A physical interpretation for the natural photosynthetic process (photosynthesis/efficiency/power production)

Transcription

1 Proc. Natl. Acad. Sci. USA Vol. 8, pp , February 1983 Biophysics A physical interpretation for the natural photosynthetic process (photosynthesis/efficiency/power production) ROBERT HILL AND PETER R. RICH Department of Biochemistry, University of Cambridge, Tennis Court Road, Cambridge CB2 IQW, United Kingdom Contributed by Robert Hill, October 26, 1982 ABSTRACT The efficiency of the process of photosynthesis is shown to depend on the molecular conversion of power. This requires establishment of a discipline that is now implicit in current thought and that offers a definition of relationship between equilibrium state and power. The quantum aspect for the microscopic process is different from the macroscopic system idealized as the heat engine and is required for the interpretation of molecular machinery. By using three postulates the ideal maximal efficiency for the molecular energy conversion is calculated from the data, which are assembled in the form of the "Z scheme" for photosynthesis. The observed and the calculated efficiencies for a green plant are substantially in agreement. Power production and equilibrium A biochemical interpretation for the activity of living organisms involves the production of power, which requires the time factor. The production of power always has to depend on making use of a spontaneous naturally occurring process. This requires some form of machinery, which involves molecular transformations both in space and in time. The process belongs to a microscopic order of events and it cannot be represented by an equilibrium state. The quantitative physical-chemical interpretation is outside the range of classical thermodynamics because the system is organized and is definitely heterogeneous as regards both temperature and time. We have to suggest the designation of a part of chemical physics in the form of a discipline that we call "molecular kinedynamics. " The distinction between work and heat as being different kinds of energy is common to both disciplines. The term "thermostatics" (1, 2) would indeed have seemed more appropriate for the discipline as we find thermodynamics in conventional physical chemistry. While the equilibrium state is an essential tool for the accurate description of both physical and chemical processes, we need a quantitative means of describing the energy conversions for any rapid chemical process. It is obvious that the production of power by any material system has to be regarded as an irreversible process. For the conservative systems in mechanics we can appreciate subjectivelythe essential parameters and for any equilibrium state the subjective notion of force seems adequate. Again, the subjective feeling of hot and cold and its description in terms of temperature is quite within our grasp. The subjective sensation of power is less commonplace, although its expression as a rate of work is only too well appreciated. The subjective sensation of a "matched load" may indeed be appreciated by the feeling of the speed of drawing a bucket of water out of a well. Significance of linear light curves In living organisms we find the principle for the conversion of power into a useful form of external work beautifully shown by The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U. S. C solely to indicate this fact. 978 the original studies of photosynthesis in green plants by Blackman (3). If we make a careful examination of his theory of the so-called "limiting factors" we can express the efficiency of this biological process on the scale that is defined by the quotient of power being converted and power being absorbed by the pigment system. The light curves of photosynthesis, which represent the steadystate rate of this process as a function of the light intensity, show two distinct regions. Rabinowitch describes them as the "roof" and "ceiling" (ref. 4, p. 87). The rate increases almost linearly with the light intensity until the dark process can no longer keep the pace. This is ideally a sharp bend to a constant rate where the light is no longer limiting. If we can measure the rate at which light is actually being absorbed the efficiency can be determined. Forthe linear part of a light curve we can represent the rate as the product of efficiency and light intensity. The apparent linearity of the light curves for the "light-limited" rate has seemed not to be in accord with the second law of classical thermodynamics. This doubt, however, may be easily dispelled with a consideration of the conditions of the experiment. This is because of the relationship between the range of intensities used in experiments and the temperature of the radiating source. The intensity of the light may be changed by a factor of 16, corresponding to a change of a factor of 2 (1 3) for the apparent temperature of a radiating black body source (5). This will put any