Which are the 'Hilbert Problems' of Biophysics?

Abstract

Whilst considering commissioning articles for QRBDiscovery as Editor-in-Chief, I would like to explain what I think could be interesting topics for new articles in addition to unexpected amazing discoveries. Recently, I submitted a somewhat philosophical paper with the title ‘The Mole and Albert Einstein’ to which I had been invited by the Swedish Physics Society. To prepare myself, I had been reading Einstein’s famous papers and PhD Thesis of 1905 (in German to avoid interpreters’ pedagogical improvements!) and was struck by his quite narrow approach in his attempt to address and generalize so many different problems. I do not want to diminish the impression of his genius, but I suddenly saw Einstein as a somewhat bewildered young (25 years) man eager to make an impact.When in 2005 the Physics world celebrated the anniversary of Einstein’smiracle year, hewas claimed to be aChemist byNature columnist Philip Ball because of his work and PhD Thesis on molecular diffusion inspired by Brownian motion and his goal to determine Avogadro’s number – but then why not call Einstein a Biophysicist? Following van’t Hoff, the first Nobel Laureate in Chemistry (1901), Einstein starts with the osmotic pressure and van’t Hoff’s formula pV* =nRT, which looks like the ideal gas law, and which he assumes to be a thermodynamic macroscopic equation of state integrating corresponding microscopic equations in which the colliding solvent molecules just balance the osmotic pressure. His analysis (including some strange detours) leads to the famous statistical error function for diffusion. His explanation of the Brownianmotion also results in the final acceptance by the science society of the atom and molecule concepts in the shape we know them today. The jumpy randommotions that Robert Brown observed pollen grains to performwhen suspended in water, Einstein explains, reflect the thermal motions of surrounding water molecules, an unequal number obviously colliding from opposite sides of the grain, telling something about the size of the numbers. The molecular dynamics and molecular-kinetic theory of heat are at the heart of Einstein’s thinking in 1905 andmany years later his endeavor to develop a universal theory for the fundamental forces can be seen as just an expansion of this early work on liquids and intermolecular forces, based on Newtonian kinetic theory of matter. Where am I heading with this? Well, I might ask: would a modern approach by molecular dynamics computation exactly agree with Einstein’s description of Brownian dynamics? Or might there be some deviations that could suggest additional, yet undiscoveredmechanisms, such as wave front-like attacks by many coherently coupled solvent molecules by which the momentum transfer between the small molecules and big pollen grains could occur? The biophysical impact of such amechanism could be earth-shattering, changing the rules for thermal activations of various processes inside the cell, adding large fluctuation forces. Unfortunately (or fortunately?), my checks in recent literature all indicate excellent agreement betweenmodern molecular dynamics simulations and Brownian motion according to the classical Langevin equation as characterized in terms of autocorrelation memory and fluctuating force functions. Nor do any reported disagreement with experiment suggest the existence of any additional effects, neither under thermodynamic equilibrium conditions nor at investigated nonequilibrium conditions (electrophoresis and sedimentation). From this, I conclude that I must probably dismiss fundamentals of molecular diffusion as a problem area worth prioritized attention. Or maybe not since MD today is still limited to rather short times? With this example, I would like to open a discussion asking: canwe identify problem areas or paradigmatic models in biophysics and molecular biology that would deserve special attention because they are particularly important and not fully understood? Of course, we may not predict discovery, but as Pasteur says we could help chance for making one by having a prepared mind. With inspiration from ‘Hilbert’s 23 Problems’, I would encourage all our readers, Editors, and Editorial Board Members to come up with suggestions for a list of such problems in contemporary biophysics-related sciences, whether theoretical, experimental, or intrinsic to the dissipative systems of living organisms. But like in my example above, before a certain problem be put forward, I would expect that effort has been made to search for evidence in the literature of any violations or conflicting data that can motivate further digging. I shall list examples here, starting with fundamentals of mechanisms in biology and then theoretical challenges and potential future method developments. I welcome your adding more points to the list or complementing/correcting the current ones. We might also eventually do a QRB Discovery