Abstract:
Proteins are found in all living organisms and constitute a large group of macromolecules
with many functions. Proteins achieve their operations by adopting distinct three-dimensional
structures encoded within the sequence of the constituent amino acids in one or more polypeptides.
New, more flexible distributions are proposed for the MCMC sampling method for predicting protein
3D structures by applying a Möbius transformation to the bivariate von Mises distribution. In
addition to this, sine-skewed versions of the proposed models are introduced to meet the increasing
demand for modelling asymmetric toroidal data. Interestingly, the marginals of the new models
lead to new multimodal circular distributions. We analysed three big datasets consisting of bivariate
information about protein domains to illustrate the efficiency and behaviour of the proposed models.
These newly proposed models outperformed mixtures of well-known models for modelling toroidal
data. A simulation study was carried out to find the best method for generating samples from the
proposed models. Our results shed new light on proposal distributions in the MCMC sampling
method for predicting the protein structure environment.
