  In extending the conventional dynamic models, we consider a simple model to
account for the environment fluctuations of particle atoms in a protein system
and derive the elastic incoherent structure factor (EISF) and the incoherent
scattering correlation function C(Q,t) for both the jump dynamics between sites
with fluctuating site interspacing and for the diffusion inside a fluctuating
sphere. We find that the EISF of the system (or the normalized elastic
intensity) is equal to that in the absence of fluctuations averaged over the
distribution of site interspacing or sphere radius a. The scattering
correlation function is $C(Q,t)=\sum_{n}<{\rm e}^{-\lambda_n(a) t}> \psi(t)$,
where the average is taken over the Q-dependent effective distribution of
relaxation rates \lambda_n(a) and \psi(t) is the correlation function of the
length a. When \psi(t)=1, the relaxation of C(Q,t) is exponential for the jump
dynamics between sites (since \lambda_n(a) is independent of a) while it is
nonexponential for diffusion inside a sphere.
