Molecular code for cooperativity in hemoglobin.

Although tetrameric hemoglobin has been studied extensively as a prototype for understanding mechanisms of allosteric regulation, the functional and structural properties of its eight intermediate ligation forms have remained elusive. Recent experiments on the energetics of cooperativity of these intermediates, along with assignments of their quaternary structures, have revealed that the allosteric mechanism is controlled by a previously unrecognized symmetry feature: quaternary switching from form T to form R occurs whenever heme-site binding creates a tetramer with at least one ligated subunit on each dimeric half-molecule. This "symmetry rule" translates the configurational isomers of heme-site ligation into six observed switchpoints of quaternary transition. Cooperativity arises from both "concerted" quaternary switching and "sequential" modulation of binding within each quaternary form, T and R. Binding affinity is regulated through a hierarchical code of tertiary-quaternary coupling that includes the classical allosteric models as limiting cases.

Hydrogen exchange measurement of the free energy of structural and allosteric change in hemoglobin.

The inability to localize and measure the free energy of protein structure and structure change severely limits protein structure-function investigations. The local unfolding model for protein hydrogen exchange quantitatively related the free energy of local structural stability with the hydrogen exchange rate of concerted sets of structurally related protons. In tests with a number of modified hemoglobin forms, the loss in structural free energy obtained locally from hydrogen exchange results matches the loss in allosteric free energy measured globally by oxygen-binding and subunit dissociation experiments.

Transduction of binding energy into hemoglobin cooperativity.

Hemoglobin is a tetrameric molecule consisting of two identical alpha beta dimers which assemble into either of two quaternary structures, T or R. Recent studies on mutant and partially ligated hemoglobins have revealed that cooperativity exists between the alpha and the beta hemes of each dimeric half-molecule and have led to a symmetry rule for quaternary T-->R switching: the quaternary R structure is energetically favored over the T structure when each dimeric half-molecule contains at least one ligated subunit.

The OR control system of bacteriophage lambda. A physical-chemical model for gene regulation.

A quantitative model has been developed for processes in the bacteriophage lambda that control the switchover from lysogenic to lytic modes of growth. These processes include the interactions of cI repressor and cro proteins at the three DNA sites of the right operator, OR, the binding of RNA polymerase at promoters PR and PRM, the synthesis of cI repressor and cro proteins, and the degradative action of recA during induction of lysis. The model is comprised of two major physical-chemical components: a statistical thermodynamic theory for relative probabilities of the various molecular configurations of the control system; and a kinetic model for the coupling of these probabilities to functional events, including synthesis of regulatory proteins cI and cro. Using independently evaluated interaction constants and rate parameters, the model was found capable of predicting essential physiological characteristics of the system over an extended time. Sufficiency of the model to predict known physiological properties lends credence to the physical-chemical assumptions used in its construction. Several major physiological characteristics were found to arise as "system properties" through the non-linear, time-dependent, feedback-modulated combinations of molecular interactions prescribed by the model. These include: maintenance of the lysogenic state in the absence of recA-mediated cI repressor degradation; induction of lysis and the phenomenon of subinduction; and autogenous negative control of cro. We have used the model to determine the roles, within the composite system, of several key molecular processes previously characterized by studies in vitro. These include: co-operativity in cI repressor binding to DNA; interactions between repressors and RNA polymerase (positive control); and the monomer-dimer association of cI repressor molecules. A major role of cI repressor co-operativity is found to be that of guaranteeing stability of the lysogenic state against minor changes in cI repressor levels within the cell. The role of positive control seems to be that of providing for a peaked, rather than monotonic, dependence of PRM activity on cI repressor level, while permitting PR activity to be a step function. The model correlates an immense body of studies in vivo and in vitro, and it makes testable predictions about molecular phenomena as well as physiological characteristics of bacteriophage lambda. The approach developed in this study can be extended to include more features of the lambda system and to treat other systems of gene regulation.

Coupled energetics of lambda cro repressor self-assembly and site-specific DNA operator binding II: cooperative interactions of cro dimers.

