The present work focuses on the dynamical aspects of cross-reactivity between myelin based protein (MBP) self-peptide and two microbial peptides (UL15, PMM) for Hy.1B11 T-cell receptor (TCR). This same TCR was isolated from a patient suffering from multiple sclerosis (MS). The study aims at highlighting the chemical interactions underlying recognition mechanisms between TCR and the peptides presented by Major Histocompatibility Complex (MHC) proteins, which form a crucial component in adaptive immune response against foreign antigens. Since the ability of a TCR to recognize different peptide antigens presented by MHC depends on its cross-reactivity, we used molecular dynamics methods to obtain atomistic detail on TCR-peptide-MHC complexes. Our results show how the dynamical basis of Hy.1B11 TCR's cross-reactivity is rooted in a similar bridging interaction pattern across the TCR-peptide-MHC interface. Our simulations confirm the importance of TCR CDR3α E98 residue interaction with MHC and a predominant role of P6 peptide residue in MHC binding affinity. Altogether, our study provides energetic and dynamical insights into factors governing peptide recognition by the cross-reactive Hy.1B11 TCR, found in MS patient.