Free energy change accompanying electron transfer from P870 to quinone in Rhodopseudomonas sphaeroides chromatophores

Delayed fluorescence of chromatophores of Rhodopseudomonas sphaeroides was measured to estimate the standard free energy change accompanying the electron transfer from the bacteriochlorophyll dimer (P) to the primary acceptor quinone (Q_A). The chromatophores emitted delayed fluorescence with a lifetime of about 60 ms in the presence of o-phenanthroline. By comparing the intensity of the delayed fluorescence with that of the prompt fluorescence, the standard free energy of the P⁺Q_A^? radical pair was evaluated. It was about 0.87 eV below the level of excited singlet state, P1Q_A, or 0.51 eV above the ground state, PQ_A, independent of pH.     

Photochemical activities of reaction centers from Rhodopseudomonas sphaeroides at low temperature and in the presence of chaotropic agents

Light-induced absorbance changes were measured at low temperatures in reaction center preparations from Rhodopseudomonas sphaeroides. Absorbance difference spectra measured at 100 °K show that ubiquinone is photoreduced at this temperature, both by continuous light and by a short actinic flash. The reduction occurred with relatively high efficiency. These results give support to the idea that ubiquinone is involved in the primary photochemical reaction in Rhodopseudomonas sphaeroides. Reduction of ubiquinone was accompanied by a shift of the infrared absorption band of bacteriopheophytin.The rate of decay of the primary photoproducts (P⁺870 and ubisemiquinone) appeared to be approximately independent of temperature below 180 °K and above 270 °K; in the region between 180 and 270 °K it increased with decreasing temperature. The rate of decay was not affected by o-phenanthroline. Secondary reactions were inhibited by lowering the temperature.The light-induced absorbance changes were inhibited by chaotropic agents, like thiocyanate and perchlorate. It was concluded that these agents lower the efficiency of the primary photoconversion. The kinetics indicated that the degree of inhibition was not the same for all reaction centers. The absorption spectrum of the photoconverted reaction centers appeared to be somewhat modified by thiocyanate.     

Delayed fluorescence from Rhodopseudomonas viridis following single flashes

Delayed fluorescence from Rhodopseudomonas viridis membrane fragments has been studied using a phosphoroscope employing single, short actinic flashes, under conditions of controlled redox potential and temperature. The emission spectrum shows that delayed fluorescence is emitted by the bulk, antenna bacteriochlorophyll. The energy for delayed fluorescence, however, must be stored in a reaction-center complex including the photooxidized form (P⁺) of the primary electron-donor (P) and the photoreduced form (X^?) of the primary electron-acceptor. This is shown by the following observations: (1) Delayed luminescence is quenched (a) at low redox potentials which allow cytochromes to reduce P⁺ rapidly after the flash, (b) at higher redox potentials which, by oxidizing P chemically, prevent the photochemical formation of P⁺X^?, and (c) upon transfer of an electron from X^? to a secondary acceptor, Y. (2) Under conditions that prevent the reduction of P⁺ by cytochromes and the oxidation of X^? by Y, the decay kinetics of delayed fluorescence are identical with those of P⁺X^?, as measured from optical absorbance changes.The main decay route for P⁺X^? under these conditions has a rate-constant of approximately 10³ s^?1. In contrast, a comparison of the intensities of delayed and prompt fluorescence indicates that the process in which P⁺X^? returns energy to the bulk bacteriochlorophyll has a rate-constant of 3.7 s^?1, at 295 °K and pH 7.8. The decay kinetics of P⁺X^? and delayed fluorescence change little with temperature, whereas the intensity of delayed fluorescence increases with increasing temperature, having an activation energy of 12.5 kcal · mol^?1. We conclude that the main decay route involves tunneling of an electron from X^? to P⁺, without the promotion of P to an excited state. Delayed fluorescence requires such a promotion, followed by transfer of energy to the bulk bacteriochlorophyll, and this combination of events is rare. The activation energy, taken with potentiometric data, indicates that the photochemical conversion of PX to P⁺X^? results in increases of both the energy and the entropy of the system, by 16.6 kcal · mol^?1 and 8.8 cal · mol^?1 · deg^?1. The intensity of delayed fluorescence depends strongly on the pH; the origin of this effect remains unclear.     

