Photosynthesis and negative entropy production

First-Principle Derivation of Single-Photon Entropy and Maxwell-Jüttner Velocity Distribution

This work is devoted to deriving the entropy of a single photon in a beam of light from first principles. Based on the quantum processes of light-matter interaction, we find that, if the light is not in equilibrium, there are two different ways, depending on whether the photon is being added or being removed from the light, of defining the single-photon entropy of this light. However, when the light is in equilibrium at temperature T, the two definitions are equivalent and the photon entropy of this light is hν/T. From first principles, we also re-derive the Jüttner velocity distribution showing that, even without interatomic collisions, two-level atoms will relax to the state satisfying the Maxwell-Jüttner velocity distribution when they are moving in blackbody radiation fields.

Entropy Perspectives of Molecular and Evolutionary Biology

Attempts to find and quantify the supposed low entropy of organisms and its preservation are revised. The absolute entropy of the mixed components of non-living biomass (approximately −1.6 × 10³ J K⁻¹ L⁻¹) is the reference to which other entropy decreases would be ascribed to life. The compartmentation of metabolites and the departure from the equilibrium of metabolic reactions account for reductions in entropy of 1 and 40–50 J K⁻¹ L⁻¹, respectively, and, though small, are distinctive features of living tissues. DNA and proteins do not supply significant decreases in thermodynamic entropy, but their low informational entropy is relevant for life and its evolution. No other living feature contributes significantly to the low entropy associated with life. The photosynthetic conversion of radiant energy to biomass energy accounts for most entropy (2.8 × 10⁵ J K⁻¹ carbon kg⁻¹) produced by living beings. The comparatively very low entropy produced in other processes (approximately 4.8 × 10² J K⁻¹ L⁻¹ day⁻¹ in the human body) must be rapidly exported outside as heat to preserve low entropy decreases due to compartmentation and non-equilibrium metabolism. Enzymes and genes are described, whose control minimizes the rate of production of entropy and could explain selective pressures in biological evolution and the rapid proliferation of cancer cells.

From leaves to roots: Biophysical models of transport of substances in plants

The transport processes of substances in various plant tissues are extremely diverse. However, models aimed at elucidating the mechanisms of such processes are almost absent in the literature. A unified view of all these transport processes is necessary, considering the laws of statistical physics and thermodynamics. A model of active ion transport was constructed based on the laws of statistical physics. Using this model, we traced the entire pathway of substances and energy in a plant. The pathway included aspects of the production of energy in the process of photosynthesis, consumption of energy to obtain nutrients from the soil, transport of such substances to the main organelles of all types of plant cells, the rise of water with dissolved substances along the trunk to the leaves, and the evaporation of water, accompanied by a change in the percentage of isotopes caused by different rates of evaporation. Models of ion transport in the chloroplasts and mitochondria of plant cells have been constructed. A generalized model comprising plant cells and their vacuoles was analyzed. A model of the transport of substances in the roots of plants was also developed. Based on this model, the problem of transport of substances in tall trees has been considered. The calculated concentrations of ions in the vacuoles of cells and resting potentials agreed well with the experimental data.

Maximum Entropy Production Theorem for Transitions between Enzyme Functional States and Its Applications

Transitions between enzyme functional states are often connected to conformational changes involving electron or proton transport and directional movements of a group of atoms. These microscopic fluxes, resulting in entropy production, are driven by non-equilibrium concentrations of substrates and products. Maximal entropy production exists for any chosen transition, but such a maximal transitional entropy production (MTEP) requirement does not ensure an increase of total entropy production, nor an increase in catalytic performance. We examine when total entropy production increases, together with an increase in the performance of an enzyme or bioenergetic system. The applications of the MTEP theorem for transitions between functional states are described for the triosephosphate isomerase, ATP synthase, for β-lactamases, and for the photochemical cycle of bacteriorhodopsin. The rate-limiting steps can be easily identified as those which are the most efficient in dissipating free-energy gradients and in performing catalysis. The last step in the catalytic cycle is usually associated with the highest free-energy dissipation involving proton nanocurents. This recovery rate-limiting step can be optimized for higher efficiency by using corresponding MTEP requirements. We conclude that biological evolution, leading to increased optimal catalytic efficiency, also accelerated the thermodynamic evolution, the synergistic relationship we named the evolution-coupling hypothesis.

