Large Language Model (LLM) development has become increasingly centralized, limiting participation to well-resourced organizations. This paper introduces MoECollab, a novel framework leveraging Mixture of Experts (MoE) architecture to enable distributed, collaborative LLM development. By decomposing monolithic models into specialized expert modules coordinated by a trainable gating network, our framework allows diverse contributors to participate regardless of computational resources. We provide a complete technical implementation with mathematical foundations for expert dynamics, gating mechanisms, and integration strategies. Experiments on multiple datasets demonstrate that our approach achieves accuracy improvements of 3-7% over baseline models while reducing computational requirements by 34%. Expert specialization yields significant domain-specific gains, with improvements from 51% to 88% F1 score in general classification and from 23% to 44% accuracy in news categorization. We formalize the routing entropy optimization problem and demonstrate how proper regularization techniques lead to 14% higher expert utilization rates. These results validate MoECollab as an effective approach for democratizing LLM development through architecturally-supported collaboration.