Delayed fluorescence from bacteriochlorophyll in Chromatium vinosum chromatophores

Delayed fluorescence from bacteriochlorophyll in Chromatium vinosum chromatophores was studied at room temperature and under intermittent illuminations.The decay of delayed fluorescence was constituted of two components; a fast component decayed with a half time of about 8 ms, a slow one decayed in parallel with the reduction of photooxidized bacteriochlorophyll (P⁺) with a half time of 100–200 ms. The biphasic decay of delayed fluorescence indicated that a rapid equilibrium was established between the primary electron acceptor and the secondary acceptor.In the presence of o-phenanthroline, the time course of the decay of delayed fluorescence was identical with that of the reduction of P⁺ in reaction center-rich subchromatophore particles, although they did not necessarily coincide with each other in “intact” chromatophores.The intensity of the slow component was increased and the decay was accelerated at basic pH values. Reagents that dissipate the proton gradient across the chromatophore membranes such as carbonylcyanide m-chlorophenylhydrazone (CCCP) and nigericin accelerated the decay of the slow component. These effects are probably resulting from changes in internal pH of chromatophore vesicles. Reagents that dissipate the membrane potential such as CCCP and valinomycin decreased the intensity.     

Effect of temperature on the photoreduction of centres A and B in Photosystem I,and the kinetics of recombination

When spinach Photosystem I particles, frozen in the dark with ascorbate, are illuminated at low temperatures, one electron is transferred from P-700 to either iron-sulphur centre A or B. It was found that the proportion of centre A or B reduced depended on the temperature of illumination. At 25 K, reduction of centre A, as detected by ESR spectroscopy, was strongly preferred. At higher temperatures, at about 150K, there was an increased proportion of reduced centre B. Reduction of B was more strongly preferred in particles frozen in 50% glycerol. The kinetics of dark reoxidation of A^? and B^? at various temperatures were followed by observing the radical signal of P-700⁺, and also by periodically cooling to 25 K to measure the ESR spectra of the iron-sulphur centres. The recombination of A^? and P-700⁺ occurred at lower temperatures than that at of B^?; at 150–200 K, centre B was the more stable electron trap. Dark reoxidation of both centres was more rapid in samples that were illuminated at 25 K than in samples illuminated at 150–215 K. In no case was net electron transfer between centres A and B observed. Differences in g values of the ESR spectra in particles illuminated at 25 and 200 K indicate that the iron-sulphur centres are in altered conformational states. It is concluded firstly that, in the frozen state, the rates of dark electron transfer decrease in the sequence A^? → P-700⁺ > B^? → P-700⁺ > B^? → A; secondly, that when centres A or B are photoreduced, a temperature-dependent conformational change takes place which slows down the rate of recombination with P-700⁺.     

Primary photochemical processes in isolated reaction centers of Rhodopseudomonas viridis

Picosecond and nanosecond spectroscopic techniques have been used to study the primary electron transfer processes in reaction centers isolated from the photosynthetic bacterium Rhodopseudomonas viridis. Following flash excitation, the first excited singlet state (P1) of the bacteriochlorophyll complex (P) transfers an electron to an intermediate acceptor (I) in less than 20 ps. The radical pair state (P⁺I^?) subsequently transfers an electron to another acceptor (X) in about 230 ps. There is an additional step of unknown significance exhibiting 35 ps kinetics. P⁺ subsequently extracts an electron from a cytochrome, with a time constant of about 270 ns. At low redox potential (X reduced before the flash), the state P⁺I^? (or P^F) lives approx. 15 ns. It decays, in part, into a longer lived state (P^R), which appears to be a triplet state. State P^R decays with an exponential time of approx. 55 μs. After continuous illumination at low redox potential (I and X both reduced), excitation with an 8-ps flash produces absorption changes reflecting the formation of the first excited singlet state, P1. Most of P1 then decays with a time constant of 20 ps. The spectra of the absorbance changes associated with the conversion of P to P1 or P⁺ support the view that P involves two or more interacting bacteriochlorophylls. The absorbance changes associated with the reduction of I to I^? suggest that I is a bacteriopheophytin interacting strongly with one or more bacteriochlorophylls in the reaction center.     