The bacteriophage lambda relies on interactions of the cI and cro repressors which self assemble and bind the two operators (O(R) and O(L)) of the phage genome to control the lysogenic to lytic switch. While the self assembly and O(R) binding of cI have been investigated in detail, a more complete understanding of gene regulation by phage lambda also requires detailed knowledge of the role of cro repressor as it dimerizes and binds at O(R) sites. Since dimerization and operator binding are coupled processes, a full elucidation of the regulatory energetics in this system requires that the equilibrium constants for dimerization and cooperative binding be determined. The dimerization constant for cro has been measured as a prelude to these binding studies. Here, the energetics of cro binding to O(R) are evaluated using quantitative DNaseI footprint titration techniques. Binding data for wild-type and modified O(R) site combinations have been simultaneously analyzed in concert with the dimerization energetics to obtain both the intrinsic and cooperative DNA binding energies for cro with the three O(R) sites. Binding of cro dimers is strongest to O(R)3, then O(R)1 and lastly, O(R)2. Adjacently bound repressors exhibit positive cooperativity ranging from -0.6 to -1.0 kcal/mol. Implications of these, newly resolved, energetics are discussed in the framework of a dynamic model for gene regulation. This characterization of the DNA-binding properties of cro repressor establishes the foundation on which the system can be explored for other, more complex, regulatory elements such as cI-cro cooperativity.

Cooperative non-specific DNA binding by octamerizing lambda cI repressors: a site-specific thermodynamic analysis.

Relationships between dimerization and site-specific binding have been characterized previously for wild-type and mutant cI repressors at the right operator (OR) of bacteriophage lambda DNA. However, the roles of higher-order oligomers (tetramers and octamers) that are also formed from these cI molecules have remained elusive. In this study, a clear correlation has been established between repressor oligomerization and non-specific DNA-binding activity. A modification of the quantitative DNase I footprint titration technique has been used to evaluate the degree of saturation of non-specific, OR-flanking lambda DNA by cI repressor oligomers. With the exception of one mutant, only those repressors capable of octamerizing were found to exhibit non-specific DNA-binding activity. The non-specific interaction was accurately modeled using either a one-dimensional, univalent, site-specific Ising lattice approximation, or a more traditional, multivalent lattice approach. It was found that non-specific DNA-binding by repressor oligomers is highly cooperative and energetically independent from site-specific binding at OR. Furthermore, the coupling free energy resolved for non-specific binding was similar to that of site-specific binding for each repressor, suggesting that similar structural elements may mediate the cooperative component of both binding processes. It is proposed that the state of assembly of the repressor molecule modulates its relative affinity for specific and non-specific DNA sequences. These specificities are allosterically regulated by the transmission of assembly-state information from the C-terminal domain, which mediates self-association and cooperativity, to the N-terminal domain, which primarily mediates DNA-binding. While dimers have a high affinity for their cognate sites within OR, tetramers and octamers may preferentially recognize non-specific DNA sequences. The concepts and findings developed in this study may facilitate quantitative characterization of the relationships between specific, and non-specific binding in other systems that utilize multiple modes of DNA-binding cooperativity.

Free energy coupling within macromolecules. The chemical work of ligand binding at the individual sites in co-operative systems.

Individual-site binding curves such as those obtainable from techniques of DNase footprinting or nuclear magnetic resonance spectroscopy can be used to monitor structurally localized events within biopolymers. This paper discusses thermodynamic aspects of individual-site ligand binding for co-operative systems where the binding of ligand at a local site is coupled to binding of the same ligand species at other sites within the macromolecule. Individual-site binding isotherms have the following properties. (1) They provide a direct indication of the role played by the particular site in the overall binding reaction. (2) They can be used to determine the energetic contribution of loading the site regardless of the complexity of the system. (3) They can be used to resolve microscopic equilibrium constants and co-operativity constants in cases where the classical isotherm is incapable of such resolution. The microscopic constants bear a complex relation to the chemical work of loading each individual site. For a system with two interacting sites we derive analytical relationships between the individual-site loading energies and the microscopic constants. These relationships prescribe, for any values of the microscopic constants, how the co-operative energy is partitioned between events at the two sites. At fixed ligand activity the binding free energy can be estimated directly from an individual-site isotherm. This quantity, which is also a composite of the microscopic constants, provides a useful measure of site--site interaction. Several examples and applications are discussed for these properties of individual-site binding reactions.

Hydropathic analysis of the non-covalent interactions between molecular subunits of structurally characterized hemoglobins.