precision for determining curvature far beyond the experimental accuracy under the most ideal conditions. For the chemical transformation the efficiency of the process may be given as the quantum requirement. This is the quotient of the number of oxygen molecules being liberated and the number of quanta being absorbed. The reciprocal is the quantum efficiency. The energy corresponding to the nhv is given by the absorption profiles of the photochemically active constituents. The imperceptible nature of a curvature in the relationship between light intensity and the rate of photosynthesis shows us that the entropy changes little with the intensity of radiation within a narrow region of the spectrum. One of us had already considered this approach for the photochemical system (5). This was expressed in the form of two-dimensional diagrams illustrating the distribution of energy in the spectrum according to the well-known formula of Max Planck. It was then concluded that the quality of the radiation required for a photosynthetic system can be expressed quantitatively simply as a function of the wavelength and the temperature of the system that receives it. We consider it axiomatic that the transformation of energy in a photochemical system is essentially an adiabatic process, meaning that it occurs in a stateof thermal isolation. The energy does not equilibrate with the material at the ambient temperature. In fact, no photochemical system can behave like a black body. By the use of the most sensitive calorimetry, Arnold (6) measured the energy conservation of the alga Chlorella. The ex-

2 perimental technique depended on the irreversible destruction, by ultraviolet light, of the photochemical activity without otherwise changing the other cellular activities. This remains an outstanding example of the application of classical thermodynamics, involving the first law alone, to a biological process. Developments in thermostatics and thermodynamics and their relationship to photosynthetic energy conversion Conventional thermostatics has no quantitative time factor, although the second law provides its qualitative direction. For its application to be strictly valid, the system must be at equilibrium with no net flux. Regardless of this, many situations exist in which there is sufficient time for system equilibration such that useful parameters may be measured. This is clearly illustrated, for example, in the usefulness of the application of Carnot cycle considerations to the efficiency of steam engines, where the internal system equilibrations are rapid compared with the turnover time of the system. The developments of nonequilibrium or irreversible thermodynamics provided a possible method for application of the thermostatic parameters to systems through which a steadystate energy flux was occurring. In this connection the important papers of Onsager should be mentioned (7). He used linear flux/force relationships of the form: ii = Li * Xi, in which J = flux, X = force, and L = coupling coefficient. With the aid of the postulate of microscopic reversibility, the reciprocal relationships were derived, and these have had a clear application to such physical events as heat conduction and thermoelectric phenomena. More recently, efforts have been made to apply the linear flux/force relationships to the biological reactions of energy conversion (8-11), and indeed evidence of such linearity has been noted under some conditions. However, as noted by Onsager, "In order to obtain proportionality between the forces X and the displacement x we must limit ourselves to the consideration of cases where the system is nearly in equilibrium" (ref. 7, p. 412). In physical chemistry, the thermodynamic force is the difference in AG of the driving and driven reactions. Because rate is linearly related to concentration, whereas AG is logarithmically related to concentration, it can be seen that a linear relationship between flux and thermodynamic force will hold only for a small range of variation. Such a restriction places serious limitations on the application of such equations to molecular machine systems, which are operating far from equilibrium. Even in more classical enzymological reactions the linear relationships may be highly distorted by other factors (12), although their validity has been experimentally demonstrated in some cases (13). Prigogine (14, 15) and co-workers have investigated chemical systems far from equilibrium. Such systems are able to maintain macroscopic stable order or periodic macroscopic oscillations and are of interest from a number of biological perspectives. However, as discussed most recently by Blumenfeld (16), in such nonequilibrium systems there do not exist precise thermodynamic quantities such as entropy production or free energy. For these systems the chemical kinetic approach has been much more useful for the modeling of their behavior. The possible application of such an approach to photochemical energy conversion