Enthalpy and volume changes accompanying electron transfer from P-870 to quinones in Rhodopseudomonas sphaeroides reaction centers

A capacitor microphone was used to measure the enthalpy and volume changes that accompany the electron transfer reactions, $\text{PQ}{}_{\mathrm{A}}\text{→}\text{hv}\text{P}{}^{\mathrm{+}}\text{Q}{}^{\mathrm{?}}{}_{\mathrm{A}}\text{and PQ}{}_{\mathrm{A}}\text{Q}{}_{\mathrm{B}}\text{→}\text{hv}\text{P}{}^{\mathrm{+}}\text{Q}{}_{\mathrm{A}}\text{Q}{}^{\mathrm{?}}{}_{\mathrm{B}}$, following flash excitation of photosynthetic reaction centers isolated from Rhodopseudomonas sphaeroides. P is a bacteriochlorophyll dimer (P-870), and Q_A and Q_B are ubiquinones. In reaction centers containing only Q_A, the enthalpy of P⁺Q^?_A is very close to that of the PQ_A ground state (ΔH_r = 0.05 ± 0.03 eV). The free energy of about 0.65 eV that is captured in the photochemical reaction evidently takes the form of a substantial entropy decrease. In contrast, the formation of P⁺Q_AQ^?_B in reaction centers containing both quinones has a ΔH_r of 0.32 ± 0.02 eV. The entropy change must be near zero in this case. In the presence of o-phenanthroline, which blocks electron transfer between Q^?_A and Q_B, ΔH_r for forming P⁺Q^?_AQ_B is 0.13 ± 0.03 eV. The influence of flash-induced proton uptake on the results was investigated, and the ΔH_r values given above were measured under conditions that minimized this influence. Although the reductions of Q_A and Q_B involve very different changes in enthalpy and entropy, both reactions are accompanied by a similar volume decrease of about 20 ml/mol. The contraction probably reflects electrostriction caused by the charges on P⁺ and Q^?_A or Q^?_B.     

Orientation of reaction center complexes fromRhodobacter sphaeroides in proteoliposomes and the effect ofo-phenanthroline on electrogenesis during primary photochemical reaction

The orientation ofRhodobacter sphaeroides reaction center complexes (RC complexes) in proteoliposomal membranes was investigated by a direct electrometric method. Conditions were found that allow monitoring of only that RC complex fraction that is oriented with its donor side to the inner part of the proteoliposome. It is shown thato-phenanthroline, an inhibitor of electron transfer between primary (Q_A) and secondary (Q_B) quinone acceptors, can also inhibit the photoinduced Q_A reduction. The efficiency of this inhibition depends on the concentration of added ubiquinone. It is assumed that the laser flash-inducedo-phenanthroline inhibition of primary dipole (P-870⁺ · Q _A ^– ) formation is of a competitive nature.     

Voltage dependent potassium fluxes and the significance of action potentials in Acetabularia

Membrane potential, V_m, and K⁺(⁸⁶Rb⁺) fluxes have been measured simultaneously on individual cells of Acetabularia mediterranea. During resting state (resting potential approx. ?170 mV) the K⁺ influx amounts to 0.24–0.6 pmol · cm^?2 · s^?1 and the K⁺ efflux to 0.2–1.5 pmol · cm^?2 s^?1. According to the K⁺ concentrations inside and outside the cell (40 : 1) the voltage dependent K⁺ flux (zero at V_m = E_K = ?90 mV) is stimulated approx. 40-fold for V_m more positive than E_K.It is calculated that during one action potential (temporary depolarization to V_m more positive than E_K) a cell looses the same amount of K⁺, which leaks in during 10–20 min in the resting state (V_m = ?170 mV). Since action potentials occur spontaneously in Acetabularia, they are therefore suggested to have a significant function for the K⁺ balance of this alga.     

