The Critical Roles of Information and Nonequilibrium Thermodynamics in Evolution of Living Systems

Abstract

Living cells are spatially bounded, low entropy systems that, although far from thermodynamic equilibrium, have persisted for billions of years. Schrödinger, Prigogine, and others explored the physical principles of living systems primarily in terms of the thermodynamics of order, energy, and entropy. This provided valuable insights, but not a comprehensive model. We propose the first principles of living systems must include: (1) Information dynamics, which permits conversion of energy to order through synthesis of specific and reproducible, structurally-ordered components; and (2) Nonequilibrium thermodynamics, which generate Darwinian forces that optimize the system.

Living systems are fundamentally unstable because they exist far from thermodynamic equilibrium, but this apparently precarious state allows critical response that includes: (1) Feedback so that loss of order due to environmental perturbations generate information that initiates a corresponding response to restore baseline state. (2) Death due to a return to thermodynamic equilibrium to rapidly eliminate systems that cannot maintain order in local conditions. (3) Mitosis that rewards very successful systems, even when they attain order that is too high to be sustainable by environmental energy, by dividing so that each daughter cell has a much smaller energy requirement. Thus, nonequilibrium thermodynamics are ultimately responsible for Darwinian forces that optimize system dynamics, conferring robustness sufficient to allow continuous existence of living systems over billions of years.

Appendix: Relation Between Flux F and Information I at the NM

The average flux F of proteins at the NM is defined as

$$ F = \frac{dN/dt}{A} \approx\frac{N}{t_{a}A} $$

(11)

where t _a is the time for each to travel from the CM to NM. This assumes dN/dt is approximately constant over a time interval (0,t _a ). Also, A is the surface area of the spherical NM.

Let N proteins leave essentially one point on the CM and move to the NM during the transit time t _a . We now further clarify the meaning of position x ₀ in Eq. (2) of the text. It was regarded as the ideal position on the NM of the nth such protein. The position x ₀ is ‘ideal’ in that it follows the principle I=max. (see text Sect. 3). Likewise, the added ‘noise’ positions x≡x _n in (2) represent an added random perturbation of random walk arising out of interactions with molecules of the cytoplasm. Therefore Eq. (2) now becomes (see above Eq. (4) of text)

$$ y_{n} = x_{0} - x_{n}, \quad n = 1,\ldots,N $$

(12)

over the N protein arrivals. The random variable x obeys some probability law with variance σ ². This probability law then, defines a level of Fisher information about the ideal position x ₀ of the nth protein.

Let the N positions x _n be processed, in some presently unknown way, by the NM so as to estimate the ideal position x ₀. By additivity of the information, the N independent readings give a total Fisher information

$$ I = N/\sigma^{2}. $$

(13)

The well-known diffusion formula for random walk expresses

$$ \sigma^{2} = 2Dt_{a}, \quad \mbox{with\ constant}\ D = 2.5\times 10^{-12}~\mbox{m$^{2}$/s} $$

(14)

in cytoplasm. In summary, σ is the standard deviation, or rms fluctuation, due to the diffusion of any one protein during the transit time t _a through the cytoplasm.

Then

$$ 2D\frac{I}{A} = \frac{\sigma^{2}}{t_{a}}\frac{I}{A} = \frac{\sigma^{2}}{t_{a}}\biggl( \frac{N}{\sigma^{2}} \biggr)\frac{1}{A} = \frac{N}{t_{a}A} = F. $$

(15)

The first equality is by (14), the second is by (13), the third is after a cancellation, and the last is by definition (11). Thus, from the outer equality,

$$ I = \biggl( \frac{A}{2D} \biggr)F. $$

(16)

This is the relation between flux and information at the NM that we sought.