$M$ is moles per liter and $s$ is in seconds. The values of the chosen rate constants do not correspond to any particular experiment. However, the order of magnitude is similar to the parameters found in the literature of protein polymerisation. [@tuomas_review] The initial conditions are chosen to be small but non-zero, because of the necessity to seed the polymerisation process in the limit of $k_n^+ \rightarrow 0$.[]{data-label="fig2"}](Fig2.eps){width="4in"}

The resulting dynamical equations become, after employing the approximations and rearranging terms in Eqs \[eq6\] and \[eq7\], \[eq11\] &=& ( M(t)-(2 n\_c -1) P(t) ), for the polymer number concentration, and \[eq12\] &=& -M(t) (+ M(t)) + P(t) (- M(t)), for the polymerised mass, where we introduce new dynamical constants $\alpha \equiv \kmb -\kpb \mtot$, $\beta \equiv 2(\kmb-\kme)+\kpb\mtot+2\kpe \mtot$ and $\gamma \equiv \kpb+2\kpe$. It should be emphasized that we define the parameters $\alpha$, $\beta$ and $\gamma$ merely for notational simplicity and do not associate any physical meaning to them. Eqs. \[eq11\] and \[eq12\] are nonlinear in nature, hence, the first trivial analysis demands the linearisation of these equations. Researchers have analysed similar equations for variety of pathways and obtained $t^2$ or $t^3$ time dependence for the polymerised mass fraction. [@ferron_early] However, for 