Chemical machines, Maxwell's demon and living organisms

The problem considered in this paper is whether conventional chemical machines can be used in living organisms. I first point out that, due to their molecular nature, living systems pose unique thermodynamic problems, particularly in relation to Maxwell's demon. I then show that these problems may be solved by introducing time into the fundamental statement of the second law so that it becomes valid at the molecular level. This proposal, while clarifying certain logical anomalies in classical thermodynamics, makes no difference to that science in practice. However, I deduce from this statement that there are only two general ways of obtaining useful work from a chemical reaction: the first, a “constrained equilibrium” mechanism, is that employed by conventional chemical engines, but the second, a “molecular energy” mechanism, which depends upon the rapidity of resonant energy-transfer, may not have been suggested before. I then argue that because the former mechanism is essentially macroscopic in character it cannot, in fact, be used in those biological processes, like muscular contraction or active transport, in which useful molecular work is done and that only the latter may be so used. I also suggest reasons why this conclusion has been overlooked. Muscular contraction is used to illustrate these arguments and it is shown that all models of this process so far proposed fall into the first category. Although it is possible to eliminate such models a priori, several examples are finally criticized in detail to clarify the points raised. It is shown that in fact each of these models would have to be a Maxwell's demon machine.     

Co-operativity in biological machines

McClare has recently discussed the properties of machines which operate too fast for there to be appreciable thermalization between components. We argue that co-operative behaviour is likely in those machines and that if there is co-operativity, the machine cannot be treated as the superposition of a large number of “molecular energy machines”. This point may be relevant to models of muscle contraction.     

The causes of altered chlorophyll fluorescence quenching induction in the Arabidopsis mutant lacking all minor antenna complexes

Non-photochemical quenching (NPQ) of chlorophyll fluorescence is the process by which excess light energy is harmlessly dissipated within the photosynthetic membrane. The fastest component of NPQ, known as energy-dependent quenching (qE), occurs within minutes, but the site and mechanism of qE remain of great debate. Here, the chlorophyll fluorescence of Arabidopsis thaliana wild type (WT) plants was compared to mutants lacking all minor antenna complexes (NoM). Upon illumination, NoM exhibits altered chlorophyll fluorescence quenching induction (i.e. from the dark-adapted state) characterised by three different stages: (i) a fast quenching component, (ii) transient fluorescence recovery and (iii) a second quenching component. The initial fast quenching component originates in light harvesting complex II (LHCII) trimers and is dependent upon PsbS and the formation of a proton gradient across the thylakoid membrane (ΔpH). Transient fluorescence recovery is likely to occur in both WT and NoM plants, but it cannot be overcome in NoM due to impaired ΔpH formation and a reduced zeaxanthin synthesis rate. Moreover, an enhanced fluorescence emission peak at ~679?nm in NoM plants indicates detachment of LHCII trimers from the bulk antenna system, which could also contribute to the transient fluorescence recovery. Finally, the second quenching component is triggered by both ΔpH and PsbS and enhanced by zeaxanthin synthesis. This study indicates that minor antenna complexes are not essential for qE, but reveals their importance in electron stransport, ΔpH formation and zeaxanthin synthesis.     

