THE INFLUENCE OF ELECTROLYTES ON THE SOLUTION AND PRECIPITATION OF CASEIN AND GELATIN

1. Colloids have been divided into two groups according to the ease with which their solutions or suspensions are precipitated by electrolytes. One group (hydrophilic colloids), e.g., solutions of gelatin or crystalline egg albumin in water, requires high concentrations of electrolytes for this purpose, while the other group (hydrophobic colloids) requires low concentrations. In the latter group the precipitating ion of the salt has the opposite sign of charge as the colloidal particle (Hardy''s rule), while no such relation exists in the precipitation of colloids of the first group. 2. The influence of electrolytes on the solubility of solid Na caseinate, which belongs to the first group (hydrophilic colloids), and of solid casein chloride which belongs to the second group (hydrophobic colloids), was investigated and it was found that the forces determining the solution are entirely different in the two cases. The forces which cause the hydrophobic casein chloride to go into solution are forces regulated by the Donnan equilibrium; namely, the swelling of particles. As soon as the swelling of a solid particle of casein chloride exceeds a certain limit it is dissolved. The forces which cause the hydrophilic Na caseinate to go into solution are of a different character and may be those of residual valency. Swelling plays no rôle in this case, and the solubility of Na caseinate is not regulated by the Donnan equilibrium. 3. The stability of solutions of casein chloride (requiring low concentrations of electrolytes for precipitation) is due, first, to the osmotic pressure generated through the Donnan equilibrium between the casein ions tending to form an aggregate, whereby the protein ions of the nascent micellum are forced apart again; and second, to the potential difference between the surface of a micellum and the surrounding solution (also regulated by the Donnan equilibrium) which prevents the further coalescence of micella already formed. This latter consequence of the Donnan effect had already been suggested by J. A. Wilson. 4. The precipitation of this group of hydrophobic colloids by salts is due to the diminution or annihilation of the osmotic pressure and the P.D. just discussed. Since low concentrations of electrolytes suffice for the depression of the swelling and P.D. of the micella, it is clear why low concentrations of electrolytes suffice for the precipitation of hydrophobic colloids, such as casein chloride. 5. This also explains why only that ion of the precipitating salt is active in the precipitation of hydrophobic colloids which has the opposite sign of charge as the colloidal ion, since this is always the case in the Donnan effect. Hardy''s rule is, therefore, at least in the precipitation of casein chloride, only a consequence of the Donnan effect. 6. For the salting out of hydrophilic colloids, like gelatin, from watery solution, sulfates are more efficient than chlorides regardless of the pH of the gelatin solution. Solution experiments lead to the result that while CaCl₂ or NaCl increase the solubility of isoelectric gelatin in water, and the more, the higher the concentration of the salt, Na₂SO₄ increases the solubility of isoelectric gelatin in low concentrations, but when the concentration of Na₂SO₄ exceeds M/32 it diminishes the solubility of isoelectric gelatin the more, the higher the concentration. The reason for this difference in the action of the two salts is not yet clear. 7. There is neither any necessity nor any room for the assumption that the precipitation of proteins is due to the adsorption of the ions of the precipitating salt by the colloid.     

MEMBRANE EQUILIBRIA AND THE ELECTRIC CHARGE OF RED BLOOD CELLS

It has been shown, within the probable limit of error of the methods of measurement employed, that the Donnan equilibrium determines the distribution of H and Cl ions between the cell and the surrounding fluid. This equilibrium is a consequence of the impermeability of the cell membrane to the inorganic cations of the cell. The mechanism responsible for this equilibrium is suggested as that concerned in the secretion of HCl by the cells of the gastric mucosa. If the salt concentration of the medium is low there may result from the Donnan equilibrium a thermodynamic P.D. of considerable magnitude. In the presence of low concentrations of electrolytes, this P.D. is to be regarded as positive in sign at reactions of the medium at which the cataphoretic charge of the cell is negative in sign. The explanation of this discrepancy in sign of charge may lie in the existence at an outer phase-boundary of a second Donnan equilibrium the nature of which is determined by the ionization of the protein of the cell membrane.     

