Equilibrium constants under physiological conditions for the reactions of the nonphosphorylated pathway of L-serine biosynthesis

The observed equilibrium constants (K_obs) for the reactions of d-2-phosphoglycerate phosphatase, d-2-Phosphoglycerate^3? + H₂O → d-glycerate^? + HPO₄^2?; d-glycerate dehydrogenase (EC 1.1.1.29), d-Glycerate^? + NAD⁺ → NADH + hydroxypyruvate^? + H⁺; and l-serine:pyruvate aminotransferase (EC 2.6.1.51), Hydroxypyruvate^? + l-H · alanine^± → pyruvate^? + l-H · serine^±; have been determined, directly and indirectly, at 38 °C and under conditions of physiological ionic strength (0.25 m) and physiological ranges of pH and magnesium concentrations. From these observed constants and the acid dissociation and metal-binding constants of the substrates, an ionic equilibrium constant (K) also has been calculated for each reaction. The value of K for the d-2-phosphoglycerate phosphatase reaction is 4.00 × 10³m [ΔG⁰ = ?21.4 kJ/mol (?5.12 kcal/mol)]([H₂0] = 1). Values of K_obs for this reaction at 38 °C, [K⁺] = 0.2 m, I = 0.25 M, and pH 7.0 include 3.39 × 10³m (free [Mg²⁺] = 0), 3.23 × 10³m (free [Mg²⁺] = 10^?3m), and 2.32 × 10³m (free [Mg²⁺] = 10^?2m). The value of K for the d-glycerate dehydrogenase reaction has been determined to be 4.36 ± 0.13 × 10^?13m (38 °C, I = 0.25 M) [ΔG⁰ = 73.6 kJ/mol (17.6 kcal/mol)]. This constant is relatively insensitive to free magnesium concentrations but is affected by changes in temperature [ΔH⁰ = 46.9 kJ/mol (11.2 kcal/mol)]. The value of K for the serine:pyruvate aminotransferase reaction is 5.41 ± 0.11 [ΔG⁰ = ?4.37 kJ/mol (?1.04 kcal/mol)] at 38 °C (I = 0.25 M) and shows a small temperature effect [ΔH⁰ = 16.3 kJ/ mol (3.9 kcal/mol)]. The constant showed no significant effect of ionic strength (0.06–1.0 m) and a response to the hydrogen ion concentration only above pH 8.5. The value of K_obs is 5.50 ± 0.11 at pH 7.0 (38 °C, [K⁺] = 0.2 m, [Mg²⁺] = 0, I = 0.25 M). The results have also allowed the value of K for the d-glycerate kinase reaction (EC 2.7.1.31), d-Glycerate^? + ATP^4? → d-2-phosphoglycerate^3? + ADP^3? + H⁺, to be calculated to be 32.5 m (38 °C, I = 0.25 M). Values for K_obs for this reaction under these conditions and at pH 7.0 include 236 (free [Mg²⁺] = 0) and 50.8 (free [Mg²⁺] = 10^?3m).     

Standard free energy maps for the hydrolysis of ATP as a function of pH and metal ion concentration: comparison of metal ions

The observed equilibrium constant K_obs for the hydrolysis of ATP to ADP and inorganic phosphate has been calculated as a function of pH and metal ion concentration pM (- log [M]) at 25 °C and μ = 0.2 with the use of literature values of the acid dissociation and complex dissociation constants for the phosphates.The resulting standard free energy changes ΔG °′ are presented by means of contour diagrams for the range pH 4–10 and pM 1–7. These maps summarize the results of some 1900 calculations per diagram, and clearly simulate a differential effect of the metal ions of interest, including Mg²⁺, Ca²⁺, Sr²⁺, Mn²⁺, Li⁺, Na⁺ and K⁺, on the equilibrium hydrolysis of ATP.     

The monomer -- dimer association of rabbit lver aryl sulfatase A and its relationship to the anomalous kinetics.