Erythrocyte death in vitro induced by starvation in the absence of Ca

Human erythrocytes (RBCs), stored at 4 °C under nominal absence of external energy sources and calcium ions, show a gradual decrease in membrane roughness (R_rms) at the end of which the appearance of morphological phenomena (spicules, vesicles and spherocytes) is observed on the cell membrane, phenomena that can mainly be ascribed to the ATP-dependent disconnection of the cortical cytoskeleton from the lipid bilayer. After depletion of the intracellular energy sources obtained under the extreme conditions chosen, treatment with a minimal rejuvenation solution makes the following remarks possible: (i) RBCs are able to regenerate adenosine triphosphate (ATP) and 2,3-bisphosphoglycerate only up to 4 days of storage at 4 °C, whereas from the eighth day energy stocks cannot be replenished because of a disorder in the transmembrane mechanisms of transport; (ii) the RBCs' roughness may be restored to the initial value (i.e. that observed in fresh RBCs) only in samples stored up to 4-5 days, whereas after the eighth day of storage the rejuvenation procedure appears to be inefficient; (iii) membrane physical properties - as measured by R_rms - are actually controlled by the metabolic production of ATP, necessary to perform the RBCs' basic functions; (iv) once energy stores cannot be replenished, a regulated sequence of the morphological events (represented by local buckles that lead to formation of spicules and vesicles of the lipid bilayer with generation of spherocytes) is reminiscent of the RBCs' apoptotic final stages; (v) the morphological phenomenology of the final apoptotic stages is passive (i.e. determined by simple mechanical forces) and encoded in the mechanical properties of the membrane-skeleton; and (vi) necrotic aspects (e.g. disruption of cell membrane integrity, so that intracellular protein content is easily released) ensue when RBCs are almost totally (≥ 90%) depleted in an irreversible way of the energetic stores.     

70% efficiency of bistate molecular machines explained by information theory,high dimensional geometry and evolutionary convergence

The relationship between information and energy is key to understanding biological systems. We can display the information in DNA sequences specifically bound by proteins by using sequence logos, and we can measure the corresponding binding energy. These can be compared by noting that one of the forms of the second law of thermodynamics defines the minimum energy dissipation required to gain one bit of information. Under the isothermal conditions that molecular machines function this is joules per bit ( is Boltzmann''s constant and T is the absolute temperature). Then an efficiency of binding can be computed by dividing the information in a logo by the free energy of binding after it has been converted to bits. The isothermal efficiencies of not only genetic control systems, but also visual pigments are near 70%. From information and coding theory, the theoretical efficiency limit for bistate molecular machines is ln 2 = 0.6931. Evolutionary convergence to maximum efficiency is limited by the constraint that molecular states must be distinct from each other. The result indicates that natural molecular machines operate close to their information processing maximum (the channel capacity), and implies that nanotechnology can attain this goal.     

An "active enzyme" muscle model

A new model of skeletal muscle contraction is presented from a unified view of muscle physiology, chemical energetics and newly obtained experimental data concerning actomyosin ATPase in vitro.In this model an interaction between actin and myosin, involving two distinct active sites, is considered to be the essential elementary mechanism for muscle contractions. These two sites are located on myosin. One site, forming a myosin-ADP-P, complex, has stored energy derived from ATP splitting before the beginning of a contraction. Another site, forming a myosin-ATP complex, upon interacting with actin, catalyzes ATP hydrolysis, using a fraction of the stored energy. The hydrolysis at the latter site is responsible for tension development, while the stored energy is released to drive the contractile reaction between actin and myosin unidirectionally. (Thus, the two sites act co-operatively and they can be viewed as forming an active enzyme.)There has been a difficulty in explaining the shortening heat production with apparent lack of corresponding chemical change at the early stage of contraction. The active enzyme model accounts for the shortening heat as the irreversible release of the stored energy. The heat production appears to precede its corresponding ATP splitting for “refueling” which occurs after complete exhaustion of the stored energy, while the actomyosin ATP hydrolysis takes place proportionally to the work. At the macroscopic level, the model is compatible with Hill's tension-velocity and heat relation.     

The role of pH on the thermodynamics and kinetics of muscle biochemistry: an in vivo study by (31)P-MRS in patients with myo-phosphorylase deficiency

In this study we assessed ΔG'(ATP) hydrolysis, cytosolic [ADP], and the rate of phosphocreatine recovery using Phosphorus Magnetic Resonance Spectroscopy in the calf muscle of a group of patients affected by glycogen myo-phosphorylase deficiency (McArdle disease). The goal was to ascertain whether and to what extent the deficit of the glycogenolytic pathway would affect the muscle energy balance. A typical feature of this pathology is the lack of intracellular acidosis. Therefore we posed the question of whether, in the absence of pH decrease, the rate of phosphocreatine recovery depends on the amount of phosphocreatine consumed during exercise. Results showed that at the end of exercise both [ADP] and ΔG'(ATP) of patients were significantly higher than those of matched control groups reaching comparable levels of phosphocreatine concentration. Furthermore, in these patients we found that the rate of phosphocreatine recovery is not influenced by the amount of phosphocreatine consumed during exercise. These outcomes provide experimental evidence that: i) the intracellular acidification occurring in exercising skeletal muscle is a protective factor for the energy consumption; and ii) the influence of pH on the phosphocreatine recovery rate is at least in part related to the kinetic mechanisms of mitochondrial creatine kinase enzyme.     