THE ORIGIN OF THE POTENTIAL DIFFERENCES RESPONSIBLE FOR ANOMALOUS OSMOSIS

1. Collodion bags coated with gelatin on the inside were filled with a M/256 solution of neutral salt (e.g., NaCl, CaCl₂, CeCl₃, or Na₂SO₄) made up in various concentrations of HNO₃ (varying from N/50,000 to N/100). Each collodion bag was put into an HNO₃ solution of the same concentration as that inside the bag but containing no salt. In this case water diffuses from the outside solution (containing no salt) into the inside solution (containing the salt) with a relative initial velocity which can be expressed by the following rules: (a) Water diffuses into the salt solution as if the particles of water were negatively charged and as if they were attracted by the cation and repelled by the anion of the salt with a force increasing with the valency of the ion. (b) The initial rate of the diffusion of water is a minimum at the hydrogen ion concentration of about N/50,000 HCl (pH 4.7, which is the point at which gelatin is not ionized), rises with increasing hydrogen ion concentration until it reaches a maximum and then diminishes again with a further rise in the initial hydrogen ion concentration. 2. The potential differences between the salt solution and the outside solution (originally free from salt) were measured after the diffusion had been going on for 1 hour; and when these values were plotted as ordinates over the original pH as abscissae, the curves obtained were found to be similar to the osmotic rate curves. This confirms the view expressed by Girard) Bernstein, Bartell, and Freundlich that these cases of anomalous osmosis are in reality cases of electrical endosmose where the driving force is a P.D. between the opposite sides of the membrane. 3. The question arose as to the origin of these P. D. and it was found that the P.D. has apparently a double origin. Certain features of the P.D. curve, such as the rise and fall with varying pH, seem to be the consequence of a Donnan equilibrium which leads to some of the free HNO₃ being forced from the solution containing salt into the outside solution containing no (or less) salt. This difference of the concentration of HNO₃, on the opposite sides of the membrane leads to a P.D. which in conformity with Nernst''s theory of concentration cells should be equal to 58 x (pH inside minus pH outside) millivolts at 18°C. The curves of the values of (pH inside minus pH outside) when plotted as ordinates over the original pH as abscissae lead to curves resembling those for the P. D. in regard to location of minimum and maximum. 4. A second source of the P.D. seems to be diffusion potentials, which exist even if no membranes are present and which seem to be responsible for the fact that the rate of diffusion of negatively charged water into the salt solution increases with the valency of the cation and diminishes with the valency of the anion of the salt. 5. The experiments suggest the possibility that the establishment of a Donnan equilibrium between membrane and solution is one of the factors determining the Helmholtzian electrical double layer, at least in the conditions of our experiments.     

THE EFFECT OF PURE PROTEIN SOLUTIONS AND OF BLOOD SERUM ON THE DIFFUSIBILITY OF CALCIUM

1. A comparative study has been made of the diffusibility of calcium in solutions of crystalline egg albumin, serum globulin, and human blood serum. 2. In all three of these solutions, at pH 7.4, molal Ca concentrations within the membrane are greater than the calcium concentrations in the outside solutions, quite in accordance with the Donnan theory. 3. At pH 7.4, the ratio of See PDF for Structure varies directly with the protein concentration whether the solution be one of egg albumin, serum globulin, or blood serum. This is also in accordance with the Donnan theory. 4. On the acid side of the isoelectric point of the proteins, the concentration of Ca outside becomes greater than the concentration in the solution of blood serum or pure protein, as is demanded by the Donnan theory. 5. The magnitude of the Ca ratios on the alkaline and acid sides of the isoelectric points is probably the resultant of the Donnan equilibrium and the formation of complex Ca-protein ions. Northrop and Kunitz have shown the probability of the existence of such ions in the case of Zn⁺⁺, K⁺, and Li⁺, where satisfactory electrodes have been developed for E.M.F. measurements.     

Note on the Donnan equilibrium

The solution for the spatial distribution of ions in a Donnan equilibrium has been given by J. H. Bartlett and R. A. Kromhout (1952). The present note gives an explicit solution for the case in which the length of the region containing the membrane is large; in biological situations this requires only that the length considered should be greater than a few hundred Ångstrom units. The Donnan equilibrium may be considered to be a special case of a situation in which forces other than electrical act upon the ions; in particular, it represents the case in which only one ion is acted upon and the energy difference on the two sides of the membrane is infinite. An expression is given for the difference in energy of theith in terms of the electrical potential and of the ion concentrations. As an illustration, the results are applied to nerve membrane potentials.     

