The system-size expans ion of the master equation\, first developed by va n Kampen\, is a well known approximation technique for deterministically monostable systems. Its use has been mostly restricted to the lowest order te rms of this expansion which lead to the determinis tic rate equations and the linear-noise approximat ion (LNA). I will here describe recent development s concerning the system-size expansion\, including (i) its use to obtain a general non-Gaussian expr ession for the probability distribution solution o f the chemical master equation\; (ii) clarificatio n of the meaning of higher-order terms beyond the LNA and their use in stochastic models of intracel lular biochemistry\; (iii) the convergence of the expansion\, at a fixed system-size\, as one consid ers an increasing number of terms\; (iv) extension of the expansion to describe gene-regulatory syst ems which exhibit noise-induced multimodality\; (v ) the conditions under which the LNA is exact up t o second-order moments\; (v i) the relationship be tween the system-size expansion\, the chemical Fok ker-Planck equation and moment-closure approximati ons.

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