Effects of body size and environment on diet-tissue δN fractionation in fishes

Nitrogen stable isotope natural abundance data are often used in trophodynamic research. The assumed nitrogen diet-tissue fractionation (Δδ¹⁵N) determines conclusions about trophic level, potential food sources and ontogenetic diet shifts. Δδ¹⁵N is usually assumed to be 3.0-3.4‰ per trophic level and unaffected by the size or age of animals or their environment. To assess the effects of body size, experimental duration and environmental conditions on fish tissue Δδ¹⁵N, two populations of European sea bass (Dicentrarchus labrax) were reared on constant diets of dab (Limanda limanda) muscle or sandeel (Ammodytes marinus) for 2 years under natural light and temperature regimes. Bass were sampled at approximately monthly intervals to determine Δδ¹⁵N for muscle, heart and liver tissue. Mean values of Δδ¹⁵N were 3.83‰, 3.54‰, 2.05‰ (sandeel diet) and 3.98‰, 3.32‰, 1.95‰ (dab diet) for muscle, heart and liver tissue respectively. The assumption that fractionation was independent of body mass was upheld for muscle and heart tissue, but not for liver. Time effects on muscle Δδ¹⁵N were explainable by a sinusoidal function with a period of 1 year and wave height ∼ 0.3‰. Time resulted in increases in heart δ¹⁵N and decreases in liver δ¹⁵N which were small compared to background variation, equating to 1/6 of a trophic level over 2 years, and unlikely to have great significance in ecological studies. Heart and liver δ¹⁵N were also affected by temperature probably reflecting the metabolic functions of these tissues and their associated rates of turnover. However in heart the explanatory power of temperature appeared tied to that of time. Although the Δδ¹⁵N for bass muscle on both diets approached 4‰, the Δδ¹⁵N values from this study, when combined with those from the literature, suggest that where fish species specific data are not available, a mean Δδ¹⁵N for fish muscle of 3.2‰ should be applied (mean white muscle Δδ¹⁵N = 3.15). The literature based mean Δδ¹⁵N for whole fish was lower than that of white muscle suggesting that a separate Δδ¹⁵N (2.9‰) should be applied when sampling whole fish.     

Lipid contribution to the affinity of antigen association with specific antibodies conjugated to liposomes

Immunoliposomes, directed to clinically relevant cell-surface molecules with antibodies, antibody fragments or peptides, are used for site-specific diagnostic evaluation or delivery of therapeutic agents. We have developed intrinsically echogenic liposomes (ELIP) covalently linked to fibrin(ogen)-specific antibodies and Fab fragments for ultrasonic imaging of atherosclerotic plaques. In order to determine the effect of liposomal conjugation on the molecular dynamics of fibrinogen binding, we studied the thermodynamic characteristics of unconjugated and ELIP-conjugated antibody molecules. Utilizing radioimmunoassay and enzyme-linked immunosorbent assay protocols, binding affinities were derived from data obtained at three temperatures. The thermodynamic functions ΔH°, ΔG° and ΔS° were determined from van't Hoff plots and equations of state. The resultant functions indicated that both specific and nonspecific associations of antibody molecules with fibrinogen occurred through a variety of molecular interactions, including hydrophophic, ionic and hydrogen bonding mechanisms. ELIP conjugation of antibodies and Fab fragments introduced a characteristic change in both ΔH° and ΔS° of association, which corresponded to a variable contribution to binding by phospholipid gel-liquid crystal phase transitions. These observations suggest that a reciprocal energy transduction, affecting the strength of antibody-antigen binding, may be a singular characteristic of immunoliposomes, having utility for optimization and further development of the technology.     