The software program, HINT (Hydropathic INTeractions), which characterizes non-polar-non-polar, polar-polar, and non-polar-polar interactions, has been used to examine subunit interface associations involved in the hemoglobin allosteric transition at a residue and atomic level. HINT differs from many other computational programs in that it is based not on a statistical method or a force-field but employs parameters experimentally determined from solvent transfer experiments. The main focus of this study is to compare HINT scores that are based upon experimentally and thermodynamically derived measurements with experimentally determined thermodynamic results. The HINT analysis yields a good first-order approximation of experimentally measured energies for these interactions as determined by free energies of dimer-tetramer assembly for mutant hemoglobins. The results provide a framework for understanding subunit stabilities based upon individual atom interactions and repulsions. HINT, in agreement with previous analyses, indicates that: (1) the alpha1beta1 and alpha2beta2 subunit contacts are stabilized via several polar and many hydrophobic interactions with few repulsive contact areas in both the T (deoxyhemoglobin) and R (oxyhemoglobin) structures; (2) the alpha1alpha2 subunit contacts are primarily stabilized by polar salt bridge linkages in both T and R states; and (3) the alpha1beta2 and alpha2beta1 contacts have both strong positive and negative interactions in both T and R states with few hydrophobic interactions. The HINT scoring methodology provides a quantitative characterization of the major role of the alpha1beta2 and alpha2beta1 interfaces in the T-->R quaternary transition. HINT also confirms the stronger hydrogen bond formation in mutant Hb Rothschild (Trp 37beta-->Arg) with Asp94alpha1 that gives rise to a low-affinity (deoxy) hemoglobin. HINT shows that the stabilization of the alpha1beta2 interface with mutant Hb Ypsilanti (Asp99alpha-->Tyr) produces a high-affinity (oxy) hemoglobin by reducing hydrophobic-polar contacts in the R state. HINT interaction maps also identified specific sites for mutagenesis at the alpha1beta2 interface that can be explored to shift the allosteric equilibrium in either direction. In addition, the HINT program provides useful diagnostic data for checking the quality of refined crystallographic structures.

The energetics of ligand-linked subunit assembly in hemoglobin require a third allosteric structure.

For partially ligated cyanomet hemoglobins, Smith and Ackers (Proc. Natl. Acad. Sci. U.S.A. 71 (1985) 4312) determined the free energies of dimer-tetramer assembly for all of the partially ligated species using a combination of kinetic and equilibrium methods. They found a third apparent cooperative free energy level in addition to those of deoxy- and cyanomethemoglobin. Using cryogenic methods, Perrella et al. (Biophys. Chem. 35 (1990) 97) confirmed the existence of the third cooperative free energy level, but found a different energy level assignment for one of the species. These combined studies have yielded a solid data base for considering mechanistic issues. The number of cooperative free energies delta Gc can, in principle, be different from the number of molecular forms which have unique free energies of heme-heme interaction, since delta Gc can be an average over conformational subspecies. Furthermore, since the delta Gc values are determined from free energies of dimer-tetramer assembly, it is necessary to evaluate possible contributions from dimeric properties, and from quaternary constraint (or enhancement) effects associated with subunit assembly. In this paper we analyze the observed distributions of apparent delta Gc values among the various ligation states in terms of mechanisms based on two interconvertible molecular forms (R and T) under the most general conditions in which (i) dimers may be cooperative, (ii) ligand affinities of alpha-subunits may be different within tetramers and dimers, and the same for beta-subunit affinities, and (iii) dimers need not be halves of R-state tetramers. It is found that the experimental distributions are inconsistent with even the most general model of the two-state class; thus, at least three molecular forms of tetramer are required, each with an individually different value of cooperative free energy (heme-heme interaction). This result implies the existence of at least three corresponding molecular structures; while a degeneracy of multiple structures into only a few dominant free energy levels is frequently to be expected, the reverse situation is extremely unlikely.

Analysis of hemoglobin oxygenation from combined equilibrium and kinetic data. Is quaternary enhancement necessary?