The polymerization of aryl sulfatase A (aryl sulfate sulfohydrolase, EC 3.1.6.1) has been studied by frontal gel chromatography on Sephadex G-200 and Bio-Gel A-5m under various conditions of pH, ionic strength, and temperature. The aryl sulfatase A molecule exists as a monomer and as a dimer at pH 7.5 and pH 4.5, respectively. The extent of dissociation is markedly pH-, protein concentration-, and ionic strength-dependent. Only a small effect of temperature was observed. The enthalpy change (ΔH^o) for the dissociation was ?2.5 ± 1 kcal/mol at pH 5.5–5.6, and the entropy change for dissociation of the enzyme dimer to two monomeric units was ?47 cal mol^?1 deg^?1. Sulfate ion has little effect on the extent of dissociation of the enzyme at pH 5.6. The present studies suggest that the dissociation of rabbit liver aryl sulfatase A is regulated by the ionization of amino acid residues whose apparent pK is between pH 5 and 6. The driving force for the association of the subunits of the enzyme is primarily ionic and/or ionic/hydrogen bond formation. The small enthalpy change and the fact that dissociation is strongly favored by an increase in the ionic strength suggest that hydrophobic interactions play only a minor role in stabilizing the dimeric quaternary structure relative to the monomeric state. The monomeric form of the enzyme exhibits the anomalous kinetics often observed with sulfatase A but the dimer does not show anomalous kinetics. Since aryl sulfatase A is probably in the dimeric form in the lysosome, the anomalous kinetics of the enzyme are unlikely to be of physiological importance in the intact lysosome.     

The binding of Ni2+ to adenylyl-3',5'-adenosine and to poly(adenylic acid)

Studies of the binding of Ni²⁺ to adenylyl-3',5'-adenosine (ApA) at pH 6-0 by ultraviolet spectrophotometry indicate the formation of a 1:1 complex in the presence of a large excess of metal ion. At 25 °C. and ionic strength μ = 0.5 M, the stability constant of Ni(ApA) is evaluated to be K = 2.6 (±0.6) M^?1. The low stability is taken as evidence that the predominant complex species is one in which the ApA acts as a monodentate ligand, mainly through the adenine group. The rate constants for complex formation and dissociation, k_f = 1430 M^?1 s^?1 and k_b = 665 s^?1 (25°C. μ = 0.5M). determined by the temperature-jump relaxation technique, are consistent with this interpretation. The binding strength of Ni²⁺ to poly(adenylic acid) [poly(A)] has been studied at pH 7.0 using murexide as an indicator of the concentration of free Ni²⁺. Within the concentration range [Ni²⁺ = 1 × 10^?5 × 10^?3 M the data can be represented in the form of a linear Scatchard plot. i.e., the process can be described as the binding of Ni²⁺ to one class of independent binding sites. The number of binding sites per monomer is 0.26, and the stability constant K = 8.2×10³ M^?1 (25°C μ = 0.1 M). In kinetic studies of the reaction of Ni²⁺ with poly(A), two relaxation effects due to complex formation were detected, one with a concentration-independent time constant of about 0.4 ms, the other with a concentration-dependent time constant in the millisecond range. The concentration dependence of the longer relaxation time can be accounted for by a three-step mechanism which consists of a fast second-order association reaction followed by two first-order steps. There is evidence, however, that the overall process is more complicated than expressed by the three-step mechanism.     

The reaction between cytochrome C1 and cytochrome C

The kinetics of electron transfer between the isolated enzymes of cytochrome c₁ and cytochrome c have been investigated using the stopped-flow technique. The reaction between ferrocytochrome c₁ and ferricytochrome c is fast; the second-order rate constant (k₁) is 3.0 · 10⁷ M^?1 · s^?1 at low ionic strength (I = 223 mM, 10°C). The value of this rate constant decreases to 1.8 · 10⁵ M^?1 · s^?1 upon increasing the ionic strength to 1.13 M. The ionic strength dependence of the electron transfer between cytochrome c₁ and cytochrome c implies the involvement of electrostatic interactions in the reaction between both cytochromes. In addition to a general influence of ionic strength, specific anion effects are found for phosphate, chloride and morpholinosulphonate. These anions appear to inhibit the reaction between cytochrome c₁ and cytochrome c by binding of these anions to the cytochrome c molecule. Such a phenomenon is not observed for cacodylate. At an ionic strength of 1.02 M, the second-order rate constants for the reaction between ferrocytochrome c₁ and ferricytochrome c and the reverse reaction are k₁ = 2.4 · 10⁵ M^?1 · s^?1 and k_?1 = 3.3 · 10⁵ M^?1 · s^?1, respectively (450 mM potassium phosphate, pH 7.0, 1% Tween 20, 10°C). The ‘equilibrium’ constant calculated from the rate constants (0.73) is equal to the constant determined from equilibrium studies. Moreover, it is shown that at this ionic strength, the concentrations of intermediary complexes are very low and that the value of the equilibrium constant is independent of ionic strength. These data can be fitted into the following simple reaction scheme: cytochrome c²⁺₁ + cytochrome c³⁺ai cytochrome c³⁺₁ + cytochrome c²⁺.     

