Electron acceptors associated with P-700 in Triton solubilized Photosystem I particles from spinach chloroplasts

Flash-induced absorption changes of Triton-solubilized Photosystem I particles from spinach were studied under reducing and/or illumination conditions that serve to alter the state of bound electron acceptors. By monitoring the decay of P-700 following each of a train of flashes, we found that P-430 or components resembling it can hold 2 equivalents of electrons transferred upon successive illuminations. This requires the presence of a good electron donor, reduced phenazine methosulfate or neutral red, otherwise the back reaction of P-700⁺ with P-430 occurs in about 30 ms. If the two P-430 sites, designated Centers A and B, are first reduced by preilluminating flashes or chemically by dithionite under anaerobic conditions, then subsequent laser flashes generate a 250 μs back reaction of P-700⁺, which we associate with a more primary electron acceptor A₂. In turn, when A₂ is reduced by background (continuous) illumination in presence of neutral red and under strongly reducing conditions, laser flashes then produce a much faster (3 μs) back reaction at wavelengths characteristic of P-700. We associate this with another more primary electron acceptor, A₁, which functions very close to P-700. The organization of these components probably corresponds to the sequence $\text{P-700-}\text{A}{}_1\text{-}\text{A}{}_2\text{-P-430[}\text{A}\text{B}\text{]}$. The relation of the optical components to acceptor species detected by EPR, by electron-spin polarization or in terms of peptide components of Photosystem I is discussed.Preliminary experiments with broken chloroplasts suggest that an analogous situation occurs there, as well.     

Influence of temperature on Photosystem II electron transfer reactions

The influence of temperature on the rate of reduction of P-680⁺, the primary donor of Photosystem II, has been studied in the range 5–294 K, in chloroplasts and subchloroplasts particles. P-680 was oxidized by a short laser flash. Its oxidation state was followed by the absorption level at 820 nm, and its reduction attributed to two mechanisms: electron donation from electron donor D₁ and electron return from the primary plastoquinone (back-reaction).Between 294 and approx. 200 K, the rate of the back-reaction, on a logarithmic scale, is a linear function of the reciprocal of the absolute temperature, corresponding to an activation energy between 3.3 and 3.7 kcal · mol^?1, in all of the materials examined (chloroplasts treated at low pH or with Tris; particles prepared with digitonin). Between approx. 200 K and 5 K the rate of the back-reaction is temperature independent, with $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 1.6}\text{ms}$. In untreated chloroplasts we measured a $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of 1.7 ms for the back-reaction at 77 and 5 K.The rate of electron donation from the donor D₁ has been measured in darkadapted Tris-treated chloroplasts, in the range 294–260 K. This rate is strongly affected by temperature. An activation energy of 11 kcal · mol^?1 was determined for this reaction.In subchloroplast particles prepared with Triton X-100 the signals due to P-680 were contaminated by absorption changes due to the triplet state of chlorophyll a. This triplet state has been examined with pure chlorophyll a in Triton X-100. An Arrhenius plot of its rate of decay shows a temperature-dependent region (292–220 K) with an activation energy of 9 kcal · mol^?1, and a temperature-independent region (below 200 K) with $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 1.1}\text{ms}$.     

Flash-induced absorption changes of the primary donor of photosystem II at 820 nm in chloroplasts inhibited by low pH or tris-treatment

A comparative study is made, at 15 °C, of flash-induced absorption changes around 820 nm (attributed to the primary donors of Photosystems I and II) and 705 nm (Photosystem I only), in normal chloroplasts and in chloroplasts where O₂ evolution was inhibited by low pH or by Tris-treatment.At pH 7.5, with untreated chloroplasts, the absorption changes around 820 nm are shown to be due to P-700 alone. Any contribution of the primary donor of Photosystem II should be in times shorter than 60 μs.When chloroplasts are inhibited at the donor side of Photosystem II by low pH, an additional absorption change at 820 nm appears with an amplitude which, at pH 4.0, is slightly higher than the signal due to oxidized P-700. This additional signal is attributed to the primary donor of Photosystem II. It decays ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ about 180 μs) mainly by back reaction with the primary acceptor and partly by reduction by another electron donor. Acid-washed chloroplasts resuspended at pH 7.5 still present the signal due to Photosystem II ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ about 120 μs). This shows that the acid inhibition of the first secondary donor of Photosystem II is irreversible.In Tris-treated chloroplasts, absorption changes at 820 nm due to the primary donor of Photosystem II are also observed, but to a lesser extent and only after some charge accumulation at the donor side. They decay with a half-time of 120 μs.     

