A New Principle of Equilibrium

Lewis, Gilbert N.

doi:10.1073/pnas.11.3.179

Cited by 174 publications

(135 citation statements)

References 0 publications

Supporting

Mentioning

134

Contrasting

Unclassified

Order By: Relevance

“…In a large network at equilibrium (say made of thousands of components), as noticed by Lewis (Lewis, 1925), between any two connected nodes, the same number of transitions is expected over time in both directions. But strikingly, introducing a single one-way arrow in the network is sufficient to break micro-reversibility everywhere in the network.…”

Section: Discussionmentioning

confidence: 99%

“…This is true for Newtonian physics, kinetic theories of molecular systems, as well as in the description of the quantum world. Time irreversibility is intimately connected to the second law (Lewis, 1925;Lebowitz, 1993) and seems to arise somewhere between micro and macrostates. Our feeling of time irreversibility is anchored in a so usual experience, that an easy way to determine if a dynamic system is time-reversible or not, is to appreciate its strangeness in a film reeled backward.…”

Section: The Time's Arrow Memory and Ageingmentioning

confidence: 99%

See 1 more Smart Citation

Basic statistical recipes for the emergence of biochemical discernment

Michel

2011

Progress in Biophysics and Molecular Biology

View full text Add to dashboard Cite

An essential step towards understanding life would be to identify the very basic mechanisms responsible for the discerning behaviour of living biochemical systems, absent from randomly reacting chemical soups. One intuitively feels that this question goes beyond the particular nature of the biological molecules and should relate to general physical principles. The preeminent physicist Ludwig Boltzmann early envisioned life as a struggle for entropy, in concordance with the subsequent principle of self-organization out of equilibrium. Reexamination of elementary steady state biochemical systems from a statistical perspective supports this view and shows that sigmoidal responses arising from microstates elimination, are sufficient to explain innermost characteristics of life, including its capacity to convert random molecular interactions into accurate biological reactions. A primary operating strategy to achieve this goal is the introduction of time-irreversible transitions in molecular state conversion cycles by injection of free energy, which confers decisional capacity to single macromolecules. Selected examples from various fields of molecular biology such as enzymology and gene expression, are provided to show that these non-equilibrium steady state mechanisms remain important in contemporary biochemical systems. But in addition, information archiving allowed the emergence of the time-reversible counterparts of these mechanisms, mediated by evolutionary preorganized macromolecular complexes capable of increasing discernment in a non-dissipative manner.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: The Time's Arrow Memory and Ageingmentioning

confidence: 99%

Basic statistical recipes for the emergence of biochemical discernment

Michel

2011

Progress in Biophysics and Molecular Biology

View full text Add to dashboard Cite

show abstract

“…Detailed balance tells us that in a chemical kinetic system at equilibrium every elementary reaction is balanced by its reverse reaction π i P i→j = π j P j→i [32], where The final steady state is emphasized as a black continuous curve; as the slope from the right of r = σu is zero, we know the net flux for r > σu is zero, as expected. Detailed balance is not satisfied between r = σ and r = σu P a→b is the transition probability from state a to b.…”

Section: Reversible Reaction-diffusion With Unbinding Radiusmentioning

confidence: 95%

A discrete stochastic formulation for reversible bimolecular reactions via diffusion encounter

Razo

Qian

2016

Communications in Mathematical Sciences

View full text Add to dashboard Cite

Abstract. The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory. As there is a clear corresponding stochastic process, the mathematical description takes both Kolmogorov forward equation for the evolution of the probability distribution function and the stochastic sample trajectories. This dual description is a fundamental characteristic of stochastic processes and allows simple particle based simulations to accurately match the expected statistical behavior. However, in the traditional theory using the back-reaction boundary condition to model reversible reactions with geminate recombinations, several subtleties arise: It is unclear what the underlying stochastic process is, which causes complications in producing accurate simulations; and it is non-trivial how to perform an appropriate discretization for numerical computations. In this work, we derive a discrete stochastic model that recovers the classical models and their boundary conditions in the continuous limit. In the case of reversible reactions, we recover the back-reaction boundary condition, unifying the back-reaction approach with those of current simulation packages. Furthermore, all the complications encountered in the continuous models become trivial in the discrete model. Our formulation brings to attention the question: With computations in mind, can we develop a discrete reaction kinetics model that is more fundamental than its continuous counterpart?

show abstract

“…Even if a stationary point is stable it may not obey the law (sometimes called Principle) of Detailed Balance (or the principle of microscopic reversibility) which is thought to be very important in chemical thermodynamics (Lewis, 1925). The content of this law is that at equilibrium all the individual subprocesses are equilibrated, which in the case of chemical reactions means that the reaction steps should be reversible and should have the same reaction rate in both directions.…”

Section: Linear Stability Analysismentioning

confidence: 99%

Dynamic modeling of biochemical reactions with application to signal transduction: principles and tools using Mathematica

Tóth

Rospars

2005

Biosystems

View full text Add to dashboard Cite

Modeling of biochemical phenomena is based on formal reaction kinetics. This requires the translation of the original reaction systems into sets of differential equations expressing the effects of the various reaction steps. The temporal behavior of the system is obtained by solving the differential equations. We present the main concepts on which the formal approach of these two problems is based and we show how the amount of work needed to treat them can be significantly reduced by using a mathematical program package (Mathematica). Symbolic and numerical calculations can be performed with the programs presented and graphic presentations of the behavior of the system be obtained. The basic ideas are illustrated with three examples taken from the area of signal transduction and ion signaling.

show abstract

A New Principle of Equilibrium

Cited by 174 publications

References 0 publications

Basic statistical recipes for the emergence of biochemical discernment

Basic statistical recipes for the emergence of biochemical discernment

A discrete stochastic formulation for reversible bimolecular reactions via diffusion encounter

Dynamic modeling of biochemical reactions with application to signal transduction: principles and tools using Mathematica

Contact Info

Product

Resources

About