  Monte Carlo simulations are performed to study structure and dynamics of a protein CoVE in random media generated by a random distribution of barriers at concentration c with a coarse-grained model in its native (low temperature) and denatured (high temperature) phase. The stochastic dynamics of the protein is diffusive in denature phase at low c, it slows down on increasing c and stops moving beyond a threshold (cth = 0.10). In native phase, the protein moves extremely slow at low c but speeds up on further increasing c in a characteristic range (c = 0.10 - 0.20) before getting trapped at high c (cth = 0.30). The radius of gyration (Rg) of CoVE shows different non-monotonic dependence on c (increase followed by decay) in native and denature phase with a higher and sharper rate of change in farmer. Effective dimension (D) of CoVE is estimated from the scaling of structure factor: in denatured phase, D = 2 (a random coil conformation) at low c (= 0.01 - 0.10) with appearance of some globularization i.e. D ? 2.3, 2.5 at higher c (= 0.2, 0.3). Increasing c seems to reduce the globularity (D = 3) of CoVE in native phase. 
A Monte Carlo simulation of a protein (CoVE) in a matrix of random   barriers