at a microscopic level does not at the present seem feasible or informative from the point of view of power production and instead an alternative treatment must be sought. For photosynthesis, we must postulate some kind of machinery. Any representation of the natural molecular machinery in living organisms has to differ from our conception of a heat Proc. Natl. Acad. Sci. USA 8 (1983) 979 engine because it belongs to a microscopic state of affairs. We cannot see the machinery in the light microscope, which uses the light that has the color of that being absorbed, say, for photosynthesis. Hence we regard the process as microscopic and subject to the rules that govern the absorption and emission of photons. It has already been pointed out that the reactions that occur in the biological energy transducing molecules are occurring adiabatically and far from equilibrium and cannot be considered in a classical heat engine analogy. This was recognized by McClare (17-21), and it was he who introduced the notion of "molecular machines" that operate between discrete energy levels and that, on the time scale of the turnover of the machine, do not thermally equilibrate with the surroundings. Further expansion of such ideas may be found in recent contributions from several authors (22, 23). A striking example of molecular machine operation may be seen in the chloroplast oxygen-evolving enzyme, which passes through a series of discrete, extremely slowly equilibrating S-states, on flash activation of the chloroplast. A number of thermodynamic treatments of the problem of radiation absorption and conversion in relation to photosynthesis have appeared, beginning with the Carnot cycle treatment of Duysens (24). Recently a comprehensive review by Landsberg and Tonge (25) of the approach as applied to several different types of system has appeared. A further useful discussion of this type of approach combined with considerations of loss processes and matched load is to be found in the work of Ross (26, 27). Our own molecular machine treatment of photosynthetic radiation conversion begins with the thermodynamic aspects of monochromatic radiation in terms of its quality (5). Natural development for photosynthesis When a black body is absorbing light the luminous energy is being degraded into heat by processes of a quasi-chemical character, that is, by a resonant transfer of electrons within the absorbing material: The energy is then emitted in the form of the complete black body radiation characteristic of the temperature of the material. The green plant conserves some of the energy in the form of a chemical potential. This process depends on the functional material being almost completely diathermous (i.e., nonabsorbing) for a considerable range of frequencies. It is in fact widely different from a completely black material because it has intense absorption for specific regions of the visible spectrum. This is shown very clearly in a photograph of trees or sunlight taken with a near-infrared filter (ref. 4, p. 692). Observed efficiency for natural photosynthesis The quantum requirement under ideal experimental conditions is at least eight photons absorbed for each molecule of oxygen liberated or of CO2 reduced. This is shown in the chemical equation [in the form given by van Niel (28) showing the oxygen arising from water]: 8hv CO2 + 2 HOH =2 + (CHOH) + H2O + 46&8 in which (CHOH) represents one carbon equivalent of carbohydrate. For a mean wavelength of 69 nm, 8hv einsteins of radiation = 1,386.9 kj. The efficiency of the energy conversion is then 468.8/1,386.9 =.338 and the energy lost as heat is kj, provided that the photochemical system is maintained at a constant temperature, T2. From classical thermodynamics, following Rabinowitch (ref. 4, p. 49), we could regard the nhv of the specific wavelength as being very nearly equivalent to AGo. kj,

3 The energy of a photon in the visible region is given approximately as -kt * In, exp(-hv/kti) for a radiating source at a temperature T1. For 1 einstein k is replaced by R and because T2 will give us a very large exponent we can write -RT2 In exp(-hv/kt2) = NOhv. The question then that concerns us is exactly how the loss of around 2/3 of the energy arises. Duysens (24) applied the equilibrium state to the study of photosynthesis so that the efficiency, A, could be given in the form q= (T1 - T2)/Tl, in which T1 corresponds to a source with the energy density of the cavity radiation corresponding very nearly to the zero intensity for an experimental light curve. This "null" point was estimated for T1 to correspond to a temperature of 1,15 or 1,1 K, giving the values of qr =.74 or.73. It seems doubtful to the present authors whether the actual procss of energy conversion in photosynthesis can be arranged in theory to be rigorously thermodynamically reversible. However, this theoretical investigation by Duysens has greafly helped towards a wider appreciation of the differences between the passive