The Origin of the Low-Energy Form of Photosystem I Light-Harvesting Complex Lhca4: Mixing of the Lowest Exciton with a Charge-Transfer State

The peripheral light-harvesting complex of photosystem I contains red chlorophylls (Chls) that, unlike the typical antenna Chls, absorb at lower energy than the primary electron donor P700. It has been shown that the red-most absorption band arises from two excitonically coupled Chls, although this interaction alone cannot explain the extreme red-shifted emission (25 nm, ∼480 cm⁻¹ for Lhca4 at 4 K) that the red Chls present. Here, we report the electric field-induced absorption changes (Stark effect) on the Q_y region of the Lhca4 complex. Two spectral forms, centered around 690 nm and 710 nm, were necessary to describe the absorption and Stark spectra. The analysis of the lowest energy transition yields a high value for the change in dipole moment, Δμ_710nm ≈ 8 Df⁻¹, between the ground and excited states as compared with monomeric, Δμ = 1 D, or dimeric, Δμ = 5 D, Chl a in solution. The high value of the Δμ demonstrates that the origin of the red-shifted emission is the mixing of the lowest exciton state with a charge-transfer state of the dimer. This energetic configuration, an excited state with charge-transfer character, is very favorable for the trapping and dissipation of excitations and could be involved in the photoprotective mechanism(s) of the photosystem I complex.     

Distributed Shared Arrays: Portable Shared-Memory Programming Interface for Multiple Computer Systems

This paper describes the design and implementation of a parallel programming environment called Distributed Shared Array (DSA), which provides a shared global array abstract across different machines connected by a network. In DSA, users can define and use global arrays that can be accessed uniformly from any machines in the network. Explicit management of array area allocation, replication, and migration is achieved by explicit calls for array manipulation: defining array regions, reading and writing array regions, synchronization, and control of replication and migration. The DSA is integrated with Grid (Globus) services. This paper also describes the use of our model for gene cluster analysis, multiple alignment and molecular dynamics simulation. In these applications, global arrays are used for storing the distance matrix, alignment matrix and atom coordinates, respectively. Large array areas, which cannot be stored in the memory of individual machines, are made available by the DSA. Scalable performance of DSA was obtained compared to that of conventional parallel programs written in MPI.     

Effects of body size and environment on diet-tissue δC fractionation in fishes

δ¹³C data are often used in trophodynamic research where diet-tissue fractionation (Δδ¹³C) is assumed to be 0-1‰ per trophic level and unaffected by the size of animals or their environment. Variation in Δδ¹³C will influence conclusions about food sources, energy pathways and trophic level. To assess the effects of body size, age and environmental conditions on Δδ¹³C, European sea bass (Dicentrarchus labrax) were reared on constant diets of dab (Limanda limanda) or (Ammodytes marinus) for 2years under natural environmental regimes. Bass were sampled approximately monthly to determine Δδ¹³C for muscle, heart and liver tissue and were 1.66‰, − 0.18‰, − 1.77‰ (sandeel diet) and 1.34‰, − 1.18‰, − 1.75‰ (dab diet) respectively. Arithmetic lipid correction increased Δδ¹³C to > 2‰ for muscle and liver. Δδ¹³C was dependent on body mass and experimental duration (age) and generally declined with weight or time even after correction for lipid content. For liver, increasing temperature increased Δδ¹³C. The Δδ¹³C estimates from this study were compared with all available published Δδ¹³C estimates for fish. Bass muscle Δδ¹³C was similar to previous estimates for fish white muscle Δδ¹³C (1.56 ± 1.10‰) and whole body Δδ¹³C (1.52 ± 1.13‰). Fractionations derived in this study, combined with those from the literature, support the use of diet-tissue fractionation values of between 1‰-2‰ for δ¹³C, rather than the commonly used 0‰ − 1‰. For muscle Δδ¹³C, 1.5‰ is appropriate.     

