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

Abstract

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.

Natural light harvesting systems: unraveling the quantum puzzles

“…Furthermore there is motivation to pursue the links between agent-based rules and the quantum predictive power proposed in Ref. [143], to examine the optimality of biomolecular structural layouts for energy transport and other information processing [163,164] properties.…”

Engineering Applications of Biomolecular Motors

“…An alternative perspective on the maximum possible efficiency is given by Schneider (36,37), who notes that a transition to a new state (e.g., a forward step) by a molecular motor constitutes a choice between alternative states. Associated with this choice is an increase in information in the system, which is equivalent to a reduction in entropy.…”

A brief review of molecular information theory

“…That is, for the energy dissipation that occurs during binding, EcoRI could make R energy = 17.3 bits of choices but from the DNA sequence we see that it only does R sequence = 12 bits. It is inefficient, and we can measure its efficiency compared to the ideal as R sequence / R energy = 12/17.3 = 69% [49]. Many other genetic systems are around 70% efficient (in preparation).…”

“…A sketch of the result is given here and details can be found in the original paper [49]. ε min from Eq.…”

“…(Readers who wish a challenge may stop at this point, read Refs. [37,38] but not [49] and see if they can find a solution. It took the author 6 years.…”