The (re)construction of biological systems is of fundamental importance to the emerging field of systems biology. Because of the complexity of these systems, computational systems biology strongly relies on the principles of mathematical modeling as an essential tool for determining the behavior of numerous and simultaneous time-dependent and space-dependent processes. In general, the empirical models are parametric and the unknown model parameters have to be estimated using experimental data, a task known as parameter estimation. Parameter estimation is essentially an optimization task, that in the highly nonlinear and constrained dynamics of biological models can turn into a hard problem for the traditional local search optimization methods. Motivated by this challenge, the paper addresses the parameter estimation in a nonlinear dynamic model (described by ordinary differential equations) with 18 parameters, which models a key cell regulatory system that switches between cargo transport and maturation in early, respectively late endosomes in the endocytosis pathway. We treated the problem using two bio-inspired metaheuristics for global optimization and one direct local search method for maximum-likelihood optimization. To better asses the performance of the applied methods, the parameters were estimated using pseudo-experimental (simulated) data.