Derivation of general equations describing tracer diffusion in any two-compartment tissue with application to ionic diffusion in cylindrical muscle bundles

A set of generalized diffusion equations have been derived which describe radioactive tracer movement in any tissue that can be modeled as a distributed two-compartment system. These equations have been applied to ionic tracer movement in cylindrical muscle bundles, and the boundary conditions used correspond to experimental conditions during various ionic tracer diffusion experiments on cardiac papillary muscles. Specifically, solutions were obtained for extra- and intracellular tracer washout as well as for the extra- and intracellular steady-state tracer diffusion experiments of Weidmann (1966). These solutions are presented in series form as well as in graphical form and are compared with the corresponding experimental data. A comparison of these solutions with those obtained using simple exponential kinetics is presented, and it is shown that there is a marked discrepancy between these two methods of analysis for bundles of any appreciable diameter.     

STUDIES ON PERMEABILITY OF MEMBRANES : I. INTRODUCTION AND THE DIFFUSION OF IONS ACROSS THE DRIED COLLODION MEMBRANE.

The theoretical aspects of the problem of sieve-like membranes are developed. The method of preparing the dried collodion membrane is described, and the method of defining the property of a particular membrane is given. It consists of the measurement of the Co P, that is the P.D. between an 0.1 and an 0.01 M KCl solution separated by the membrane. Co P is in the best dried membranes 50 to 53 millvolts, the theoretically possible maximum value being 55 millivolts. Diffusion experiments have been carried out with several arrangements, one of which is, for example, the diffusion of 0.1 M KNO₃ against 0.1 M NaCl across the membrane. The amount of K⁺ diffusing after a certain period was in membranes with a sufficiently high Co P (about 50 millivolts or more) on the average ten times as much as the amount of diffused Cl^-. In membranes with a lower Co P the ratio was much smaller, down almost to the proportion of 1:1 which holds for the mobility of these two ions in a free aqueous solution. When higher concentrations were used, e.g. 0.5 M solution, the difference of the rate of diffusion for K⁺ and Cl^- was much smaller even in the best membranes, corresponding to the fact that the P.D. of two KCl solutions whose concentrations are 10:1 is much smaller in higher ranges of concentration than in lower ones. These observations are confirmed by experiments arranged in other ways. It has been shown that, in general, the diffusion of an anion is much slower than the one of a cation across the dried collodion membrane. The ratio of the two diffusion coefficients would be expected to be calculable in connection with the potential difference of such a membrane when interposed between these solutions. The next problem is to show in how far this can be confirmed quantitatively.     

VALENCY RULE AND ALLEGED HOFMEISTER SERIES IN THE COLLOIDAL BEHAVIOR OF PROTEINS : I. THE ACTION OF ACIDS.

1. The action of a number of acids on four properties of gelatin (membrane potentials, osmotic pressure, swelling, and viscosity) was studied. The acids used can be divided into three groups; first, monobasic acids (HCl, HBr, HI, HNO₃, acetic, propionic, and lactic acids); second, strong dibasic acids (H₂SO₄ and sulfosalicylic acid) which dissociate as dibasic acids in the range of pH between 4.7 and 2.5; and third, weak dibasic and tribasic acids (succinic, tartaric, citric) which dissociate as monobasic acids at pH 3.0 or below and dissociate increasingly as dibasic acids, according to their strength, with pH increasing above 3.0. 2. If the influence of these acids on the four above mentioned properties of gelatin is plotted as ordinates over the pH of the gelatin solution or gelatin gel as abscissæ, it is found that all the acids have the same effect where the anion is monovalent; this is true for the seven monobasic acids at all pH and for the weak dibasic and tribasic acids at pH below 3.0. The two strong dibasic acids (the anion of which is divalent in the whole range of pH of these experiments) have a much smaller effect than the acids with monovalent anion. The weak dibasic and tribasic acids act, at pH above 3.0, like acids the anion of which is chiefly monovalent but which contain also divalent anions increasing with pH and with the strength of the acid. 3. These experiments prove that only the valency but not the other properties of the anion of an acid influences the four properties of gelatin mentioned, thus absolutely contradicting the Hofmeister anion series in this case which were due to the failure of the earlier experimenters to measure properly the pH of their protein solutions or gels and to compare the effects of acids at the same pH of the protein solution or protein gel after equilibrium was established. 4. It is shown that the validity of the valency rule and the non-validity of the Hofmeister anion series for the four properties of proteins mentioned are consequences of the fact that the influence of acids on the membrane potentials, osmotic pressure, swelling, and viscosity of gelatin is due to the Donnan equilibrium between protein solutions or gels and the surrounding aqueous solution. This equilibrium depends only on the valency but not on any other property of the anion of an acid. 5. That the valency rule is determined by the Donnan equilibrium is strikingly illustrated by the ratio of the membrane potentials for divalent and monovalent anions of acids. Loeb has shown that the Donnan equilibrium demands that this ratio should be 0.66 and the actual measurements agree with this postulate of the theory within the limits of accuracy of the measurements. 6. The valency rule can be expected to hold for only such properties of proteins as depend upon the Donnan equilibrium. Properties of proteins not depending on the Donnan equilibrium may be affected not only by the valency but also by the chemical nature of the anion of an acid.     