An experimental approach based on four independent techniques, in which kinetic and equilibrium measurements of subunit assembly reactions are combined with concentration-dependent oxygen-binding curves, has previously been used to resolve parameters of the linkage system for human hemoglobin over a wide range of conditions [(G.K. Ackers and H.R. Halvorson, Proc. Natl. Acad. Sci. U.S.A. 71 (1974) 4312; F.C. Mills et al., Biochemistry 15 (1976) 1093; M.L. Johnson et al., Biochemistry 15 (1976) 5363). Throughout this extensive body of results it has been found that the affinity for binding oxygen to tetramers at the fourth step exceeds the mean affinity of dissociated dimers. The existence of this "quaternary enhancement" effect has recently been questioned by Gibson and Edelstein (J. Biol. Chem. 262 (1987) 516) and by Philo and Lary (J. Biol. Chem. 265 (1990) 139) on the basis of kinetically derived oxygen-binding constants that do not exhibit quaternary enhancement. These authors have also suggested that quaternary enhancement might not be necessary to explain the oxygen-binding data mentioned above. In this study, we have explored the effect of constraining the numerical analysis of oxygen-binding data against the new kinetically derived binding constants. It is found that the sets of linkage constants which are compatible with both the oxygen-binding data and the new kinetically derived dimer binding constant require both quaternary enhancement and substantial dimer cooperativity. Increasing the dimer cooperativity to compensate completely for quaternary enhancement requires both dimeric and tetrameric binding constants that disagree with the kinetically derived values. Thus, the quaternary enhancement effect cannot be eliminated by readjustment of the remaining constants of the linkage system. Possible sources of the discrepancy between the kinetically derived binding constants and the otherwise self-consistent data from the other four techniques are discussed.

Weighting functions and parameter resolvability for oxygenation data subject to error in the independent variable.

Parameter resolvability and bias has been investigated for weighted nonlinear regression of data where the independent variable is subject to instrumental uncertainty. The specific example of cooperative oxygenation of hemoglobin was studied, where fractional saturation is determined spectrophotometrically and the oxygen activity is measured with a Clark polarographic electrode. For this system the instrumental uncertainty in the oxygen electrode was measured directly and the influence of the uncertainties on resolution of oxygen binding parameters was determined by Monte Carlo simulations. Four weighting functions were tested for their ability to minimize parameter uncertainty and bias: (1) uniform weighting; (2) "propagated weighting" whereby uncertainties in the independent variable are propagated into and added to uncertainties of the dependent variable; (3) Hill plot transform, or "end weighting"; and (4) maximum likelihood analysis, where deviations between fitting function and data are minimized as weighted horizontal and vertical distance vectors. Results of the Monte Carlo simulations favor the use of either uniform weighting, propagated weighting, or maximum likelihood weighting methods. Use of the Hill transform as a weighting function produced poorer parameter resolvability and inaccurate representation of the data in general. Bias error was negligible for all weighting functions.

The Gibbs conference on biothermodynamics: origins and evolution.

The Gibbs conference on biothermodynamics arose in the late 1980's as a 'self-organized' endeavor by researchers at eleven institutions of the US. Over a period of 10 years these annual conferences have grown steadily in size. They have fostered the development of new thermodynamic approaches and their applications in biochemistry. By emphasizing participation by students and postdoctoral fellows they have contributed significantly to the career development of young scientists in this field.

Equilibrium gel permeation: measurement of solute partitioning by direct fluorescence scanning.

The feasibility fo using fluorescence detection in quantitative gel permeation measurements has been explored. It is shown that the effect of scattering by the gel matrix can be evaluated in terms of pathlength-dependent turbidity functions for excitation and emission wavelengths. Experimental studies were carried out to evaluate these funcitons in cross-linked dextran gels (Sephadexes) and in agarose gels (Sepharoses). Empirical turbidity functions derived for these gels have a simple form, leading to accurate simplifying approximations for the scattering correction required in a fluorescence gel permeation measurement. Using this approach...

Resolvability of Adair constants from oxygenation curves measured at low hemoglobin concentration.

Analyses of low concentration oxygenation curves for apparent Adair constants in which the effects of dimers is ignored have been explored using recently determined values of the overall energy coupling parameters. For high affinity systems and favorable energy distributions, it is found that the errors in estimated binding free energies may be less than one kcal provided the measurement errors are strictly random and of small magnitude. These errors are nevertheless quite substantial as compared with the differences between values for the successive binding steps.

Tertiary and quaternary chloride effects of the partially ligated (CN-met) hemoglobin intermediates.