Thermodynamics of the interaction of daunomycin with DNA

The association constant for the interaction of daunomycin with DNA was determined as a function of temperature (using [³H] daunomycin in conventional equilibrium dialysis cells) and ionic strength (using a spectrophotometric titration method). The association constant varied between 3.1 × 10⁶ M^?1 (4°C) and 3.9 × 10⁵ M^?1 (65°C). The free energy change was ?8.2 to ?8.8 $\text{kcal}\text{mol}$, the enthalpy change ?5.3 $\text{kcal}\text{mol}$ and the entropy change +10 to +11 eu, all values being consistent with that expected of an intercalation process. The apparent number of intercalation sites detected (0.15 to 0.16 per nucleotide) was independent of temperature. The large positive entropy change accompanying the interaction appeals to be due to extensive release of water from the DNA and daunomycin. The apparent number of binding sites increased dramatically with decrease of ionic strength, although the apparent association constant remained largely unaffected by ionic strength.     

Dissociation of pig liver carboxylesterase measured by quantitative micro-complement fixation

Rate and apparent equilibrium constants for the dissociation of pig liver carboxylesterase into three subunit molecules have been determined by complement fixation. The dependence of the dissociation equilibria on pH are consistent with dissociation reactions involving the addition of two protons per subunit, a pH-independent dissociation, and a dissociation upon the loss of one proton per subunit. The rate constants for dissociation are consistent with terms first order in hydrogen and hydroxide ions and a pH-independent path. The equilibrium constants in the range 3–35 °C at pH 7.2 exhibit no dependence on temperature; the association reaction is entropy driven with $\text{ΔS = 68}\text{cal mol}{}^{\mathrm{?1}}{}^{\mathrm{°}}\text{K}{}^{\mathrm{?1}}$. The rate constants for the pH-independent dissociation follow ΔH^≠ ? 6 kcal mol^?1. The order of effectiveness of concentrated salts in promoting denaturation is correlated with their effect on the activity coefficient of acetyltetraglycine ethyl ester and suggests that peptide groups become more exposed upon dissociation. The increased dissociation in the presence of urea derivatives containing alkyl substituents suggests exposure of hydrophobic regions upon dissociation; this is also consistent with ΔH = 0 for dissociation. It is likely that hydrophobic interactions contribute to the stability of the trimeric whole molecule.     

Complexes of vitamin B6. XVI. Kinetics and reaction mechanism of iron(III) complexes with pyridoxal-5′-phosphate

The stopped flow technique has been used to study the kinetics of complex formation of iron(III) with pyridoxal-5-phosphate (PLP) in the pH range 1.00–2.50, and in the temperature range 18 °C– 30 °C, at an ionic strength of. 0.50 M (NaCl). From the initial concentration dependence of PLP (T_PLP,) of the reaction rate it can be shown that two kinetic steps can be represented as: k_obs′ = m_i + m_i′_PLP where m_i and m_i′ are pH-dependent parameters. The calculated activation data are δE* = 23.2 ± 1.8 kcal mol^?1 and 10.98 ± 0.53 kcal mol^?1 for the first and second kinetic steps, respectively and δS* are ?20.50 ± 5.96 e.u. and 24.62 ± 1.81 e.u., respeetively.     

Kinetic and thermodynamic studies on nitrobenzylthioinosine binding to the nucleoside transporter of chinese hamster ovary cells

The binding of [G-³H]nitrobenzylthioinosine to intact Chinese hamster ovary cells has been studied kinetically and thermodynamically. The association of nitrobenzylthioinosine with cells is a second-order process which proceeds at 24°C with a rate constant of 2·10⁷ M^?1·s^?1. Dissociation of the complex was characterized as a simple first-order process with rate constant on the order of 7·10^?3 s^?1. The quotient of these is comparable to the dissociation constant as measured in equilibrium binding studies, 2.2·10^?10 M. The temperature dependence of the rate of association indicated an Arrhenius activation energy of 8.4 kcal·mol^?1, while that of the equilibrium constant for dissociation indicated a standard enthalpy change of 8.8 kcal·mol^?1. The large increase in affinity of nitrobenzylthioinosine as compared to natural nucleosides is attributable to an entropy-driven interaction with the binding site. Thymidine, dipyridamole and papaverine each decrease the apparent dissociation constant for the nitrobenzylthioinosine-cell complex; the latter, inhibitors of nucleoside transport, decrease the rate of dissociation of the complex.     