Dynamics of Small Molecules in a Dense Polymer Matrix: Molecular Dynamics Studies

Abstract

The anomalous diffusion regime appearing in the self-diffusion of small molecules in bulk amorphous polymers has been extensively studied by molecular dynamics simulations. A rather long simulation of duration ～ 10 ^?8 s is performed on a polyethylene-like simple polymer model containing either oxygen molecules or helium atoms as a diffusant. Dynamic properties evaluated for these diffusants are the mean-square displacement, the van Hove self correlation function, and the self part of the density autocorrelation. It is first confirmed that the anomalous diffusion regime appears in a few hundred picoseconds for oxygen molecule, while the Einstein relation adopted beyond this regime results in the self-diffusion coefficient of the order of ～ 10^?5 cm²/s. This anomaly is still observed for helium that diffuses much faster than oxygen. In the anomalous diffusion regime, it is found that the correlation functions for the two diffusants show characteristic features and become essentially the same as time is scaled appropriately. These features allow the estimation of the two characteristic spatial scales which are probably dominated by the microstructure of the polymer matrix, namely, the cage size and the distance between adjacent cages. The time dependence of the mean-square displacements of the two diffusants can be well interpreted by these characteristic spatial scales as time is scaled with the self-diffusion coefficients. It is shown that the anomalous diffusion regime arises from the inhomogeneous microstructure of the polymer matrix.     

Computation of the Electrical Double Layer Properties of Semipermeable Membranes in Multicomponent Electrolytes

A methodology is presented for calculating of the surface potential, Donnan potential, and ion concentration profiles for semipermeable microbial membranes that is valid for an arbitrary electrolyte composition. This model for surface potential, Donnan potential, and charge density was applied to recently reported experimental data for gram-positive bacteria, including Bacillus brevis, Rhodococcus opacus, Rhodococcus erythropolis, and Corynebacterium species. These calculations show that previously unconsidered trace amounts of divalent and trivalent cations at very low concentrations (10⁻⁶ M) can have significant effects on the calculated surface and Donnan potentials, at ionic strengths of I ≤ 0.01 M, and that these effects need to be considered in accurate modeling of microbial surface. In addition, the calculated ion concentration profiles show that owing to the relatively high surface charges that can develop in microbial membranes, electrostatic effects can act to significantly concentrate divalent (factors of 5 × 10³) and trivalent (factors of 2 × 10⁴) cations within the bacterial cell wall. Comparison of the calculated concentration factors with those derived from experiments shows that a significant fraction of the uptake of metal by bacteria can be explained by the proposed electrostatic model.     

Characterization of optical clearing mechanisms in muscle during treatment with glycerol and gadobutrol solutions

The recent increasing interest in the application of radiology contrasting agents to create transparency in biological tissues implies that the diffusion properties of those agents need evaluation. The comparison of those properties with the ones obtained for other optical clearing agents allows to perform an optimized agent selection to create optimized transparency in clinical applications. In this study, the evaluation and comparison of the diffusion properties of gadobutrol and glycerol in skeletal muscle was made, showing that although gadobutrol has a higher molar mass than glycerol, its low viscosity allows for a faster diffusion in the muscle. The characterization of the tissue dehydration and refractive index matching mechanisms of optical clearing was made in skeletal muscle, namely by the estimation of the diffusion coefficients for water, glycerol and gadobutrol. The estimated tortuosity values of glycerol (2.2) and of gadobutrol (1.7) showed a longer path-length for glycerol in the muscle.     