Antenna proton sensitivity determines photosynthetic light harvesting strategy

Photoprotective non-photochemical quenching (NPQ) represents an effective way to dissipate the light energy absorbed in excess by most phototrophs. It is often claimed that NPQ formation/relaxation kinetics are determined by xanthophyll composition. We, however, found that, for the alveolate alga Chromera velia, this is not the case. In the present paper, we investigated the reasons for the constitutive high rate of quenching displayed by the alga by comparing its light harvesting strategies with those of a model phototroph, the land plant Spinacia oleracea. Experimental results and in silico studies support the idea that fast quenching is due not to xanthophylls, but to intrinsic properties of the Chromera light harvesting complex (CLH) protein, related to amino acid composition and protein folding. The pKa for CLH quenching was shifted by 0.5 units to a higher pH compared with higher plant antennas (light harvesting complex II; LHCII). We conclude that, whilst higher plant LHCIIs are better suited for light harvesting, CLHs are 'natural quenchers' ready to switch into a dissipative state. We propose that organisms with antenna proteins intrinsically more sensitive to protons, such as C. velia, carry a relatively high concentration of violaxanthin to improve their light harvesting. In contrast, higher plants need less violaxanthin per chlorophyll because LHCII proteins are more efficient light harvesters and instead require co-factors such as zeaxanthin and PsbS to accelerate and enhance quenching.

Photosystem I, when excited in the chlorophyll Qy absorption band, feeds on negative entropy

It is often suggested that Life may lay outside the normal laws of Physics and particularly of Thermodynamics, though this point of view is refuted by many. As the Living State may be thought of as an open system, often far from equilibrium, most attempts at placing Life under the umbrella of the laws of Physics have been based, particularly in recent years, on non-equilibrium Thermodynamics and particularly the Maximum Entropy Production Principle. In this view it is the dissipation of entropy (heat) which permits the ever increasing complexity of Living Systems in biological evolution and the maintenance of this complexity. However, these studies usually consider such biological entities as whole cells, organs, whole organisms and even Life itself at the entire terrestrial level. This requires making assumptions concerning the Living State, which are often not soundly based on observation and lack a defined model structure. The present study is based on an entirely different approach, in which a classical thermodynamic analysis of a well-defined biological nanoparticle, plant Photosystem I, is performed. This photosynthetic structure, which absorbs light and performs primary and secondary charge separation, operates with a quantum efficiency close to one. It is demonstrated that when monochromatic light is absorbed by the lowest lying electronic transition, the chlorophyll Q_y transition, entropy production in the system bath plus entropy changes internal to the system are numerically less than the entropy decrease of the light field. A Second Law violation is therefore suggested for these experimental conditions. This conclusion, while at first sight is supportive of the famous and much discussed statement of Schroedinger, that "Life feeds on negentropy", is analysed and the conditions in which this statement may be considered valid for a Plant Photosystem are defined and delimited. The remarkably high quantum efficiency, leading to minimal entropy production (energy wastage), seems to suggest that evolution of Photosystem I has gone down the road of maximal energy efficiency as distinct from maximal entropy production. Photosystem I cannot be considered a maximum entropy dissipation structure.

Antenna entropy in plant photosystems does not reduce the free energy for primary charge separation

We have investigated the concept of the so-called "antenna entropy" of higher plant photosystems. Several interesting points emerge: 1. In the case of a photosystemwhich harbours an excited state, the “antenna entropy” is equivalent to the configurational (mixing) entropy of a thermodynamic canonical ensemble. The energy associated with this parameter has been calculated for a hypothetical isoenergetic photosystem, photosystem I and photosystem II, and comes out in the range of 3.5 - 8% of the photon energy considering 680 nm. 2. The “antenna entropy” seems to be a rather unique thermodynamic phenomenon, in as much as it does not modify the free energy available for primary photochemistry, as has been previously suggested. 3. It is underlined that this configurational (mixing) entropy, unlike heat dispersal in a thermal system, does not involve energy dilution. This points out an important difference between thermal and electronic energy dispersal.