Simultaneous determination of ΔG, ΔH and ΔS by an automatic microcalorimetric titration technique. Application to protein ligand binding

A methodological study has been made with a syringe titration unit attached to an LKB batch microcalorimeter. The presicion and accuracy of the instrument assembly have been evaluated by neutralization reactions and by dilution of sucrose solutions. As an example, heat quantities on the order of 10 mJ accompanying the addition of 10 μl titrant solution could be determined with an accuracy of better than 1%. A stepwise titration procedure was used to characterize the binding of indole-3-propionic acid to α-chymotrypsin. The following thermodynamic data were obtained (25°C, acetate buffer, pH 5.80): ΔG⁰ = ?18.46±0.17 kJ·mol^?1, ΔH⁰ = ?15.26±0.20 kJ·mol^?1, ΔS⁰ = 10.85±1.21 JK^?·mol^?1.     

Kinetics of interaction of some α- and β-D-monosaccharides with concanavalin A

The rates of formation and dissociation of concanavalin A with some 4-methylumbelliferyl and p-nitrophenyl derivatives of α- and β-D-mannopyranosides and glucopyranosides were measured by fluorescence and spectral stopped-flow methods. All process examined were uniphasic. The second-order formation rate constants varied only from 6.8 · 10⁴ to 12.8 · 10⁴ M^?. s^?1, whereas the first-order dissociation rate constants ranged from 4.1. to 220 s^?1, all at ph 5.0, I = 0.3 M, and 25°C. Dissociation rates thus controlled the value of binding constant. The effect of temperature on these reactions was examined, from which enthalpies and entropies of activation and of reaction could be calculated. The effects of pH at 25°C on the reaction rates of 4-methylumbelliferyl α-D-mannopyranoside and 4-methylumbelliferyl α-D-glucopyranoside with concanavalin A were examined. The value of the binding constant K_ap (derived from the kinetics) at any pH could be related to the intrinsic binding constant K by the expression K_ap = K_aK(K_a + [H⁺])^?1. The values of K_a, the ionization constant of the protein segment responsive to sugar binding, were 3 · 10^?4 M and 1 · 10^?4 M for 4-methylumbelliferyl α-D-mannopyranoside and 4-methylumbelliferyl α-D-glucopyranoside, respectively. The binding constant of p-nitrophenyl α-D-mannopyranoside is surprisingly much less sensitive to a pH change from 5.0 to 2.7. Ionic strength had little effect on the binding characteristics of 4-methylumbelliferyl α-D-mannopyranoside to concanavalin A at pH 5.2 and 25°C.     

Detection of interaction between lysionotin and bovine serum albumin using spectroscopic techniques combined with molecular modeling

A combination of fluorescence, UV–Vis absorption, circular dichroism (CD), Fourier transform infrared (FT-IR) and molecular modeling approaches were employed to determine the interaction between lysionotin and bovine serum albumin (BSA) at physiological pH. The fluorescence titration suggested that the fluorescence quenching of BSA by lysionotin was a static procedure. The binding constant at 298 K was in the order of 10⁵ L mol^?1, indicating that a high affinity existed between lysionotin and BSA. The thermodynamic parameters obtained at different temperatures (292, 298, 304 and 310 K) showed that the binding process was primarily driven by hydrogen bond and van der Waals forces, as the values of the enthalpy change (ΔH°) and entropy change (ΔS°) were found to be ?40.81 ± 0.08 kJ mol^?1 and ?35.93 ± 0.27 J mol^?1 K^?1, respectively. The surface hydrophobicity of BSA increased upon interaction with lysionotin. The site markers competitive experiments revealed that the binding site of lysionotin was in the sub-domain IIA (site I) of BSA. Furthermore, the molecular docking results corroborated the binding site and clarified the specific binding mode. The results of UV–Vis absorption, CD and FT-IR spectra demonstrated that the secondary structure of BSA was altered in the presence of lysionotin.     

