PhiSiCal

PhiSiCal models the joint distributions of protein backbone and sidechain dihedral angles in folded amino acids to provide continuous probabilistic representations for structural analysis.

Key Features:

• Mixture model framework: Represents joint distributions of mainchain and sidechain dihedral angles (〈ϕ,ψ,χ1,χ2,…〉) using a mixture of product von Mises probability distributions.
• Multi-dimensional torus mapping: Maps dihedral angles onto a multi-dimensional torus to provide a continuous angular representation distinct from discrete rotamer libraries like the Dunbrack rotamer library.
• Model efficiency and fidelity: Achieves performance comparable to the Dunbrack rotamer library while reducing model complexity by three orders of magnitude and providing approximately 20% greater compression of observed dihedral-angle data across experimental resolutions.
• Unsupervised learning and model selection: Estimates parameters in an unsupervised manner and uses information-theoretic criteria to determine optimal model complexity, avoiding underfitting and overfitting.
• Computational efficiency: Produces models that are computationally inexpensive to sample from.

Scientific Applications:

• Experimental structure refinement: Provides accurate dihedral-angle distributions to inform refinement of experimentally determined protein structures.
• De novo protein design: Supplies continuous dihedral-angle models to support design of novel proteins with specified structural properties.
• Protein structure prediction: Enhances probabilistic modeling of local backbone and sidechain conformations for structure-prediction tasks.

Methodology:

Fits mixtures of product von Mises distributions to dihedral-angle vectors 〈ϕ,ψ,χ1,χ2,…〉 mapped onto a multi-dimensional torus, with unsupervised parameter estimation and information-theoretic model complexity selection, producing models that are inexpensive to sample.