Damping of oscillations in the semiquinone absorption in reaction centers after successive flashes. Determination of the equilibrium between QA−QB and QAQB−

A quantitative model for the damping of oscillations of the semiquinone absorption after successive light flashes is presented. It is based on the equilibrium between the states Q_A^?Q_B and Q_AQ_B^?. A fit of the model to the experimental results obtained for reaction centers from Rhodopseudomonas sphaeroides gave a value of $\text{α =}\text{[}\text{Q}{}_{\mathrm{<mtext>A</mtext>}}{}^{\mathrm{?}}\text{Q}{}_{\mathrm{<mtext>B</mtext>}}\text{]}\text{([}\text{Q}{}_{\mathrm{<mtext>A</mtext>}}{}^{\mathrm{?}}\text{Q}{}_{\mathrm{<mtext>B</mtext>}}\text{] + [}\text{Q}{}_{\mathrm{<mtext>A</mtext>}}\text{Q}{}_{\mathrm{<mtext>B</mtext>}}{}^{\mathrm{?}}\text{])}\text{= 0.065 ± 0.005}$ (T = 21°C, pH 8).     

Flash-induced photophosphorylation in chloroplasts with activated ATPase

Chloroplasts which were rapidly isolated from illuminated leaves showed activity of ATP hydrolysis at a level much higher than that of the dark control. Under the high-intensity illumination or under repetitive flash excitation, the activated chloroplasts synthesized more ATP than those with a low ATP hydrolysis activity. formed under repetitive flashes was smaller in the activated chloroplasts than in the inactive chloroplasts. The inhibition of ATP yield per flash by valinomycin or nigericin in the presence of K⁺ was stronger in the inactive chloroplasts than in the activated chloroplast. ATP synthesis in the activated chloroplasts seems to have a lower threshold.     

New experimental approach to the estimation of rate of electron transfer from the primary to secondary acceptors in the photosynthetic electron transport chain of purple bacteria

A method for calculating the rate constant ($\text{K}{}_{\mathrm{<mtext>A</mtext><mtext>1</mtext><mtext>A</mtext><mtext>2</mtext>}}$) for the oxidation of the primary electron acceptor (A₁) by the secondary one (A₂) in the photosynthetic electron transport chain of purple bacteria is proposed.The method is based on the analysis of the dark recovery kinetics of reaction centre bacteriochlorophyll (P) following its oxidation by a short single laser pulse at a high oxidation-reduction potential of the medium. It is shown that in Ectothiorhodospira shaposhnikovii there is little difference in the value of $\text{K}{}_{\mathrm{<mtext>A</mtext><mtext>1</mtext><mtext>A</mtext><mtext>2</mtext>}}$ obtained by this method from that measured by the method of Parson ((1969) Biochim. Biophys. Acta 189, 384–396), namely: $\text{(4.5±1.4) · 10}{}^3\text{s}{}^{\mathrm{?1}}$ and $\text{(6.9±1.2) · 10}{}^3\text{s}{}^{\mathrm{?1}}$, respectively.The proposed method has also been used for the estimation of the $\text{K}{}_{\mathrm{<mtext>A</mtext><mtext>1</mtext><mtext>A</mtext><mtext>2</mtext>}}$ value in chromatophores of Rhodospirillum rubrum deprived of constitutive electron donors which are capable of reducing P⁺ at a rate exceeding this for the transfer of electron from A₁ to A₂. The method of Parson cannot be used in this case. The value of $\text{K}{}_{\mathrm{<mtext>A</mtext><mtext>1</mtext><mtext>A</mtext><mtext>2</mtext>}}$ has been found to be $\text{(2.7±0.8) · 10}{}^3\text{s}{}^{\mathrm{?1}}$.The activation energies for the A₁ to A₂ electron transfer have also been determined. They are 12.4 kcal/mol and 9.9 kcal/mol for E. shaposhnikovii and R. rubrum, respectively.     