near-equilibrium condition and the active condition of power conversion. We note that the idea of equilibrium state is an almost central idea in conventional physical chemistry and suggest that this, in part, has prevented the real appreciation of McClare's contributions (17-21). Chemical events in photosynthesis The energy relationships for green plant photosynthesis can be represented as a linear sequence of electron transfers resulting from two different photochemical systems. These electron transfers can be given in the form of redox potentials referred to a normal hydrogen electrode. This was the basis for the twodimensional diagram that came to be called the "Z scheme." The base of the diagram, regarded as an x axis, had no definite significance. Therefore, the zig-zag line joining the two systems is confusing. We now propose to divide the x axis into a series of five steps, each step representing the number of quanta passing in unit time through unit area (see Fig. 1). This will show the conversion of energy for each system and for the reaction between them as discrete quantum processes. The rectangles on the diagram represent power per unit area, upon which we base an estimate for the efficiency of the photochemical conversion of energy. Values for the operative potentials of the acceptor side of photosystem II and the donor side of photosystem I have been taken from the usual Z scheme (29) and are positioned on the y axis so that the mean of the reaction between them is at.2 V, a value that we take as the average potential of the hydrogen and oxygen electrodes. We note the outstanding difference of.2 V on the reduced sides of photosystems II and I between our diagram and that given in the literature. The scheme we give is based on biochemical evidence, whereas other schemes are derived from biophysical data. We suggest that this difference of.2 V will be an important factor in subsequent theoretical development. For the present, we assume that ph is-determined classically, so that such a positioning dictates that the positive end of photosystem II is 75 mv above the oxygen electrode, indicating a ph of 5.75 and-the negative end of photosystem I is 38 mv below the hydrogen electrode, indicating [ U 1.6 [ 1.4 > 1.2 i 1. a na [ Proc. Natl. Acad. Sci. USA 8 (1983) > [.8 [ 1. ) H2/H Cytf /H2( 1. 7/"7i w',o hvii: V7// :, hvi: PSI * ATP ATP ATP * PS 11~~. Extensive factor, quanta per step per unit time FIG. 1. Modified diagram for the Z scheme. (Upper) The Z scheme with data taken from ref. 29. (Lower) The modification of this scheme, constructedifrom the following data: 68 nm = ev; 7 mnn = ev; primary acceptor of photosystem.ii (PSI) = -.2 V; donor side of photosystem I = V; efficiency of absorption =.962. This -diagram has been presented in preliminary form (3). a ph of The diagram can then represent the conversion of energy for a steady state under the condition that the rate of the process is limited only by the intensity of light. This means that the rate is not to be limited by the temperature, or by the concentration of carbon dioxide, or by the intensity of the absorption of the chlorophyll-containing system (these conditions are essential for any simple formulation of the energy conversion steps). The modified diagram is derived from three postulates. 1. The "thermal temperature" of nearly monochromatic radiation determines its quality. We define the thermal temperature, OH, as the vibration temperature divided by 2.71 (OH = hv/2.7k or hc/k * 1/2.7A, in which A is the mean wavelength for the activation of a reaction center). The factor 2.71 is the

4 value of the exponent x = hi!k6h = 2.71 when x corresponds to the mean quantum energy for the distribution of energy in cavity radiation (5, 31). 2. The "thermal temperature" determines the effective production of power by reaction centers. We define the activation of reaction centers as a reversible microscopic process. There is no change of wavelength. The efficiency of activation is given in a classical form as -q = 1 - T2/OH, in which T2 is the temperature of the photochemical system. This function represents the ratio of the number of quanta being absorbed to the number of quanta actually available. For a wavelength of 69 nm il = q represents the relative quality of the radiation being absorbed. 