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.     

Plausible view on the biological molecular energy machines.

A qualitative picture of operation modes of biological molecular energy machines is presented. It is suggested that there is mutual control between the flow of molecular energy stored in a biological molecular energy machine and the sequence of nonequilibrium conformational states through which the machine passes in doing work. If the structure of the conformational space is favorable, the set of trajectories in this space decomposes into two families, each of which accomplishes another task. This divergence of trajectories enables to distinguish molecular objects according to differences in interaction between the machine and the object, i.e., to perform a measurement on a molecular object and process the object according to the result of that measurement.     

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.     

Fluctuation as a tool of biological molecular machines

The mechanism for biological molecular machines is different from that of man-made ones. Recently single molecule measurements and other experiments have revealed unique operations where biological molecular machines exploit thermal fluctuation in response to small inputs of energy or signals to achieve their function. Understanding and applying this mechanism to engineering offers new artificial machine designs.     

The Extended Synthesis: The Law of the Conditions of Existence

A unified theory of biology must incorporate a naturalistic explanation for the origin of life, namely that given certain conditions, it was highly probable that life would originate. That theory, however, cannot be solely a theory of the origin of life. The same general mechanisms that allowed life to originate must also explain its subsequent evolution as embodied in the Extended Synthesis, including the origin of the inherent constraints and regularities that allowed natural selection to emerge as a natural process. A naturalistic grounding for the origin of life and its subsequent evolution, what Darwin called the Law of the Conditions of Existence, can be found in the natural law of history, the Second Law of Thermodynamics.     

Reply to “Commentary on Photosynthesis and Negative Entropy Production by Jennings and coworkers” by J. Lavergne

It is argued that the chemical potential analogy does not provide useful information on the thermodynamics of photosystems, as the thermodynamic efficiency of an absorbed quantum is not considered. Instead, the approach based on either entropy balance or entropy flux considerations does provide this information. At high thermodynamic efficiencies, primary photochemistry can, in principle, violate the Second Law of Thermodynamics.     

Critical analysis of objections against the biological molecular energy machines.

In the past, two important objections against McClare's idea of biological molecular energy machines were raised. One of the criticisms was concerned with the origin of energy gained in ATP cleavage and with an interpretation of McClare's "excited vibrational state." The former argument reveals a failure of the critics to comprehend McClare's approach. As to the excited vibrational state, it can be identified with nonequilibrium conformational states of the unit rather than with a single vibrational mode. The other criticism based on Brillouin's energy cost of measurement argued that reversible operation of biological molecular energy machines would be virtually impossible. Using propagation velocities of deformations of the unit's structure (instead of velocity of light), the objections against reversibility are invalidated even in the framework of the critic's approach. McClare's idea and relevant definitions are thus physically correct.     

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.     

Twisted Radio Waves and Twisted Thermodynamics

We present and analyze a gedanken experiment and show that the assumption that an antenna operating at a single frequency can transmit more than two independent information channels to the far field violates the Second Law of Thermodynamics. Transmission of a large number of channels, each associated with an angular momenta ‘twisted wave’ mode, to the far field in free space is therefore not possible.     

A dynamical field theory for dissipative thermal systems. The first and second laws of irreversible thermodynamics

The thermodynamics of irreversible processes is derived from the principles of dynamical field theory independently of all elements of thermostatics, in particular the assumption of local equilibrium. Field thermodynamics proceeds from the premise that all driving forces experienced by the molecules in a continuum are conservative and arise from scalar potential functions. Dynamically the temperature potentialT is no different from the pressure potentialp. A field is converted to a force upon multiplication by a scale factor. A potential is converted to potential energy by the same scale factor. To scale the field −∇p to the force per mole of molecular speciesk, the partial molar, volume is the scale factor. Similarly the partial molar entropy, , scales the temperature field. The transition from the scale factors (which are physical parameters) to the systemic variables, for example , is not trivial. From the dynamics and the structure of the derived potential energy function are inducted the conjugate variables such as (p, V _I) and (T, s). The meta-mechanical properties of the thermal variables (T, s) are discovered via the local First Law of Thermodynamics, which relates internal energy, thermal flux, and work, and from the local Second Law, which prescribes, the possible partitions of internal energy between kinetic, potential, and thermal energies. From the form of the potential energy come Maxwell's relationships. From the energy partition comes the equation of continuity for entropy, with its important source term. In contrast to earlier theories of irreversible thermodynamics, the dissipation function does not include the stress tensor, a constitutive parameter.     

Obesity wars: molecular progress confronts an expanding epidemic

The worldwide prevalence of obesity is increasing at an alarming rate, with major adverse consequences for human health. This "obesity epidemic" is paralleled by a rapid and substantive increase in our understanding of molecular pathways and physiologic systems underlying the regulation of energy balance. While efforts to address the environmental factors that are responsible for the recent "epidemic" must continue, new molecular and physiologic insights into this system offer exciting possibilities for future development of successful therapies.     