Reactions between primary and secondary acceptors of Photosystem II in Chlorella Pyrenoidosa under anaerobic conditions as studied by chlorophyll a fluorescence

The kinetics of the fluorescence yield Ф of chlorophyll a in Chlorella pyrenoidosa were studied under anaerobic conditions in the time range from 50 μs to several minutes after short ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 30}\text{ns}$ or 5 μs) saturating flashes. The fluorescence yield “in the dark” increased from $\text{Ф = 1}$ at the beginning to $\text{Ф ≈ 5}$ in about 3 h when single flashes separated by dark intervals of about 3 min were given.After one saturating flash, Ф increased to a maximum value (4–5) at 50 μs, then Ф decreased to about 3 with a half time of about 10 ms and to the initial value with a half time of about 2 s. When two flashes separated by 0.2 s were given, the first phase of the decrease after the second flash occurred within 2 ms. After one flash given at high initial fluorescence yield, the 10-ms decay was followed by a 10 s increase to the initial value. After the two flashes 0.2 s apart, the rapid decay was not follewed by a slow increase.These and other experiments provided additional evidence for and extend an earlier hypothesis concerning the acceptor complex of Photosystem II (Bouges-Bocquet, B. (1973) Biochim. Biophys. Acta 314, 250–256; Velthuys, B. R. and Amesz, J. (1974) Biochim. Biophys. Acta 333, 85–94): reaction center 2 contains an acceptor complex QR consisting of an electron-transferring primary acceptor molecule Q, and a secondary electron acceptor R, which can accept two electrons in succession, but transfers two electrons simultaneously to a molecule of the tertiary acceptor pool, containing plastoquinone (A). Furthermore, the kinetics indicate that 2 reactions centers of System I, excited by a short flash, cooperate directly or indirectly in oxidizing a plastohydroquinone molecule (A^2?). If initially all components between photoreaction 1 and 2 are in the reduced state the following sequence of reactions occurs after a flash has oxidised A^2? via System I: Q^?R^2? + A → Q^?R + A^2? → QR^? + A^2?. During anaerobiosis two slow reactions manifest themselves: the reduction of R (and A) within 1 s, presumably by an endogenous electron donor D₁, and the reduction of Q in about 10 s when R is in the state R^? and A in the state A^2?. An endogenous electron donor, D₂, and Q^? compete in reducing the photooxidized donor complex of System II in reactions with half times of the order of 1 s.     

Photosystem II energy coupling in chloroplasts with H2O2 as electron donor

NH₂OH-treated, non-water-splitting chloroplasts can oxidize H₂O₂ to O₂ through Photosystem II at substantial rates (100–250 μequiv · h^?1 · mg^?1 chlorophyll with 5 mM H₂O₂) using 2,5-dimethyl-p-benzoquinone as an electron acceptor in the presence of the plastoquinone antagonist dibromothymoquinone. This H₂O₂ → Photosystem II → dimethylquinone reaction supports phosphorylation with a $\text{P}\text{e}{}_2$ ratio of 0.25–0.35 and proton uptake with $\text{H}{}^{\mathrm{+}}\text{e}$ values of 0.67 (pH 8)–0.85 (pH 6). These are close to the $\text{P}\text{e}{}_2$ value of 0.3–0.38 and the $\text{H}{}^{\mathrm{+}}\text{e}$ values of 0.7–0.93 found in parallel experiments for the H₂O → Photosystem II → dimethylquinone reaction in untreated chloroplasts. Semi-quantitative data are also presented which show that the donor → Photosystem II → dibromothymoquinone (→O₂) reaction can support phosphorylation when the donor used is a proton-releasing reductant (benzidine, catechol) but not when it is a non-proton carrier (I^?, ferrocyanide).     