Thermodynamics of primary photosynthesis

The thermodynamics of photosynthesis has been much discussed, but recent articles have pointed to some confusion on the subject. The aim of this review is to clarify a limited part of this state of affairs.

Analytical model of ion transport and conversion of light energy in chloroplasts

An analytical model, which describes the stationary transformation of light energy to the energy of pigment electronic excitation, has been constructed. A proton pump of the thylakoid membrane has been considered as a two-level conformon. The difference between the energies of the excited and ground states of both the pigment and the protein complex is assumed to be the energy of an absorbed photon. It has been found how the concentration of ions in a lumen and the potential across the thylakoid membrane depend on the concentration of ions in the stroma and the brightness temperature of absorbed radiation. Conditions for the maximum efficiency of the photosynthesis process have been analyzed. This model has been used to determine the electric potential (phi approximately 6.7mV) at the chloroplast thylakoid membrane. The calculated value of the electric potential is in good agreement with the experimental data. A limitation on the stoichiometric coefficient of the proton transport through ATP-synthase, m>3, has been found theoretically.

Entropy production and the Second Law in photosynthesis

An assertion that the primary photochemistry of photosynthesis can violate the Second Law of thermodynamics in certain efficient systems has been put forward by Jennings et al., who maintain their position strongly despite an argument to the contrary by Lavergne. We identify a specific omission in the calculation of Jennings et al. and show that no violation of the Second Law occurs, regardless of the photosynthetic efficiency.

Entropy consumption in primary photosynthesis

Knox and Parson have objected to our previous conclusion on possible negative entropy production during primary photochemistry, i.e., from photon absorption to primary charge separation, by considering a pigment system in which primary photochemistry is not specifically considered. This approach does not address our proposal. They suggest that when a pigment absorbs light and passes to an excited state, its entropy increases by hnu/T. This point is discussed in two ways: (i) from considerations based on the energy gap law for excited state relaxation; (ii) using classical thermodynamics, in which free energy is introduced into the pigment (antenna) system by photon absorption. Both approaches lead us to conclude that the excited state and the ground state are isoentropic, in disagreement with Knox and Parson. A discussion on total entropy changes specifically during the charge separation process itself indicates that this process may be almost isoentropic and thus our conclusions on possible negentropy production associated with the sequence of reactions which go from light absorption to the first primary charge separation event, due to its very high thermodynamic efficiency, remain unchanged.

Commentary on: “Photosynthesis and negative entropy production” by Jennings and coworkers

This commentary argues against the view that photochemical energy conversion violates the second law of thermodynamics, as expressed in a recent paper [R.C. Jennings, E. Engelmann, F. Garlaschi, A.P. Casazza, G. Zucchelli. Photosynthesis and negative entropy production. Biochim. Biophys. Acta 1709 (2005) 251-255]. The basic principles of free energy conversion by a photo-electrochemical cell are outlined, emphasizing the fact that the potential depends on the relative population of the excited state and thus on the illumination intensity.

Photosynthesis research in Italy: a review

This historical review was compiled and edited by Giorgio Forti, whereas the other authors of the different sections are listed alphabetically after his name, below the title of the paper; they are also listed in the individual sections. This review deals with the research on photosynthesis performed in several Italian laboratories during the last 50 years; it includes research done, in collaboration, at several international laboratories, particularly USA, UK, Switzerland, Hungary, Germany, France, Finland, Denmark, and Austria. Wherever pertinent, references are provided, especially to other historical papers in Govindjee et al. [Govindjee, Beatty JT, Gest H, Allen JF (eds) (2005) Discoveries in Photosynthesis. Springer, Dordrecht]. This paper covers the physical and chemical events starting with the absorption of a quantum of light by a pigment molecule to the conversion of the radiation energy into the stable chemical forms of the reducing power and of ATP. It describes the work done on the structure, function and regulation of the photosynthetic apparatus in higher plants, unicellular algae and in photosynthetic bacteria. Phenomena such as photoinhibition and the protection from it are also included. Research in biophysics of photosynthesis in Padova (Italy) is discussed by G.M. Giacometti and G. Giacometti (2006).