We apply the formulation of a
stochastic mode reduction method developed in a recent paper of Majda, Timofeyev, and Vanden-Eijnden [Comm. Pure Appl.
Math., 54 (2001), pp. 891--974] (MTV) to obtain simplified equations for
the dynamics of structures immersed in a thermally fluctuating fluid at low
Reynolds (or Kubo) number, as simulated by a recent extension of the immersed
boundary (IB) method by Kramer and Peskin [Proceedings
of the Second MIT Conference on Computational Fluid and Solid Mechanics,
Elsevier Science, Oxford, UK, 2003, pp. 1755--1758]. The effective dynamics of
the immersed structures are not obvious in the primitive equations, which
involve both fluid and structure dynamics, but the procedure of MTV allows the
rigorous derivation of a reduced stochastic system for the immersed structures
alone. We find, in the limit of small Reynolds (or Kubo) number, that the Lagrangian particle constituents of the immersed structures
undergo a drift-diffusive motion with several physically correct features,
including the coupling between dynamics of different particles. The MTV
procedure is also applied to the spatially discretized
form of the IB equations with thermal fluctuations to assist in the design and
assessment of numerical algorithms