Exchange diffusion of alkali ions through the apoplast of the potato (Soianum tuberosum L.) storage parenchyma

Interdiffusion coefficients of K and Na for tangential transport through cell walls were found to be independent of ion strength and only moderately (c. 50%) lower than values known for diffusion in water. Although at low salt concentrations alkali ion exchange diffusion on the cell wall pathway is facilitated by accumulation of diffusing species in the Donnan space, at all concentrations the resistance of the whole tissue for apoplastic cation exchange diffusion remained significantly higher than that of unstirred liquid of equal thickness, as the area fraction of the cell wall pathway in the parenchyma is small.     

Theoretical evaluation of a possible nature of the outer membrane potential of mitochondria

A possibility of generation of the outer membrane potential in mitochondria has been suggested earlier in the literature, but the potential has not been directly measured yet. Even its nature, metabolic impact and a possible range of magnitudes are not clear, and require further theoretical and experimental analysis. Here, using simple mathematical model, we evaluated a possible contribution of the Donnan and metabolically derived potentials to the outer membrane potential, concluding that the superposition of both is most probable; exclusively Donnan origin of the potential is doubtful because unrealistically high concentrations of charged macromolecules are needed for maintaining its relatively high levels. Regardless of the mechanism(s) of generation, the maximal possible potential seems to be less than 30 mV because significant osmotic gradients, created at higher values, increase the probability of the outer membrane rupture. New experimental approaches for direct or indirect determination of true value of the outer membrane potential are suggested here to avoid a possible interference of the surface electrical potential of the inner membrane, which may change as a result of the extrusion of matrix protons under energization of mitochondria.     

Physical descriptions of experimental selectivity measurements in ion channels

Three experiments that quantify the amount of selectivity exhibited by a biological ion channel are examined with Poisson-Nernst-Planck (PNP) theory. Conductance ratios and the conductance mole fraction experiments are examined by considering a simple model ion channel for which an approximate solution to the PNP equations with Donnan boundary conditions is derived. A more general result is derived for the Goldman-Hodgkin-Katz permeability ratio. The results show that (1) the conductance ratio measures the ratio of the diffusion coefficients of the ions inside the channel, (2) the mole fraction experiment measures the difference of the excess chemical potentials of the ions inside the channel, and (3) the permeability ratio measures both diffusion coefficients and excess chemical potentials. The results are used to divide selectivity into two components: partitioning, an equilibrium measure of how well the ions enter the channel, and diffusion, a nonequilibrium measure of how well the ions move through the channel.     

Error analysis in equilibrium dialysis: evaluation of adsorption phenomena

Various sources of error in equilibrium dialysis may lead to inaccurate results of binding experiments: (i) the finite time of dialysis; (ii) the Donnan effects; (iii) the adsorption of ligand to the membrane; and (iv) release of contaminating material from dialysis casings. These errors were analyzed for a polynucleotide-oligopeptide model system with particular regard to adsorption phenomena and the underlying mechanisms. Adsorption data were treated according to Freundlich and Langmuir isotherms. The latter turned out to be more appropriate for the consideration of adsorption phenomena with respect to a minimum error propagation. Furthermore, it was shown that the degree of adsorption varies with ionic strength and temperature and could be interpreted in terms of polyelectrolyte theory. The kinetics of both adsorption and of the ligand distribution between the polymer and buffer compartments follow first order at the beginning of dialysis which is in line with a simple diffusion process. After 13-15 h data deviate from first order kinetics indicating an alteration in the transport mechanism. The effects of errors on binding parameters were determined and a detailed protocol for correction is presented allowing one to obtain binding data from equilibrium dialysis experiments with the required degree of accuracy. The fundamental principles and results for the system under investigation generally apply to all protein-ligand systems.     

