On the beneficent thickness of water

Abstract

In the 1930s, Lars Onsager published his famous 'reciprocal relations' describing free energy conversion processes. Importantly, these relations were derived on the assumption that the fluxes of the processes involved in the conversion were proportional to the forces (free energy gradients) driving them. For chemical reactions, however, this condition holds only for systems operating close to equilibrium-indeed very close; nominally requiring driving forces to be smaller than k _B T. Fairly soon thereafter, however, it was quite inexplicably observed that in at least some biological conversions both the reciprocal relations and linear flux-force dependency appeared to be obeyed no matter how far from equilibrium the system was being driven. No successful explanation of how this 'paradoxical' behaviour could occur has emerged and it has remained a mystery. We here argue, however, that this anomalous behaviour is simply a gift of water, of its viscosity in particular; a gift, moreover, without which life almost certainly could not have emerged. And a gift whose appreciation we primarily owe to recent work by Prof. R. Dean Astumian who, as providence has kindly seen to it, was led to the relevant insights by the later work of Onsager himself.

Keywords: abiogenesis; alkaline vent theory; disequilibria; far-from-equilibrium thermodynamics.

Figure 1.

Overdamped diffusion with drift; how macromolecules move in water and bring matter to life. A macromolecule in water (black dot) moves under the effect of three forces: a ‘biasing’ force (F) (in biology, typically a free energy gradient), viscous drag (D) and a random force due to thermal impacts which generates a Gaussian fluctuation distribution in the particle’s position (fuzzy cloud). The drag is oppositely directed from, but proportional to, the particle’s instantaneous velocity (D = −vγ), where γ is the molecule’s coefficient of friction in water—which constant is, in turn, proportional to the viscosity of water: γ ∝ η. The force F produces a statistical bias in the fluctuations in the particle’s position, favouring those directed along the force over those directed against it by the factor exp(FΔx/k_BT). Because the movement of particles of the size of macromolecules in water is overdamped, the biasing force and the drag force instantaneously balance, and there is no acceleration. However, the fluctuation bias induced by F causes the particle to move with a ‘terminal’ average velocity proportional to, and in the direction of, F; specifically, ${\overline{\mathbf{v}}}_{\mathrm{term}}=\mathbf{F}/\gamma$ (see [13] and §3.2.4). We argue here that we owe to this stunningly humble bit of physics two remarkable gifts. The first is that in all biological free energy conversions, Onsager’s flux–force linearity and reciprocal relations hold at all force strengths. The second, which puts ‘remarkable’ to shame, is the conclusion that were the first gift not reality, living organizations of matter would be functionally infeasible; i.e. the second gift is life itself. (Online version in colour.)