Kinetics of luminescence in the 10−6–10−4-s range in Chlorella

The decay of luminescence in the 6–600-μs range following a microsecond flash has been studied in Chlorella. The decay is highly polyphasic; three kinetic components are outlined, in confirmation of the results of K. L. Zankel (1971, Biochim. Biophys. Acta 245, 373–385).Extrapolation of the decay to zero dark time suggests that a unique metastable species C^?₊, resulting from photochemical charge separation in the System II reaction center, is the substrate of the recombination reaction which gives rise to luminescence.The fast (5–10 μs) and medium (50–70 μs) phases of the decay denote different stabilization steps, preceding relaxation of the centers by electron and proton transduction to the photosynthetic chain.NH₂OH specifically inhibits the fast phase and enhances the medium phase. This effect is explained by assuming that the fast phase results from electron transfer from the water splitting system Z to the oxidized primary donor Y.3-(3,4-Dichlorophenyl)-1,1-dimethylurea (DCMU), in the presence of NH₂OH elicits another fast phase. It is believed that DCMU affords a parasitic stabilization of C^?₊ by forming a complex with Q^?.     

The location of redox centers in the profile structure of a reconstituted membrane containing a photosynthetic reaction center-cytochrome c complex by resonance X-ray diffraction

The technique of resonance X-ray diffraction (Blasie, J.K. and Stamatoff, J. (1981) Annu. Rev. Biophys. Bioeng. 10, 451–452) utilizing synchrotron radiation was used to determine the locations of the cytochrome c heme iron atom and the photosynthetic reaction center iron atom within the profile of a reconstituted membrane. The accuracy of these determinations was better than ±2 ?. The cytochrome c heme iron atom → reaction center iron atom vector was determined to have a magnitude of approx. 44 ? projected onto the membrane profile and to span most of the lipid hydrocarbon core of the membrane profile. Since the reaction center iron atom interacts magnetically with the primary quinone electron acceptor Q_I over a distance of less than 10 ?, the primary light-induced electron-transfer reactions for this system generate the electric charge separation between oxidized cytochrome c⁺ and Fe-Q^?_I across most (approx. $\text{2}\text{3}$) of the membrane profile including most or all of the lipid hydrocarbon core of the membrane.     

A study of the current-voltage relationships of electrogenetic active and passive membrane elements in riccia fluitans

Potassium- and proton-dependent membrane potential, conductance, and current-voltage characteristics (I–V curves) have been measured on rhizoid cells of the liverwort Riccia fluitans. The potential difference (E_m) measured with microelectrodes across plasmalemma and tonoplast is depolarized to the potassium-sensitive diffusion potential (E_D) in the presence of 1 mM NaCN, 1 mM NaN₃, or at temperatures below 6°C. Whereas the temperature change from 25°C to 5°C decreases the membrane conductance (g_m) from 0.71 to 0.43 S ? m^?2, 1 mM NaCN increases g_m by about 25%. The membrane displays potassium-controlled rectification which gradually disappears at temperatures below 5°C. The potassium pathway can be described by an equivalent circuit of a diode and an ohmic resistor in parallel. In the potential interval of E_D ± 100 mV the measured I-V curves roughly fit the theoretical curves obtained from a modified diode equation. ⁸⁶Rb⁺(K⁺)-influx is voltage sensitive: In the presence of 1 mM NaCN, ⁸⁶Rb⁺-influx follows a hyperbolic function corresponding to a low conductance at low [K⁺]_o and high conductance at high [K⁺]_o. On the contrary ⁸⁶Rb⁺-influx is linear with [K⁺]_o when pump activity is normal. It is believed that there are two K⁺-transport pathways in the Riccia membrane, one of which is assigned to the low conductance (0.2 S · m^?2), the other to a temperature-dependent facilitated diffusion system with a higher conductance (7.7 S · m^?2). The electrogenic pump essentially acts as a current source and consumes about 39% of the cellular ATP-turnover. In the presence of 30 μM CCCP the saturation current of 0.1 A · m^?2 is doubled to about 0.2 A · m^?2, and the electromotive force of ?360 mV switches to ?250 mV. It is suggested that this may be due to a change in stoichiometry from one to two transported charges per ATP hydrolyzed.     

Effect of hydrogen bonds on the energetics of macromolecules in the course of electron transfer

For a model system consisting of a bacteriochlorophyll dimer (P) and a primary quinone with the nearest environment (Q_A), which are the electron donor and acceptor in the recombination reaction in the Rhodobacter spheroides reaction center, the energies of states P⁺Q _A ^? and PQ_A have been calculated at several stable conformations of Q_A that differ in the positions of the proton involved in the hydrogen bond. It is shown that the position of the proton has a considerable influence on the energy of vertical transition P⁺Q _A ^? → PQ_A.     