Irrelevance of the Power Stroke for the Directionality,Stopping Force,and Optimal Efficiency of Chemically Driven Molecular Machines

A simple model for a chemically driven molecular walker shows that the elastic energy stored by the molecule and released during the conformational change known as the power-stroke (i.e., the free-energy difference between the pre- and post-power-stroke states) is irrelevant for determining the directionality, stopping force, and efficiency of the motor. Further, the apportionment of the dependence on the externally applied force between the forward and reverse rate constants of the power-stroke (or indeed among all rate constants) is irrelevant for determining the directionality, stopping force, and efficiency of the motor. Arguments based on the principle of microscopic reversibility demonstrate that this result is general for all chemically driven molecular machines, and even more broadly that the relative energies of the states of the motor have no role in determining the directionality, stopping force, or optimal efficiency of the machine. Instead, the directionality, stopping force, and optimal efficiency are determined solely by the relative heights of the energy barriers between the states. Molecular recognition—the ability of a molecular machine to discriminate between substrate and product depending on the state of the machine—is far more important for determining the intrinsic directionality and thermodynamics of chemo-mechanical coupling than are the details of the internal mechanical conformational motions of the machine. In contrast to the conclusions for chemical driving, a power-stroke is very important for the directionality and efficiency of light-driven molecular machines and for molecular machines driven by external modulation of thermodynamic parameters.     

A hill-type muscle model expansion accounting for effects of varying transverse muscle load

Recent studies demonstrated that uniaxial transverse loading (F_G) of a rat gastrocnemius medialis muscle resulted in a considerable reduction of maximum isometric muscle force (ΔF_im). A hill-type muscle model assuming an identical gearing G between both ΔF_im and F_G as well as lifting height of the load (Δh) and longitudinal muscle shortening (Δl_CC) reproduced experimental data for a single load.Here we tested if this model is able to reproduce experimental changes in ΔF_im and Δh for increasing transverse loads (0.64 N, 1.13 N, 1.62 N, 2.11 N, 2.60 N). Three different gearing ratios were tested: (I) constant G_c representing the idea of a muscle specific gearing parameter (e.g. predefined by the muscle geometry), (II) G_exp determined in experiments with varying transverse load, and (III) G_f that reproduced experimental ΔF_im for each transverse load.Simulations using G_c overestimated ΔF_im (up to 59%) and Δh (up to 136%) for increasing load. Although the model assumption (equal G for forces and length changes) held for the three lower loads using G_exp and G_f, simulations resulted in underestimation of ΔF_im by 38% and overestimation of Δh by 58% for the largest load, respectively. To simultaneously reproduce experimental ΔF_im and Δh for the two larger loads, it was necessary to reduce F_im by 1.9% and 4.6%, respectively. The model seems applicable to account for effects of muscle deformation within a range of transverse loading when using a linear load-dependent function for G.     

The rise in inosine monophosphate and l-lactate concentrations in muscle of live penaeid prawns (Penaeus japonicus,Penaeus monodon) stressed by storage out of water

• 1.1. This work aimed to establish why some species of prawns survived longer than others during simulated commercial shipment.
• 2.2. Metabolism of kuruma prawns, Penaeus japonicus, and black tiger prawns, P. monodon, stored for up to 24 hr in dry sawdust was studied by measuring concentrations of l-lactate, adenylate nucleotides and inosine monophosphate (IMP) in abdominal muscle.
• 3.3. When P. japonicus was stored in sawdust at 12°C the adenylate energy charge (AEC) did not fall and no lactate or IMP accumulated after 24 hr. However, the AEC fell in P. monodon stored at a temperature of 12°C and in P. japonicus stored at higher temperatures. When AEC fell below 0.5–0.6 there was an increase in muscle lactate and IMP concentration.
• 4.4. The results show that high concentrations of lactate and IMP in muscle tissue, at a given temperature, can be used to demonstrate that a prawn has been out of water for too long.