The reduction of the oxygen-evolving system in chloroplasts by thylakoid components

Using thoroughly dark-adapted thylakoids and an unmodulated Joliot-type oxygen electrode, the following results were obtained. (i) At high flash frequency (4 Hz), the oxygen yield at the fourth flash (Y₄) is lower compared to Y₃ than at lower flash frequency. At 4 Hz, the calculated S₀ concentration after thorough dark adaptation is found to approach zero, whereas at 0.5 Hz the apparent $\text{S}{}_0\text{(}\text{S}{}_0\text{+}\text{S}{}_1\text{)}$ ratio increases to about 0.2. This is explained by a relatively fast donation ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 1.0–1.5}\text{s}$) of one electron by an electron donor to S₂ and S₃ in 15–25% of the Photosystem II reaction chains. The one-electron donor to S₂ and S₃ appears to be rereduced very slowly, and may be identical to the component that, after oxidation, gives rise to ESR signal II_s. (ii) The probability for the fast one-electron donation to S₂ and S₃ has nearly been the same in triazine-resistant and triazine-susceptible thylakoids. However, most of the slow phase of the S₂ decay becomes 10-fold faster ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 5–6}\text{s}$) in the triazine-resistant ones. In a small part of the Photosystem II reaction chains, the S₂ decay was extremely slow. The S₃ decay in the triazine-resistant thylakoids was not significantly different from that in triazine-susceptible thylakoids. This supports the hypothesis that S₂ is reduced mainly by Q^?_A, whereas S₃ is not. (iii) In the absence of CO₂/HCO^?_A and in the presence of formate, the fast one-electron donation to S₂ and S₃ does not occur. Addition of HCO^?₃ restores the fast decay of part of S₂ and S₃ to almost the same extent as in control thylakoids. The slow phase of S₂ and S₃ decay is not influenced significantly by CO₂/HCO^?₃. The chlorophyll a fluorescence decay kinetics in the presence of DCMU, however, monitoring the Q^?_A oxidation without interference of Q_B, were 2.3-fold slower in the absence of CO₂/HCO^?₃ than in its presence. (iv) An almost 3-fold decrease in decay rate of S₂ is observed upon lowering the pH from 7.6 to 6.0. The kinetics of chlorophyll a fluorescence decay in the presence of DCMU are slightly accelerated by a pH change from 7.6 to 6.0. This indicates that the equilibrium Q^?_A concentration after one flash is decreased (by about a factor of 4) upon changing the pH from 7.6 to 6.0. When direct or indirect protonation of Q^?_B is responsible for this shift of equilibrium Q^?_A concentration, these data would suggest that the pK_a value for Q^?_B protonation is somewhat higher than 7.6, assuming that the protonated form of Q^?_B cannot reduce Q_A.     

Kinetics of reduction of the oxidized primary electron donor of Photosystem II in spinach chloroplasts and in Chlorella cells in the microsecond and nanosecond time ranges following flash excitation

Absorption changes (ΔA) at 820 nm, following laser flash excitation of spinach chloroplasts and Chlorella cells, were studied in order to obtain information on the reduction time of the photooxidized primary donor of Photosystem II at physiological temperatures.In the microsecond time range the difference spectrum of ΔA between 750 and 900 nm represents a peak at 820 nm, attributable to a radical-cation of chlorophyll a. In untreated dark-adapted material the signal can be attributed solely to P⁺?700; it decays in a polyphasic manner with half-times of 17 μs, 210 μs and over 1 ms. The oxidized primary donor of Photosystem II (P⁺_II) is not detected with a time resolution of 3 μs. After treatment with 3–10 mM hydroxylamine, which inhibits the donor side of Photosystem II, P⁺_II is observed and decays biphasically (a major phase with $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 20–40 μ}\text{s}$, and a minor phase with $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 200 μ}\text{s}$), probably by reduction by an accessory electron donor.In the nanosecond range, which was made accessible by a new fast-response flash photometer operating at 820 nm, it was found the P⁺_II is reduced with a half-time of 25–45 ns in untreated dark-adapted chloroplasts. It is assumed that the normal secondary electron donor is responsible for this fast reduction.     

Dual action of ionophore A23187 on intact chloroplasts

1. Ionophore A23187 induces uncoupling of potassium ferricyanide-dependent O₂ evolution by envelope-free chloroplasts and oxaloacetate-dependent O₂ evolution by intact chloroplasts. The half maximal concentration ($\text{C}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) for stimulation of oxygen evolution in both cases is approximately 4 μM · 100 μg chlorophyll · ml^?1.2. Ionophore A23187 also induces inhibition of CO₂ and 3-phosphoglycerate-dependent O₂ evolution by intact chloroplasts in the presence of 3 mM MgCl₂. The half maximal concentrations ($\text{C}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) for inhibition of O₂ evolution are 3 μM and 5 μM respectively · 100 μg^?1 chlorophyll · ml^?1.3. A very high concentration of ionophore A23187 (10 μM · 20 μg^?1 chlorophyll · ml^?1) plus 0.1 mM EDTA lowers the fluorescence yield of intact chloroplasts suspended in a cation-free medium in the presence of 3-(3,4-dichlorophenyl)-1,1-dimethylurea, indicating loss of divalent cation from the diffuse double layers of the thylakoid membranes.4. These results are discussed in relation to ionophore A23187-induced divalent cation/proton exchange at both the thylakoid and the envelope membranes of intact chloroplasts.     

