergent-insoluble fraction of neurons. After extraction from the membrane, it is readily soluble in water. NAP-22 will partition only into membranes with specific lipid compositions. The lipid specificity is not expected for a monomeric myristoylated protein. We have studied the self-association of NAP-22 in solution. Sedimentation velocity experiments indicated that the protein is largely associated. The low concentration limiting s value is ∼1.3 S, indicating a highly asymmetric monomer. In contrast, a nonmyristoylated form of the protein shows no evidence of oligomerization by velocity sedimentation and has an s value corresponding to the smallest component of NAP-22, but without the presence of higher oligomers. Sedimentation equilibrium runs indicate that there is a rapidly reversible equilibrium between monomeric and oligomeric forms of the protein followed by a slower, more irreversible association into larger aggregates. In situ atomic force microscopy of the protein deposited on mica from freshly prepared dilute solution revealed dimers on the mica surface. The values of the association constants obtained from the sedimentation equilibrium data suggest that the weight concentration of the monomer exceeds that of the dimer below a total protein concentration of 0.04 mg/ml. Since the concentration of NAP-22 in the neurons of the developing brain is ∼0.6 mg/ml, if the protein were in solution, it would be in oligomeric form and bind specifically to cholesterol-rich domains. We demonstrate, using fluorescence resonance energy transfer, that at low concentrations, NAP-22 labeled with Texas Red binds equally well to liposomes of phosphatidylcholine either with or without the addition of 40 mol% cholesterol. Thus, oligomerization of NAP-22 contributes to its lipid selectivity during membrane binding.

Design and characterization of a homodimeric antiparallel coiled coil.

We report the first successful design of a self-associating antiparallel coiled coil, APH. The simultaneous application of Coulombic and hydrophobic components results in a decided preference for the antiparallel alignment as judged by HPLC, sedimentation equilibrium, and chemical denaturation data. The designed peptide is of comparable stability to naturally occurring leucine zipper peptides and can be expressed in bacteria. These properties of APH suggest potential in vivo protein fusion and biomaterials applications.

The Extended Multidomain Solution Structures of the Complement Protein Crry and its Chimeric Conjugate Crry-Ig by Scattering, Analytical Ultracentrifugation and Constrained Modelling: Implications for Function and Therapy

Complement receptor-related gene/protein y (Crry) is a cell membrane-bound regulator of complement activation found in mouse and rat. Crry contains only short complement/consensus repeat (SCR) domains. X-ray and neutron scattering was performed on recombinant rat Crry containing the first five SCR domains (rCrry) and mouse Crry with five SCR domains conjugated to the Fc fragment of mouse IgG1 (mCrry-Ig) in order to determine their solution structures at medium resolution. The radius of gyration R G of rCrry was determined to be 4.9–5.0 nm, and the R G of the cross-section was 1.2–1.5 nm as determined by X-ray and neutron scattering. The R G of mCrry-Ig was 6.6–6.7 nm, and the R G of the cross-section were 2.3–2.4 nm and 1.3 nm. The maximum dimension of rCrry was 18 nm and that for mCrry-Ig was 26 nm. The neutron data indicated that rCrry and mCrry-Ig have molecular mass values of 45,000 Da and 140,000 Da, respectively, in agreement with their sequences, and sedimentation equilibrium data supported these determinations. Time-derivative velocity experiments gave sedimentation coefficients of 2.4 S for rCrry and 5.4 S for mCrry-Ig. A medium-resolution model of rCrry was determined using homology models that were constructed for the first five SCR domains of Crry from known crystal and NMR structures, and linked by randomly generated linker peptide conformations. These trial-and-error calculations revealed a small family of extended rCrry structures that best accounted for the scattering and ultracentrifugation data. These were shorter than the most extended rCrry models as the result of minor bends in the inter-SCR orientations. The mCrry-Ig solution data were modelled starting from a fixed structure for rCrry and the crystal structure of mouse IgG1, and was based on conformational searches of the hinge peptide joining the mCrry and Fc fragments. The best-fit models showed that the two mCrry antennae in mCrry-Ig were extended from the Fc fragment. No preferred orientation of the antennae was identified, and this indicated that the accessibility of the antennae for the molecular targets C4b and C3b was not affected by the covalent link to Fc. A structural comparison between Crry and complement receptor type 1 indicated that the domain arrangement of Crry SCR 1-3 is as extended as that of the CR1 SCR 15-17 NMR structure.

Toward beta-peptide tertiary structure: self-association of an amphiphilic 14-helix in aqueous solution.

A major frontier in foldamer research is creation of unnatural oligomers that adopt discrete tertiary structures; at present, only biopolymers are known to fold into such compact conformations. We report an initial step toward helix-bundle tertiary structure in the beta-peptide realm by showing that a 10-residue beta-peptide designed to adopt an amphiphilic helical conformation forms small soluble aggregates in water. Sedimentation equilibrium data indicate that the aggregated state falls in the tetramer-hexamer size range. [structure: see text]

Monomer-dimer equilibrium and oxygen binding properties of ferrous Vitreoscilla hemoglobin.