     

Quantitative estimates of steric effects: Intramolecular strain energy effects on the activation energy for aquation of some trans-dichlorotetraaminecobalt(III) complexes

In an effort to quantitatively estimate steric contributions to the aquation rates of a series of structurally related cobalt(III) tetraamine complexes, strain energy minimization calculations have been performed on the reactant and some plausible transition state structures. Free energies of activation ΔG*_obs, are factored as: ΔG*_obs, = ΔG*_bb + ΔG*_strain + Δ_G*_CF + ΔG*_solvation + … where ΔG*_bb is the free energy change associated with bond breaking, ΔG*_solvation is the solvation free energy difference between the reactant and a proposed transition stare, ΔG*_CF is the difference in crystal field stabilization between the reactant and a proposed transition state, and ΔG*_strain is the strain energy difference between the reactant complex and a proposed transition state. The activation energy for the aquation of a hypothetical ‘strain free’ complex is defined as ΔG*_int and reflects the energy required for the bond breaking step with all other terms. For the cations trans-(RR,SS)-dichloro-1,8- diamino-3,6-diazaoctanecobalt(III)(trans [Co(2,2,2- tet)Cl₂]⁺), trans-(RR,SS)- or trans-(RS)-dichloro-1.9- diamino-3,7-diazanonanecobalt(III)(trans [Co(2,3,2- tet)Cl₂]⁺ and trans-(RS)-dichloro-1,10-diamino-4,7- diazadecanecobalt(III)(trans[Co(3,2,3-tet)Cl₂]⁺) ΔG*_int is found to be a constant 123 kJ/mol. For the trans-dichlorocobalt(III) complexes with the ligands 1,4,7,10-tetraazacyclotridecane([13]-ane-N₄), 1,4,8, 11-tetraazacyclotetradecane([14]-ane-N₄), 1,4,8,12- tetraazacyclopentadecane([15]-ane-N₄) and 1,5,9,13- tetraazacyclohexadecane([16]-ane-N₄), ΔG*_int lies in the range 133–139 kJ/mol.     

Theory of molecular machines. I. Channel capacity of molecular machines

Like macroscopic machines, molecular-sized machines are limited by their material components, their design, and their use of power. One of these limits is the maximum number of states that a machine can choose from. The logarithm to the base 2 of the number of states is defined to be the number of bits of information that the machine could "gain" during its operation. The maximum possible information gain is a function of the energy that a molecular machine dissipates into the surrounding medium (Py), the thermal noise energy which disturbs the machine (Ny) and the number of independently moving parts involved in the operation (dspace): Cy = dspace log2 [( Py + Ny)/Ny] bits per operation. This "machine capacity" is closely related to Shannon's channel capacity for communications systems. An important theorem that Shannon proved for communication channels also applies to molecular machines. With regard to molecular machines, the theorem states that if the amount of information which a machine gains is less than or equal to Cy, then the error rate (frequency of failure) can be made arbitrarily small by using a sufficiently complex coding of the molecular machine's operation. Thus, the capacity of a molecular machine is sharply limited by the dissipation and the thermal noise, but the machine failure rate can be reduced to whatever low level may be required for the organism to survive.     

Role of the Transmembrane Potential in the Membrane Proton Leak

The molecular mechanism responsible for the regulation of the mitochondrial membrane proton conductance (G) is not clearly understood. This study investigates the role of the transmembrane potential (ΔΨ_m) using planar membranes, reconstituted with purified uncoupling proteins (UCP1 and UCP2) and/or unsaturated FA. We show that high ΔΨ_m (similar to ΔΨ_m in mitochondrial State IV) significantly activates the protonophoric function of UCPs in the presence of FA. The proton conductance increases nonlinearly with ΔΨ_m. The application of ΔΨ_m up to 220 mV leads to the overriding of the protein inhibition at a constant ATP concentration. Both, the exposure of FA-containing bilayers to high ΔΨ_m and the increase of FA membrane concentration bring about the significant exponential G_m increase, implying the contribution of FA in proton leak. Quantitative analysis of the energy barrier for the transport of FA anions in the presence and absence of protein suggests that FA⁻ remain exposed to membrane lipids while crossing the UCP-containing membrane. We believe this study shows that UCPs and FA decrease ΔΨ_m more effectively if it is sufficiently high. Thus, the tight regulation of proton conductance and/or FA concentration by ΔΨ_m may be key in mitochondrial respiration and metabolism.