Properties of human growth hormone binding sites solubilized from female rabbit kidney

Human growth hormone binding sites from female rabbit kidney microsomes were solubilized by treatment with the nonionic detergent Triton X-100. The binding of ¹²⁵I-labelled human growth hormone to the solubilized sites retains many of the properties observed in the particulate fraction, such as saturability, reversibility, high affinity and structural specificity. The association and the dissociation process are time- and temperature-dependent. The association rate constant, k₁, is 1.6·10⁷ mol^?1·l·min^?1 at 25°C, and the dissociation rate constant, k_?1, is 2.8·10^?4 min^?1 at 25°C. Solubilization causes an increase in affinity as well as in binding capacity. Scatchard plots from saturation curves suggest the presence of a single class of binding site with a dissociation equilibrium constant, K_d, of 1.3·10^?11 M and a binding capacity of 133 fmol/mg of protein. Similar results were obtained from competition experiments. Specificity studies revealed the lactogenic characteristics of the solubilized sites. The Stokes radii of the free binding sites and of the ¹²⁵I-labelled human growth hormone-binding site complex, determined on a Sepharose CL-6B column, are 57 and 53 Å, respectively.     

The standard Gibbs free energy change of hydrolysis of alpha-D-ribose 1-phosphate

The standard Gibbs free energy change of hydrolysis of α-d-ribose 1-phosphate has been measured at pH 7.0, ionic strength 0.1 m, and 25 °C by combining the corresponding values of the two following reactions: adenosine + H₂O ág adenine + ribose (ΔG^0′ = ?2.3 ± 0.1 kcal/mol), catalyzed by adenosine nucleosidase, and ribose 1-phosphate + adenine ág adenosine + P_i (ΔG^0′ = ?3.1 ± 0.1 kcal/mol), catalyzed by adenosine phosphorylase. The standard Gibbs free energy changes were calculated for both reactions from the equilibrium constant. A value of -5.4 ± 0.15 kcal/mol, comparable to that of other hemiacetal phosphoric esters, was obtained for the hydrolysis of ribose 1-phosphate.     

Thermodynamics of gelation of sickle cell deoxyhemoglobin.

This paper describes the thermodynamic behavior of gels of deoxyhemoglobin S. The solubility of the protein with respect to assembled hemoglobin fibers has been measured using a sedimentation technique. The solubility in 0.15 m-potassium phosphate buffer (pH 7.15) is found to decrease with increasing temperature, attain a minimum value of 0.16 g cm^?3 at 37 °C, and then increase at higher temperatures. The amount of polymer present at various hemoglobin concentrations and temperatures is presented as part of a phase diagram that may be useful for the calibration of other measurement techniques. The effects of varying pH and urea concentration upon the solubility have also been studied.The heat absorption accompanying gelation has been measured by scanning calorimetry. Using sedimentation data on the amount of polymer formed, molar enthalpy changes are obtained. There is a large negative heat capacity change of ? 197 cal deg. mol^?1 and ΔH = 0 near 37 °C. Calorimetric molar enthalpy changes are found to agree with those calculated from the temperature dependence of the solubility by the van't Hoff equation.Our previous two-phase, two-component thermodynamic model of gelation is extended to include the effects of solution non-ideality. A large contribution to the activity of the hemoglobin in the solution phase results from the geometric effect of excluded volume. Incorporating solution phase non-ideality permits the calculation of standard state thermodynamic quantities for the gelation process at 37 °C: ΔG^O ? ?3 k cal mol^?1, ΔH^O ~ 0, ΔS^O ~ 10 cal deg.^?1 mol^?1. The excluded volume effect is also capable of explaining observations of the minimum gelling concentrations of hemoglobin mixtures containing deoxyhemoglobin S without requiring copolymerization of the non-S hemoglobin.     

A simple procedure for resolution of Escherichia coli RNA polymerase holoenzyme from core polymerase.