Heterotropic effects of NaCl were studied using CN-met hemoglobin, which has been found to follow the same rules of homotropic cooperativity as CO-Hb and O2-Hb [Huang and Ackers, Biochemistry, 35 (1996) 704; Huang et al., Biophys. J., 71 (1996) 2094]. Modulation of heme site cooperativity by NaCl was determined in this study for all partially ligated CN-met intermediates by measuring their dimer-to-tetramer assembly free energies as a function of NaCl concentration (0.08-1.4 M; pH 7.4, T = 21.5 degrees C). Thermodynamic linkage analysis yielded the contributions to heme site binding cooperativity for all 16 reactions of the binding cascade, and also their apparent changes in bound salt. The principal findings were as follows: (i) At each [NaCl] the ten tetrameric species exhibited three discrete cooperative free energy levels; (ii) positional isomers of the doubly ligated tetramers were distributed among two of these levels according to their specific configurations of ligated sites, in conformity with the symmetry rule mechanism of hemoglobin cooperativity [Ackers et al., Science 255 (1992) 54]; (iii) the apparent moles of NaCl release followed the same configuration-specific distribution as that of heme site cooperativity, i.e., this parameter was synchronized according to the same response clusters. The system thus manifests both a "tertiary chloride effect" and a "quaternary chloride effect", which parallel the tertiary and quaternary Bohr effects [Daugherty et al., Biochemistry, 33 (1994) 10345; Perrella et al., Biochemistry, 33 (1994) 10358] and the tertiary and quaternary enthalpy effects [Huang and Ackers, Biochemistry, 34 (1995) 6316]. Comparison with findings on the stoichiometric O2-binding linkages over an identical range of conditions [Doyle et al., Biophys. Chem., 64 (1997)] revealed that the overall NaCl release upon ligating all four hemes is identical for O2 and CN-met, whereas the detailed distributions of apparent chloride release showed variations between the two ligands, i.e., CN-met Hb showed only a negligible quaternary enhancement at all [NaCl] conditions and a larger tertiary chloride effect compared with O2-Hb. Possible origins of these variations are considered.

Subunit hybridization studies of partially ligated cyanomethemoglobins using a cryogenic method. Evidence for three allosteric states.

Reaction of tetrameric hemoglobin with ligands at the four heme sites yields nine species that have structurally unique combinations of ligated and unligated subunits. Using hemoglobins where the ligated subunits contain cyanomethemoglobin, Smith and Ackers studied the dimer-tetramer assembly reactions in all nine of the partially ligated species (F. R. Smith and G. K. Ackers, Proc. Natl. Acad. Sci. U.S.A. 82 (1985) 5347). They found a third assembly free energy in addition to those of unligated hemoglobin and fully ligated cyanomethemoglobin. The observed distribution of the three assembly free energies among the ten species was found to be incompatible with the two-state mechanism of allosteric control (J. Monod, J. Wyman and J. P. Changeaux, J. Mol. Biol. 12 (1965) 81). The results indicated a mechanism of 'combinatorial switching' in which the binding free energies per site change with configuration of occupied sites and not just their number. In this study, we have confirmed the existence of three assembly free energies among the ten ligation species using a cryogenic method (M. Perrella and L. Rossi-Bernardi, Methods Enzymol. 76 (1981) 133). For one of the species we find a different free energy assignment from that reported by Smith and Ackers; for all other species we observe the same assignments as in earlier work. The revised distribution also requires a 'combinatorial' mechanism of allosteric switching among the three states.

Effects of NaCl on the linkages between O2 binding and subunit assembly in human hemoglobin: titration of the quaternary enhancement effect.