ON THE CAUSE OF THE INFLUENCE OF IONS ON THE RATE OF DIFFUSION OF WATER THROUGH COLLODION MEMBRANES. I

1. In three previous publications it had been shown that electrolytes influence the rate of diffusion of pure water through a collodion membrane into a solution in three different ways, which can be understood on the assumption of an electrification of the water or the watery phase at the boundary of the membrane; namely, (a) While the watery phase in contact with collodion is generally positively electrified, it happens that, when the membrane has received a treatment with a protein, the presence of hydrogen ions and of simple cations with a valency of three or above (beyond a certain concentration) causes the watery phase of the double layer at the boundary of membrane and solution to be negatively charged. (b) When pure water is separated from a solution by a collodion membrane, the initial rate of diffusion of water into a solution is accelerated by the ion with the opposite sign of charge and retarded by the ion with the same sign of charge as that of the water, both effects increasing with the valency of the ion and a second constitutional quantity of the ion which is still to be defined. (c) The relative influence of the oppositely charged ions, mentioned in (b), is not the same for all concentrations of electrolytes. For lower concentrations the influence of that ion usually prevails which has the opposite sign of charge from that of the watery phase of the double layer; while in higher concentrations the influence of that ion begins to prevail which has the same sign of charge as that of the watery phase of the double layer. For a number of solutions the turning point lies at a molecular concentration of about M/256 or M/512. In concentrations of M/8 or above the influence of the electrical charges of ions mentioned in (b) or (c) seems to become less noticeable or to disappear entirely. 2. It is shown in this paper that in electrical endosmose through a collodion membrane the influence of electrolytes on the rate of transport of liquids is the same as in free osmosis. Since the influence of electrolytes on the rate of transport in electrical endosmose must be ascribed to their influence on the quantity of electrical charge on the unit area of the membrane, we must conclude that the same explanation holds for the influence of electrolytes on the rate of transport of water into a solution through a collodion membrane in the case of free osmosis. 3. We may, therefore, conclude, that when pure water is separated from a solution of an electrolyte by a collodion membrane, the rate of diffusion of water into the solution by free osmosis is accelerated by the ion with the opposite sign of charge as that of the watery phase of the double layer, because this ion increases the quantity of charge on the unit area on the solution side of the membrane; and that the rate of diffusion of water is retarded by the ion with the same sign of charge as that of the watery phase for the reason that this ion diminishes the charge on the solution side of the membrane. When, therefore, the ions of an electrolyte raise the charge on the unit area of the membrane on the solution side above that on the side of pure water, a flow of the oppositely charged liquid must occur through the interstices of the membrane from the side of the water to the side of the solution (positive osmosis). When, however, the ions of an electrolyte lower the charge on the unit area of the solution side of the membrane below that on the pure water side of the membrane, liquid will diffuse from the solution into the pure water (negative osmosis). 4. We must, furthermore, conclude that in lower concentrations of many electrolytes the density of electrification of the double layer increases with an increase in concentration, while in higher concentrations of the same electrolytes it decreases with an increase in concentration. The turning point lies for a number of electrolytes at a molecular concentration of about M/512 or M/256. This explains why in lower concentrations of electrolytes the rate of diffusion of water through a collodion membrane from pure water into solution rises at first rapidly with an increase in concentration while beyond a certain concentration (which in a number of electrolytes is M/512 or M/256) the rate of diffusion of water diminishes with a further increase in concentration.     

Protein-ligand interactions measured by 15N-filtered diffusion experiments

NMR diffusion coefficient measurements have been shown to be sensitive to the conformational and oligomeric states of proteins. Recently, heteronuclear-filtered diffusion experiments have been proposed [Dingley et al. (1997) J. Biomol. NMR, 10, 1–8]. Several new heteronuclear-filtered diffusion pulse sequences are proposed which are shown to have superior sensitivity to those previously proposed. One of these new heteronuclear-filtered diffusion experiments has been used to study the binding of an SH3 domain to a peptide. Using this system, we show that it is possible to measure binding constants from diffusion coefficient measurements.     

lambda-Repressor oligomerization kinetics at high concentrations using fluorescence correlation spectroscopy in zero-mode waveguides

Fluorescence correlation spectroscopy (FCS) has demonstrated its utility for measuring transport properties and kinetics at low fluorophore concentrations. In this article, we demonstrate that simple optical nanostructures, known as zero-mode waveguides, can be used to significantly reduce the FCS observation volume. This, in turn, allows FCS to be applied to solutions with significantly higher fluorophore concentrations. We derive an empirical FCS model accounting for one-dimensional diffusion in a finite tube with a simple exponential observation profile. This technique is used to measure the oligomerization of the bacteriophage lambda repressor protein at micromolar concentrations. The results agree with previous studies utilizing conventional techniques. Additionally, we demonstrate that the zero-mode waveguides can be used to assay biological activity by measuring changes in diffusion constant as a result of ligand binding.