Isolation and characterization of isocitrate lyase of castor endosperm

Isocitrate lyase (threo-D_S-isocitrate glyoxylate-lyase, EC 4.1.3.1) has been purified to homogeneity from castor endosperm. The enzyme is a tetrameric protein (molecular weight about 140,000; gel filtration) made up of apparently identical monomers (subunit molecular weight about 35,000; gel electrophoresis in the presence of sodium dodecyl sulfate). Thermal inactivation of purified enzyme at 40 and 45 °C shows a fast and a slow phase, each accounting for half of the intitial activity, consistent with the equation: , where A₀ and A_t are activities at time zero at t, and k₁ and k₂ are first-order rate constants for the fast and slow phases, respectively. The enzyme shows optimum activity at pH 7.2–7.3. Effect of [S]on enzyme activity at different pH values (6.0–7.5) suggests that the proton behaves formally as an “uncompetitive inhibitor.” A basic group of the enzyme (site) is protonated in this pH range in the presence of substrate only, with a pK_a equal to 6.9. Successive dialysis against EDTA and phosphate buffer, pH 7.0, at 0 °C gives an enzymatically inactive protein. This protein shows kinetics of thermal inactivation identical to the untreated (native) enzyme. Full activity is restored on adding Mg²⁺ (5.0 mm) to a solution of this protein. Addition of Ba²⁺ or Mn²⁺ brings about partial recovery. Other metal ions are not effective.     

Respiration-driven proton translocation with nitrite and nitrous oxide in Paracoccus denitrificans

(1) $\text{H}$⁺/electron acceptor ratios have been determined with the oxidant pulse method for cells of denitrifying Paracoccus denitrificans oxidizing endogenous substrates during reduction of O₂, NO^?₂ or N₂O. Under optimal H⁺-translocation conditions, the ratios $\text{H}{}^{\mathrm{+}}\text{O}$, $\text{H}{}^{\mathrm{+}}\text{N}{}_2\text{O}$, $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂ and $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂O were 6.0–6.3, 4.02, 5.79 and 3.37, respectively. (2) With ascorbate/N,N,N′,N′-tetramethyl-p-phenylenediamine as exogenous substrate, addition of NO^?₂ or N₂O to an anaerobic cell suspension resulted in rapid alkalinization of the outer bulk medium. $\text{H}{}^{\mathrm{+}}\text{N}{}_2\text{O}$, $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂ and $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂O were ?0.84, ?2.33 and ?1.90, respectively. (3) The $\text{H}{}^{\mathrm{+}}\text{oxidant}$ ratios, mentioned in item 2, were not altered in the presence of $\text{valinomycin}\text{K}{}^{\mathrm{+}}$ and the triphenylmethylphosphonium cation. (4) A simplified scheme of electron transport to O₂, NO^?₂ and N₂O is presented which shows a periplasmic orientation of the nitrite reductase as well as the nitrous oxide reductase. Electrons destined for NO^?₂, N₂O or O₂ pass two H⁺-translocating sites. The $\text{H}{}^{\mathrm{+}}\text{electron}$ acceptor ratios predicted by this scheme are in good agreement with the experimental values.     

Temperature-jump-induced release of hydrogen ions from chloroplasts and its relaxation characteristics in the presence of ionophores

Temperature-jump-induced absorption changes of bromocresol purple in chloroplast suspensions in the dark were studied. After a rapid rise in temperature (<10 μs), a slow absorbance decrease of bromocresol purple ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{≈ 0.2}\text{s}$) following a fast absorbance decrease of chloroplasts and bromocresol purple ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{< 1}\text{ms}$) was observed. The slow absorbance decrease corresponds to acidification of the suspending medium, indicating H⁺ efflux from chloroplasts after the temperature jump. Nigericin and gramicidin D suppressed the slow absorbance change completely in the presence of 10 mM KCl, while valinomycin did not affect it. The fast absorbance change was not affected by the above ionophores. 3-(3,4-dichlorophenyl)-1,1-dimethylurea also diminished the slow absorbance change.     