Oxygen binding by human hemoglobin (Hb) and the coupled reactions of dimer-tetramer assembly were studied over a range of NaCl concentrations (from 0.08 M to 1.4 M) at pH 7.4 and 21.5 degrees C. A strategy of multi-dimensional analysis was employed [G.K. Ackers and H.R. Halvorson, Proc. Natl. Acad. Sci. U.S.A., 91, (1974) 4312] to optimize the resolution of the contributions to cooperativity and their heterotropic salt linkages at each stoichiometric degree of O2 binding. A wide range of Hb concentration was utilized at each [NaCl] in which O2-linked subunit assembly reactions contributed significantly to the positions and shapes of the binding isotherms. Kinetic determinations yielded forward and reverse rate constants for assembly of the unligated species. Amplitudes for the assembly rate data had concentration dependences in agreement with the independently determined dimer-tetramer assembly constants of oxyhemoglobin. Concentration-dependent binding isotherms were analyzed, in combination with the kinetically determined equilibrium constants, to yield salt-linked components of cooperativity at the four stages of oxygenation. The principal results of this study were as follows. (i) Assembly of fully oxygenated Hb tetramers is opposed by NaCl: the dimer-to-tetramer equilibrium constant becomes two orders of magnitude less favorable over the [NaCl] range 0.08 M to 1.4 M. By contrast, for deoxy-Hb the assembly equilibrium constant is reduced only two-fold. (ii) Oxygen binding to dimers is non-cooperative over the entire salt range, whereas dimer affinity is slightly favored by increasing the NaCl concentration. (iii) Overall affinity of tetramers for O2 is opposed by NaCl, becoming an order of magnitude less favorable over the range employed. Most of this decrease occurs at the fourth binding step, which shows a large, salt-mediated quaternary enhancement effect; i.e., the assembly of dimers into tetramers at 0.08 M NaCl is accompanied by an eight-fold increase in O2 affinity. (iv) The quaternary enhancement effect at the last O2-binding step is titrated progressively by salt until it reaches a negligible value near the highest [NaCl] of this study. The lowest [NaCl] condition (0.08 M) elicits the greatest tetramer cooperativity with the largest maximal Hill coefficient and the greatest suppression of intermediates. Possible origins and mechanistic implications of these phenomena are considered.

Active enzyme gel chromatography. I. Experimental aspects.

Transport properties of active enzyme species can be studied effectively by layering a small band of enzyme-containing sample on a gel chromatographic column previously saturated with substrate. The column is optically scanned at successive time intervals to yield profiles representing the appearance of chromophoric product or disappearnce of chromophoric substrate. These profiles permit determination of the specific activity and rate of transport of the active species. Initial studies on mechanic of the technique establish the feasibility of accurately determining transport properties of active enzyme species chromatographed on gel columns. Illustrative results are presented for L-glutamate dehydrogenase and for homoserine dehydrogenase studied in both forward and reverse reactions. It is shown that the partititon cross sections derived from the rates of motion of catalytic activity are the same as those determined by equilibrium saturation experiments which directly measure the degree of partitioning by the protein. These results establish the validity of the technique for a variety of future studies. Active enzyme gel chromatography appears comparable in precision to the active enzyme sedimentation technique at current stages of development.

Scanning gel chromatography: determination of transport parameters from dynamic profiles measured at low solute concentration.

Direct optical scanning of solute boundaries in large zone gel chromatography experiments provides an accurate means of determining boundary profile shapes and rates of motion. A method has been developed for correcting such boundaries to a constant time frame, eliminating the distortion which arises from finite column scanning rate. Centroids of the corrected profiles can be used to determine the partition cross section for the solute of interest. The partition cross section and flow rate determine translational motion within the column. The axial dispersion coefficient, L, which characterizes rate of boundary spreading may also be calculated from the profiles. In order to explore these procedures a study of four noninteracting solutes was conducted. Partition cross sections determined from rates of motion of boundary centroids were found to be in good agreement with those determined by the equilibrium saturation method on the same column. In order to explore the lowest concentration limits of the technique and to illustrate the boundary characteristics for a self-associating solute, a study of carboxyhemoglobin was conducted over a wide concentration range. From measurements at 220 nm the lowest concentration where useful data could be obtained was 2 micrograms per ml (0.12muM heme). These results establish validity of the procedures used in analyzing the rates of boundary transport and in studying solute transport over a wide range of conditions.

Equilibrium gel permeation: a single-photon counting spectrophotometer for studies of protein interaction.

When a small column or flow cell packed with gel particles is completely saturated with a solution containing molecular species of interest, the average cross-sectional area occupied by the solute (partition cross section) is conveniently and precisely determined by direct optical scanning. For a mixture of interacting solutes this equilibrium gel permeation measurement yields the weight average of the species partition cross sections and the variation of this quantity with solute concentration permits determination of the solute interaction parameters (stoichiometry, equilibrium constants). We have developed a computer-controlled single-photon counting spectrophotometer for these measurements. The instrument exhibits high precision over a wide range of optical density. With counting times in the range of 10-1000 s the standard deviations on optical densities of protein solutions measured at 220 nm are typically 0.0006 at 1 OD, 0.002 at 2 OD, 0.005 at 4 OD. Beer's law tests show that deviations from linearity are less than these precision limits. Partition cross-section measurements for proteins can be made with an accuracy of better than 0.001 and information can be obtained with protein solutions at least as low as 1 mug/ml.