The monomer-dimer equilibrium and the oxygen binding properties of ferrous recombinant Vitreoscilla hemoglobin (Vitreoscilla Hb) have been investigated. Sedimentation equilibrium data indicate that the ferrous deoxygenated and carbonylated derivatives display low values of equilibrium dimerization constants, 6 x 10(2) and 1 x 10(2) M(-1), respectively, at pH 7.0 and 10 degrees C. The behavior of the oxygenated species, as measured in sedimentation velocity experiments, is superimposable to that of the carbonylated derivative. The kinetics of O(2) combination, measured by laser photolysis at pH 7.0 and 20 degrees C, is characterized by a second-order rate constant of 2 x 10(8) M(-1) s(-1) whereas the kinetics of O(2) release at pH 7.0 is biphasic between 10 and 40 degrees C, becoming essentially monophasic below 10 degrees C. Values of the first-order rate constants (at 20 degrees C) and of the activation energies for the fast and slow phases of the Vitreoscilla Hb deoxygenation process are 4.2 s(-1) and 19.2 kcal mol(-1) and 0.15 s(-1) and 24.8 kcal mol(-1), respectively. Thus the biphasic kinetics of Vitreoscilla Hb deoxygenation is unrelated to the association state of the protein. The observed biphasic oxygen release may be accounted for by the presence of two different conformers in thermal equilibrium within the monomer. The two conformers may be assigned to a structure in which the heme-iron-bound ligand is stabilized by direct hydrogen bonding to TyrB10 and a structure in which such interaction is absent. The slow interconversion between the two conformers may reflect a very large conformational rearrangement in the disordered distal pocket segment connecting helices C and E.

Spectroscopic and Thermodynamic Characterization of the Transcription Antitermination Factor NusE and Its Interaction with NusB from Mycobacterium tuberculosis

N-utilizing proteins (Nus) form a complex involved in the regulation of rRNA biosynthesis in enteric bacteria by modulating the efficiency of transcriptional termination [Nodwell, J. R., and Greenblatt, J. (1993) Cell 72, 261-268]. The protein NusE (identical to the protein S10 of the small ribosomal subunit) from the pathogenic mycobacterium M. tuberculosis has been cloned and overexpressed in Escherichia coli. The pure protein has been characterized by circular dichroism, ultracentrifugation, NMR, and binding to NusB. The near-ultraviolet circular dichroism spectrum of this protein suggests that it has a moderate (ca. 12-16%) alpha-helical content at 30 degrees C. The protein undergoes cold denaturation, with a temperature of maximum stability near 40 degrees C, implying a substantial heat capacity difference between the folded and unfolded states. The sedimentation equilibrium and velocity data indicate that the protein is monomeric and expanded in solution. NMR spectroscopy shows that there is no significant tertiary structure, and confirms the low secondary structure content at low temperatures. Furthermore, there was evidence for more structure at 30 degrees C than at 10 degrees C. Well-defined shifts in peaks in the HSQC spectrum of (15)N labeled NusE/NusB when the unlabeled counterpart was added at approximately stoichiometric concentrations showed the formation of a NusE-NusB complex in the absence of RNA. The far-UV CD and ultracentrifuge experiments, however, indicated relatively weak binding. Isothermal titration calorimetry showed the binding was weak and endothermic at 15 degrees C, with a total DeltaH of > or =10 kcal/mol. This weak binding is consistent with a small interaction interface and lack of large conformational rearrangements in the predominantly unfolded NusE protein. The conformational flexibility of NusE may be important for its roles in both the ribosome and antitermination complexes.

Self-association of human protein S.

Protein S functions as a cofactor with activated protein C in the down-regulation of the blood coagulation cascade. In vitro studies have historically produced conflicting data with regard to the extent of various protein S activity in clotting assays which typically involve adding CaCl(2) to initiate reactions. We report here that protein S reversibly self-associates in the absence of Ca(2+). Sedimentation experiments showed a transition in sedimentation velocity from 7.2 to 4.2 S with a transition midpoint (T(m)) of 0.42 mM Ca(2+) for intact protein S. Studies of thrombin cleaved (Arg(70)) protein S revealed similar results with a transition in sedimentation velocity from 7.9 to 4.4 S with a T(m) of 0.42 mM Ca(2+). This transition is reversible with the addition of 10 mM EDTA. Sedimentation equilibrium data suggest at a minimum, a monomer-dimer-trimer association. Sedimentation velocity experiments were also performed on mixtures of protein S and prothrombin which showed no heterodimer formation in either Ca(2+) or EDTA solutions. These data suggest that previous interpretations of protein S structure and function may have been confounded by the self-associative behavior of protein S in non-Ca(2+) solutions.

Optimal data analysis using transmitted light intensities in analytical ultracentrifuge

This chapter describes the optimal data analysis, using transmitted light intensities, in analytical ultracentrifuge. Analytical ultracentrifugation machines, such as the Beckman XL-A, may be equipped with absorbance optics that is essentially a dual-beam spectrophotometer, with a xenon lamp and a monochromator. To investigate the state of the solution, solute behavior models are assumed and corresponding mathematical models for the expected concentration profiles are written. The suitability of the assumed models is then tested by attempting to curve fit the mathematical models to the collected absorbance data. The chapter provides assumptions for the correct model and the adequate data points are: (1) the data are independent of each other, (2) there is no other systematic error, and (3) the noise probability distribution is Gaussian. Usually, quantities, such as molecular masses and association constants or sedimentation and diffusion coefficients, are used as the fitting parameters, for modeling sedimentation equilibrium or velocity data, respectively.