Interaction of exogenous benzoquinone with Photosystem II in chloroplasts. The semiquinone form acts as a dichlorophenyldimethylurea-insensitive secondary acceptor

Chloroplasts were submitted to a sequence of saturating short flashes and then rapidly mixed with dichlorophenyldimethylurea (DCMU). The amount of singly reduced secondary acceptor (B^?) present was estimated from the DCMU-induced increase in fluorescence in the dark caused by the reaction: QB^?

Q^?B. By varying the time interval between the preillumination and the mixing, the time course of B^? reoxidation by externally added benzoquinone was investigated. It was found that benzoquinone oxidizes B^? in a bimolecular reaction, and does not interact directly with Q^?. When a sufficient delay after the preillumination was allowed in order to let benzoquinone reoxidize B^? before the injection of DCMU, the fluorescence increase caused by one subsequent flash fired in the presence of DCMU was followed by a fast decay phase ($\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 100 μ}\text{s}$). The amplitude of this phase was proportional to the amount of B^? produced by the preillumination. This fast decay was observed only after the first flash in the presence of DCMU. These results are interpreted by assuming a binding of the singly reduced benzoquinone to Photosystem II where it acts as an efficient, DCMU-insensitive, secondary (exogenous) acceptor.     

Evidence for general catalysis and formation of nitrobenzene in the oxidation of phenylhydroxylamine in aqueous phosphate buffer

N-Phenylhydroxylamine is oxidized in aqueous phosphate buffer to nitrosobenzene, nitrobenzene, and azoxybenzene. Degradation is O₂ dependent and shows general catalysis by $\text{H}{}_2\text{PO}{}_4{}^{\mathrm{?}}$ (k₁ = 2.3 M^?2 sec^?1) and $\text{PO}{}_4{}^{\mathrm{?3}}$ (k₂ = 2.3 × 10⁵M^?2 sec^?1) or kinetically equivalent terms. Evidence is presented suggesting the intermediacy of a highly reactive species leading to these products.     

The composition-dependence of the extent of reaction between a multivalent acceptor and a bivalent ligand: Implications of self-interaction of the ligand in precipitin effects

Theory is presented relating to the reversible interaction of an f-valent acceptor, A, with a bivalent ligand, B, which leads to the formation of a series of complexes comprising networks of alternating A and B molecules. An explicit expression is derived for the overall extent of reaction in terms of the total molar concentrations of reactants $\text{(}\text{m}{}_{\mathrm{A}}$ and $\text{m}{}_{\mathrm{B}}\text{)}$, the valency of the acceptor and the site-binding constant, k, governing the equilibria. It is shown by differentiation of this expression holding $\text{m}{}_{\mathrm{A}}$ (or $\text{m}{}_{\mathrm{B}}$) fixed that relations are available for the independent evaluation of f and k from a combination of precipitin and radioimmunoassay experiments. Moreover, it is established that dilution with solvent ($\text{m}{}_{\mathrm{A}}\text{/}\text{m}{}_{\mathrm{B}}$ fixed) cannot lead to the appearance of a precipitate with this type of crosslinking system. The latter observation forms the background for the development of theory pertaining to the joint operation of ligand dimerization, 2B?B₂, and crosslinking of the multivalent acceptor with bivalent B₂. The theoretical examination of this system is developed in terms of site-probability functions and involves the delineation of unique solutions for the extent of crosslinking reaction aided by the definition of the extent of binding in defined limits. It is shown with the use of numerical examples that the system involving self-associating ligand may result in the appearance of a precipitate on dilution with solvent and the conditions for the operation of this phenomenon are elucidated. It is noted that other types of ligand self-interaction may lead to similar effects in crosslinking systems, and the general principles emerging from this study are discussed in terms of systems in which antibody ligands are known to be involved in association reactions or are suspected to be so involved on the basis of precipitation effects observed on dilution with solvent.