In order to present our algorithm, we have defined the dynamical system corresponding to the log-likelihood function and the PSSM. The key contribution of the paper is the development of this nonlinear dynamical system which will enable us to realize the geometric and dynamic nature of the likelihood surface by allowing us to understand the topology and convergence behaviour of any given subspace on the surface. We construct the following gradient system in order to locate critical points of the objective function (4):