$\mu$ and $\lambda$, but are strictly bounded below by $\sim \exp(-\alpha)$. In contrast, the simplified free energy expression (13) has solutions with non-zero and strictly zero protein concentrations, because of the $\alpha \rightarrow \infty$ limit. It therefore allows for straightforward classification of the bulk protein ordering into a phase with finite protein concentration and a phase with no proteins at all. We need a similar criterion for the case of the full free energy expression (7) with $\alpha$ finite, allowing us to distinguish in a categorical manner the presence of proteins from the absence of proteins, even in the inevitable presence of an exponentially small (in $\alpha$) protein concentration. We adopt the simple criterion which consists of calculating the Laplacian of the protein concentration in the parameter space $(\mu, 
\lambda)$, $$\frac{\partial^2 \phi_i}{\partial \mu^2}+
\frac{\partial^2 \phi_i}{\partial \lambda^2}$$ in the two coexisting phases $\phi_1$ and $\phi_2$. This scalar quantity shows a pronounced line of maxima in the parameter space, separating two phases with small and large concentrations of proteins. The position of this ridge is determined numerically and defined as the boundary between the two phases rich and devoid of proteins, respectively, for each solution $\phi_i$. The result of this operation leads 