Field theory in superfluid 3He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?

There are several classes of homogeneous Fermi systems that are characterized by the topology of the energy spectrum of fermionic quasiparticles: (i) gapless systems with a Fermi surface, (ii) systems with a gap in their spectrum, (iii) gapless systems with topologically stable point nodes (Fermi points), and (iv) gapless systems with topologically unstable lines of nodes (Fermi lines). Superfluid 3He-A and electroweak vacuum belong to the universality class 3. The fermionic quasiparticles (particles) in this class are chiral: they are left-handed or right-handed. The collective bosonic modes of systems of class 3 are the effective gauge and gravitational fields. The great advantage of superfluid 3He-A is that we can perform experiments by using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3He-A one can simulate event horizons, Hawking radiation, rotating vacuum, etc. High-temperature superconductors are believed to belong to class 4. They have gapless fermionic quasiparticles with a “relativistic” spectrum close to gap nodes, which allows application of ideas developed for superfluid 3He-A.

Computational method to reduce the search space for directed protein evolution

We introduce a computational method to optimize the in vitro evolution of proteins. Simulating evolution with a simple model that statistically describes the fitness landscape, we find that beneficial mutations tend to occur at amino acid positions that are tolerant to substitutions, in the limit of small libraries and low mutation rates. We transform this observation into a design strategy by applying mean-field theory to a structure-based computational model to calculate each residue's structural tolerance. Thermostabilizing and activity-increasing mutations accumulated during the experimental directed evolution of subtilisin E and T4 lysozyme are strongly directed to sites identified by using this computational approach. This method can be used to predict positions where mutations are likely to lead to improvement of specific protein properties.