The generation of complexity in evolution: a thermodynamic and information-theoretical discussion.

It is argued that the evolutionary tendency toward complexity derives from the Second Law of thermodynamics and the set of physicochemical constraints provided by the biosphere. Complexity-generating processes provide the means by which thermodynamic information resulting from solar energy influxes can be dissipated. In particular, reductions in energetic information promote the growth of molecular size, and reductions in configurational information promote aperiodicity in molecular sequences. Natural selection converts the sequence entropy generated in these processes into molecular information.     

Elastic energy storage in an unmineralized collagen type I molecular model with explicit solvation and water infiltration

Collagen type I is a structural protein that provides tensile strength to tendons and ligaments. Type I collagen molecules form collagen fibers, which are viscoelastic and can therefore store energy elastically via molecular elongation and dissipate viscous energy through molecular rearrangement and fibrillar slippage. The ability to store elastic energy is important for the resiliency of tendons and ligaments, which must be able to deform and revert to their initial lengths with changes in load.In an earlier paper by one of the present authors, molecular modeling was used to investigate the role of mineralization upon elastic energy storage in collagen type I. Their collagen model showed a similar trend to their experimental data but with an over-estimation of elastic energy storage. Their simulations were conducted in vacuum and employed a distance-dependent dielectric function. In this study, we performed a re-evaluation of Freeman and Silver's model data incorporating the effects of explicit solvation and water infiltration, in order to determine whether the model data could be improved with a more accurate representation of the solvent and osmotic effects. We observed an average decrease in the model's elastic energy storage of 45.1%±6.9% in closer proximity to Freeman and Silver's experimental data. This suggests that although the distance-dependent dielectric implicit solvation approach was favored for its increased speed and decreased computational requirements, an explicit representation of water may be necessary to more accurately model solvent interactions in this particular system. In this paper, we discuss the collagen model described by Freeman and Silver, the present model building approach, the application of the present model to that of Freeman and Silver, and additional assumptions and limitations.     

Flight and heat dissipation in birds A possible molecular mechanism

Birds during normal sustained flight must be able to dissipate more than 8 times as much heat as during rest in order not to be overheated. The experiments reported in this note on the hemoglobin systems from two different birds indicate the existence of a molecular mechanism by which hemoglobin is used simultaneously for oxygen transport and heat dissipation.     

Elastic molecular machines in metabolism and soft-tissue restoration.

Elastic protein-based machines (bioelastic materials) can be designed to perform diverse biological energy conversions. Coupled with the remarkable energy-conversion capacity of cells, this makes possible a tissue-restoration approach to tissue engineering. When properly attached to the extracellular matrix, cells sense the forces to which they are subjected and respond by producing an extracellular matrix that will withstand those forces. Elastic protein-based polymers can be designed as temporary functional scaffoldings that cells can enter, attach to, spread, sense forces and remodel, with the potential to restore natural tissue.     

Evolution of biological information

How do genetic systems gain information by evolutionary processes? Answering this question precisely requires a robust, quantitative measure of information. Fortunately, 50 years ago Claude Shannon defined information as a decrease in the uncertainty of a receiver. For molecular systems, uncertainty is closely related to entropy and hence has clear connections to the Second Law of Thermodynamics. These aspects of information theory have allowed the development of a straightforward and practical method of measuring information in genetic control systems. Here this method is used to observe information gain in the binding sites for an artificial ‘protein’ in a computer simulation of evolution. The simulation begins with zero information and, as in naturally occurring genetic systems, the information measured in the fully evolved binding sites is close to that needed to locate the sites in the genome. The transition is rapid, demonstrating that information gain can occur by punctuated equilibrium.     

Protonation free energy levels in complex molecular systems

All proteins, nucleic acids, and other biomolecules contain residues capable of exchanging protons with their environment. These proton transfer phenomena lead to pH sensitivity of many molecular processes underlying biological phenomena. In the course of biological evolution, Nature has invented some mechanisms to use pH gradients to regulate biomolecular processes inside cells or in interstitial fluids. Therefore, an ability to model protonation equilibria in molecular systems accurately would be of enormous value for our understanding of biological processes and for possible rational influence on them, like in developing pH dependent drugs to treat particular diseases. This work presents a derivation, by thermodynamic and statistical mechanical methods, of an expression for the free energy of a complex molecular system at arbitrary ionization state of its titratable residues. This constitutes one of the elements of modeling protonation equilibria. Starting from a consideration of a simple acid-base equilibrium of a model compound with a single tritratable group, we arrive at an expression which is of general validity for complex systems. The only approximation used in this derivation is the postulating that the interaction energy between any pair of titratable sites does not depend on the protonation states of all the remaining ionizable groups.