3. Conversion of the effective power into a chemical potential is a quantized process. When the energy of the quantum is greatly in excess of kt2, one-half of the energy taken can be converted thus: = 1 - hv2/hvj. When v2 = v1/2, rq = 1/2. Maximal power output occurs when the efficiency of conversion is 5%. The change in frequency occurs in accordance with this maximal power requirement. For the power conversion 1/2 of the energy taken is left, but this residual energy may constitute a second step represented by hv3 - hi'2 = hv2/2. For the singlet state absorption by chlorophyll a: hv = 72kT2 when T2 = 293 K. As the quantum energy is diminished so does the adiabatic condition become unrealizable. We assume the existence of one additional step involving a second kind of reaction center corresponding to a wavelength of 1,38 nm, which is a region in the near infrared. This additional power produces the ionic separations giving the noncyclic photophosphorylations associated with each of the photosystems I and IL. In view of the carotenoid class of pigments being functional in the optic energy conversion for vision, we might suggest a similar type of system for a second kind of reaction center in chloroplasts. We postulate a third ionic separation mediated by the dark reaction between the two photochemical systems. The diagram shows the three molecular equivalents of ATP required for the reduction of one molecular equivalent of CO2 according to the Benson-Calvin cycle. Each equivalent of ATP in the steady state then results from the passage of four electrons, which itself requires a total of eight quanta. Theoretical estimate of maximal efficiency We can use the diagram incorporating our postulates to give an estimate of the maximal possible efficiency for the complete process of photosynthesis in the green plant. The ratio of power converted divided by the power absorbed by the photochemical reaction centers comes out as.361 (see Table 1 for calculation) when the dark reactions are not limited in rate by temperature. If we now assume that the rate of oxygen production measures the rate of CO2 fixation by the Benson-Calvin cycle, we find from thermochemical data referring to a condensed system at 298 K (ref. 4, p. 49): AH/8 photons =.342, in which AH is the energy stored per carbon equivalent conversion into carbohydrate. The ratio.342/ = is somewhat surprising, being so close to unity. We can conclude provisionally that the green plants have developed a nearly maximal possible efficiency for a system that depends on chlorophyll. Proc. Natl. Acad. Sci. USA 8 (1983) 981 Table 1. Calculation for maximal theoretical efficiency System I = 7 nm, System II = 68 nm, V, V, 4.81 kcal/einstein kcal/einstein Energy received/intensity factor = V, kcal/einstein Power gained Power Quantal conversion kcal/ lost, Fraction Volts einstein fraction Power being absorbed Quantum conversion* 3/ /4 (includes two ATP steps) (/4) (.898) (2.69) Thermal reaction 3A4 - '/ '/16 between systems I and II (1 ATP) (Q/I6) (.224) (5.16) Power converted thermally in dark 1/2 (3/4-1/16) /2 (3/4-1/16) Totals 11X32 (.344) 21/32 (.656) AH = 113 kcal for one carbon equivalent in carbohydrate = V (28.36 kcal/einstein) for one hydrogen equivalent Thermal efficiency = 1.231/3.593 =.342 * From the model with two sets of quantum converters, the final hv/ 4 being lost as heat. Discussion The molecular kinedynamics will have to have a foot in both camps-the classical reflection or scattering of radiation, which refers to the wave aspect, and the absorption and emission, which refer to the quantal process. We may look at each of the two separately but never together (32). We have to define the boundary between the two aspects as precisely as possible and OH can act as a password for crossing it. The great achievement of McClare (21) was his success in bringing in the conception of vibrational energy and resonant molecules for the chemical and physical processes that govern the activity of living organisms. However this may be, the conversion of the different forms of energy by an efficient molecular machine must consist of a number of discrete events. This idea seems to be implicit in current biological thought. Our own theoretical interpretation of the efficiency of photosynthesis was carried out before we were aware of the published work of McClare. (We thank D. B. Kell for bringing the work of McClare to our attention.) We were actually surprised that the process of photosynthesis represented by the Benson- Calvin cycle, when expressed as a series of discrete events, was in accord with experimental results. About theoretical efforts it can often be said, "well, you knew the answer before you started. " Any value in the present contribution can only be judged as the theory develops. At present the theory is obviously incomplete. We thank Professor Sir Hans Kornberg, F. R. S., for offering us all the facilities of his Department and we are also grateful to Professors U. Heber and D. A. Walker and to Dr. D. S. Bendall for their interest and help. Financial support from the Agricultural Research Council to R. H. and from the Venture Research Unit, British Petroleum Company, p.l.c., to P.R.R. is also gratefully acknowledged. 1. Denbigh, K. G. (1951) The Thermodynamics of the Steady State, Methuens Monographs on Chemical Subjects (Methuen, London). 2. Tribus, M. (1961) Thermodynamics and Thermostatics, ed. Hagerty, W. W. (Van Nostrand, Princeton, NJ). 3. Blackman, F. F. (195) Ann. Bot. 19, Rabinowitch, E. J. (1951) Photosynthesis and Related Processes, (Interscience, New York), Vols. 1 and 2.

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