  The Chemical Master Equation (CME) is well known to provide the highest
resolution models of a biochemical reaction network. Unfortunately, even
simulating the CME can be a challenging task. For this reason more simple
approximations to the CME have been proposed. In this work we focus on one such
model, the Linear Noise Approximation. Specifically, we consider implications
of a recently proposed LNA time-scale separation method. We show that the
reduced order LNA converges to the full order model in the mean square sense.
Using this as motivation we derive a network structure preserving reduction
algorithm based on structured projections. We present convex optimisation
algorithms that describe how such projections can be computed and we discuss
when structured solutions exits. We also show that for a certain class of
systems, structured projections can be found using basic linear algebra and no
optimisation is necessary. The algorithms are then applied to a linearised
stochastic LNA model of the yeast glycolysis pathway.
