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.

Peptide design by artificial neural networks and computer-based evolutionary search

A technique for systematic peptide variation by a combination of rational and evolutionary approaches is presented. The design scheme consists of five consecutive steps: (i) identification of a “seed peptide” with a desired activity, (ii) generation of variants selected from a physicochemical space around the seed peptide, (iii) synthesis and testing of this biased library, (iv) modeling of a quantitative sequence-activity relationship by an artificial neural network, and (v) de novo design by a computer-based evolutionary search in sequence space using the trained neural network as the fitness function. This strategy was successfully applied to the identification of novel peptides that fully prevent the positive chronotropic effect of anti-β1-adrenoreceptor autoantibodies from the serum of patients with dilated cardiomyopathy. The seed peptide, comprising 10 residues, was derived by epitope mapping from an extracellular loop of human β1-adrenoreceptor. A set of 90 peptides was synthesized and tested to provide training data for neural network development. De novo design revealed peptides with desired activities that do not match the seed peptide sequence. These results demonstrate that computer-based evolutionary searches can generate novel peptides with substantial biological activity.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Visual attention to surfaces in three-dimensional space.

Although attention plays a significant role in vision, its spatial deployment and spread in the third dimension is not well understood. In visual search experiments we show that we cannot easily focus attention across isodepth loci unless they are part of a well-formed surface with locally coplanar elements. Yet we can easily spread our attention selectively across well-formed surfaces that span an extreme range of stereoscopic depths. In cueing experiments, we show that this spread of attention is, in part, obligatory. Attentional selectivity is reduced when targets and distractors are coplanar with or rest on a common receding stereoscopic plane. We conclude that attention cannot be efficiently allocated to arbitrary depths and extents in space but is linked to and spreads automatically across perceived surfaces.