Effect of the P700 pre-oxidation and point mutations near A0 on the reversibility of the primary charge separation in Photosystem I from Chlamydomonas reinhardtii

Time-resolved fluorescence studies with a 3-ps temporal resolution were performed in order to: (1) test the recent model of the reversible primary charge separation in Photosystem I (Müller et al., 2003; Holwzwarth et al., 2005, 2006), and (2) to reconcile this model with a mechanism of excitation energy quenching by closed Photosystem I (with P700 pre-oxidized to P700⁺). For these purposes, we performed experiments using Photosystem I core samples isolated from Chlamydomonas reinhardtii wild type, and two mutants in which the methionine axial ligand to primary electron acceptor, A₀, has been change to either histidine or serine. The temporal evolution of fluorescence spectra was recorded for each preparation under conditions where the “primary electron donor,” P700, was either neutral or chemically pre-oxidized to P700⁺. For all the preparations under study, and under neutral and oxidizing conditions, we observed multiexponential fluorescence decay with the major phases of ∼ 7 ps and ∼ 25 ps. The relative amplitudes and, to a minor extent the lifetimes, of these two phases were modulated by the redox state of P700 and by the mutations near A₀: both pre-oxidation of P700 and mutations caused slight deceleration of the excited state decay. These results are consistent with a model in which P700 is not the primary electron donor, but rather a secondary electron donor, with the primary charge separation event occurring between the accessory chlorophyll, A, and A₀. We assign the faster phase to the equilibration process between the excited state of the antenna/reaction center ensemble and the primary radical pair, and the slower phase to the secondary electron transfer reaction. The pre-oxidation of P700 shifts the equilibrium between the excited state and the primary radical pair towards the excited state. This shift is proposed to be induced by the presence of the positive charge on P700⁺. The same charge is proposed to be responsible for the fast A⁺A₀⁻ → AA₀ charge recombination to the ground state and, in consequence, excitation quenching in closed reaction centers. Mutations of the A₀ axial ligand shift the equilibrium in the same direction as pre-oxidation of P700 due to the up-shift of the free energy level of the state A⁺A₀⁻.     

Sub-microsecond chlorophyll A delayed fluorescence from Photosystem I Magnetic field-induced increase of the emission yield

(1) In photosystem I (PS I) particles in the presence of dithionite and intense background illumination at 290 K, an external magnetic field (0–0.22 T) induced an increase, ΔF, of the low chlorophyll a emission yield, F ($\text{ΔF}\text{F}\text{? 1–1.5\%}$). Half the effect was obtained at about 35–60 mT and saturation occurred for magnetic fields higher than about 0.15 T. In the absence of dithionite, no field-induced increase was observed. Cooling to 77 K decreased ΔF at 685 nm, but not at 735 nm, to zero. Measuring the emission spectra of F and ΔF, using continuous excitation light, at 82, 167 and 278 K indicated that the spectra of F and ΔF have about the same maximum at about 730, 725 and 700 nm, respectively. However, the spectra of ΔF show more long-wavelength emission than the corresponding spectra of F. (2) Only in the presence of dithionite and with (or after) background illumination, was a luminescence (delayed fluorescence) component observed at 735 nm, after a 15 ns laser flash (530 nm), that decayed in about 0.1 μs at room temperature and in approx. 0.2 μs at 77 K. A magnetic field of 0.22 T caused an appreciable increase in luminescence intensity after 250 ns, probably mainly caused by an increase in decay time. The emission spectra of the magnetic field-induced increase of luminescence, ΔL, at 82, 167 and 278 K coincided within experimental error with those of ΔF mentioned above. The temperature dependence of ΔF and ΔL was found to be nearly the same, both at 685 and at 735 nm. (3) Analogously to the proposal concerning the 0.15 μs luminescence in photosystem II (Sonneveld, A., Duysens, L.N.M. and Moerdijk, A. (1980) Proc. Natl. Acad. Sci. U.S.A. 77, 5889–5893), we propose that recombination of the oxidized primary donor P-700⁺ and the reduced acceptor A^?, probably A^?₁, of PS I causes the observed fast luminescence. The effect of an external magnetic field on this emission may be explained by the radical pair mechanism. The field-induced increase of the 0.1–0.2 μs luminescence seems to be at least in large part responsible for the observed increase of the total (prompt + delayed) emission measured during continuous illumination in the presence of a magnetic field.     