The association constant, K_A, for myosin subfragment-1 binding to actin was measured as a function of ionic strength [KCl, LiCl, and tetramethylammonium chloride (TMAC)]and temperature by the method of time-resolved fluorescence depolarization. The following thermodynamic values were obtained from solutions of 0.20 × 10^?6m S-1, 1.00 × 10^?6m actin in 0.15 m KCl, pH 7.0, at 25 °C: ΔG ° = ?39 ± 1 kJ M^?1, ΔH⁰ = 44 ± 2 kJ M^?1 and $\text{ΔS}{}^0\text{= 0.28 ± 0.01 kJ}\text{M}{}^{\mathrm{?1}}{}^0\text{K}{}^{\mathrm{?1}}$. For measurements in KCl (0.05 to 0.60 m), In $\text{K}{}_{\mathrm{a}}\text{= ?8.36 (KCl)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. Thus, the binding is endothermic and strongly inhibited by high ionic strength. When KCl was replaced by LiCl or TMAC the ionic effects on the binding were cation specific. The nature of actin-(S-1) binding in the rigor state is discussed in terms of these results.     

Kinetics and thermodynamics of the P870+Q−A → P870+Q−B reaction in isolated reaction centers from the photosynthetic bacterium Rhodopseudomonas sphaeroides

The temperature dependences of the P870⁺Q^?_A → P870Q_A and P870⁺Q^?_B → P870Q_B recombination reactions were measured in reaction centers from Rhodopseudomonas sphaeroides. The data indicate that the P870⁺Q^?_B state decays by thermal repopulation of the P870⁺Q^?_A state, followed by recombination. ΔG° for the P870⁺Q^?_A → P870⁺Q^?_B reaction is ?6.89 kJ · mol^?1, while ΔH° = ?14.45 kJ · mol^?1 and ?TΔS° = + 7.53 kJ · mol^?1. The activation ethalpy, $\text{H}{}^3$, for the P870⁺Q^?_A Δ P870⁺Q^?_B reaction is +56.9 kJ · mol^?1, while the activation entropy is near zero. The results permit an estimate of the shape of the potential energy curve for the P870⁺Q^?_A → P870⁺Q^?_B electron transfer reaction.     

Acid dissociation of cyclohexaamylose and cycloheptaamylose

Acid dissociation constants of aqueous cyclohexaamylose (6-Cy) and cycloheptaamylose (7-Cy) have been determined at 10–47 and 25–55°C, respectively, by pH potentiometry. Standard enthalpies and entropies of dissociation derived from the temperature dependences of these pK_a's are ΔH⁰ = 8.4 ± 0.3 kcal mol^?1, $\text{Δ}\text{S}{}^0\text{= ?28. ± 1}\text{cal mol}{}^{\mathrm{?1}}{}^0\text{K}{}^{\mathrm{?1}}$ for 6-Cy and ΔH⁰ = 10.0 ± 0.1 kcal mol^?1, $\text{Δ}\text{S}{}^0\text{= ?22.4 ±0.3}\text{cal mol}{}^{\mathrm{?1}}{}^0\text{K}{}^{\mathrm{?1}}$ for 7-Cy. Intrinsic ¹³C nmr resonance displacements of anionic 6- and 7-Cy were measured at 30°C in 5% D₂O ($\text{v}\text{v}$). These results indicate that the dissociation of 6- and 7-Cy involves both C2 and C3 2⁰-hydroxyl groups. The thermodynamic and nmr parameters are discussed in terms of interglucosyl hydrogen bonding.     

A thermodynamic description of the self-association of flavin mononucleotide.

Systematic heat of dilution studies of the self-association of flavin mononucleotide (FMN) have been conducted as a function of ionic strength (0.05 – 2.0 m) and pH (5–9) in aqueous solution. The data are adequately described by the expression $\text{Q}{}_{\mathrm{T}}\text{= ΔH ? (}\text{ΔH}\text{K}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(}\text{Q}{}_{\mathrm{T}}\text{c}{}_{\mathrm{T}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ for an isodesmic self-association. Q_T is the molar heat of dilution, ΔH and K are the derived enthalpy and equilibrium constants for the process FMN + (FMN)_i?1 ? (FMN)_i, and c_T is the concentration of FMN expressed in monomer units. Typical values derived for the various thermodynamic parameters at 25 °C are ΔG = ?3.56 kcal mol^?1, ΔH = ?3.72 kcal mol^?1, and ΔS = ?0.54 cal (mol · deg)^?1. These data, plus nuclear magnetic resonance evidence (Yagi, K., Ohishi, N., Takai, A., Kawano, K., and Kyogoku, Y., 1976, Biochemistry15, 2877–2880) argue in favor of an open-ended association of flavin molecules. The signs of the various thermodynamic parameters suggest that both hydrophobic and surface energy forces contribute significantly to the association, while the lack of any significant ionic strength dependence indicates the lack of any ionic centers in the association.