Acid-sensitive TWIK and TASK Two-pore Domain Potassium Channels Change Ion Selectivity and Become Permeable to Sodium in Extracellular Acidification

Two-pore domain K⁺ channels (K2P) mediate background K⁺ conductance and play a key role in a variety of cellular functions. Among the 15 mammalian K2P isoforms, TWIK-1, TASK-1, and TASK-3 K⁺ channels are sensitive to extracellular acidification. Lowered or acidic extracellular pH (pH_o) strongly inhibits outward currents through these K2P channels. However, the mechanism of how low pH_o affects these acid-sensitive K2P channels is not well understood. Here we show that in Na⁺-based bath solutions with physiological K⁺ gradients, lowered pH_o largely shifts the reversal potential of TWIK-1, TASK-1, and TASK-3 K⁺ channels, which are heterologously expressed in Chinese hamster ovary cells, into the depolarizing direction and significantly increases their Na⁺ to K⁺ relative permeability. Low pH_o-induced inhibitions in these acid-sensitive K2P channels are more profound in Na⁺-based bath solutions than in channel-impermeable N-methyl-d-glucamine-based bath solutions, consistent with increases in the Na⁺ to K⁺ relative permeability and decreases in electrochemical driving forces of outward K⁺ currents of the channels. These findings indicate that TWIK-1, TASK-1, and TASK-3 K⁺ channels change ion selectivity in response to lowered pH_o, provide insights on the understanding of how extracellular acidification modulates acid-sensitive K2P channels, and imply that these acid-sensitive K2P channels may regulate cellular function with dynamic changes in their ion selectivity.     

Diacylglycerol-transporting lipoproteins and flight in Locusta

Evidence from chromatographic and heparin precipitation studies shows that the ‘heparin-soluble’ lipoprotein, A⁺, forms in the haemolymph during flight. In locusts flown continuously for 60 min, lipoprotein A⁺ occurs in the haemolymph at low concentrations but accumulates during a short rest period following flight. After injections of tissue extracts containing adipokinetic hormone (AKH), A⁺ accumulates in the haemolymph but disappears more rapidly in flying locusts than in resting locusts. This difference in the rate of disappearance of diacylglycerol from the lipoprotein A⁺ can be used to estimate its rate of utilization during sustained flight (approx. 100μg. min^?1 from 45–90 min of flight). It is suggested that lipoprotein A⁺ is the major carrier of diacylglycerol from the fat body to the flight muscles during prolonged flight. The steady state concentrations of total diacylglycerol and ‘heparin-soluble’ diacylglycerol during continuous flight are unaffected when tissue extracts containing AKH are injected before flight. This suggests that there is a close homeostatic control over the steady state concentration of haemolymph lipid during flight.     

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.     

Kinetics and models of the Drosophila heat-shock system

The puffing of Drosophila heat-shock genes after (1) a step-wise temperature increase (“heat-shock”); (2) recovery from anaerobiosis; and (3) incubation with uncoupling reagents was expressed as percent of the maximal size and normalized to the time scale. Data were taken from the literature and new measurements. In addition, puffing was measured after a 30-min temperature pulse and after two 30-min pulses. The latter experiment revealed a second, smaller increase in puff-size. Data on RNA and protein synthesis in Drosophila cells were collected from the literature and also normalized. From the available data, a feed-back control system is derived that consists of a controlled variable x, possibly a metabolic function of the mitochondria, interacting with an activator molecule which exists in an active (A⁺) and an inactive (A^?) configuration. A⁺ activates the heat-shock genes which in turn produce their mRNA (y) and proteins (z) which then change the controlled variable x into a new steady state. A modified version of this model assumes a feed-back control of the heat-shock proteins on the activator molecule. A mathematical model of this system (Goodwin, 1965) was simulated by computer and compared with the experimental results.