The formulas according to with the fittings were done are in this page. Please cite the literature if used.

The characteristic equation for standard Zimm-Bragg model is [1]: \begin{equation}\label{characteristicequation} \lambda^{2}-(s+1)\lambda+s(1-\sigma)=0 \end{equation} The eigenvalues including solvent effects are: \begin{equation}\label{eigenvalues} \lambda_{1,2}=\frac{1}{2}\left[1+\widetilde{s}\pm \sqrt{(1-\widetilde{s})^{2}+4\sigma \widetilde{s}}\right] \end{equation} Here \(s\) was renormalized to \(\widetilde{s}\) in order to include solvent effects [2].
The partition function including chain size effects is [3]: \begin{equation} Z(\widetilde{s},\sigma,N)=\frac{1-\lambda_2}{\lambda_1-\lambda_2}\lambda_1^N+\frac{\lambda_1-1}{\lambda_1-\lambda_2}\lambda_2^N \end{equation} When the protein chain is long enough to not consider size effects the partition function of the system reads as [4]: \begin{equation} Z(\widetilde{s},\sigma,N)=\lambda_1^N \end{equation} The general degree of helicity is: \begin{equation} \label{Degreeofhelsolventfinal} \theta(\widetilde{s},\sigma, N)=\frac{\widetilde{s}+\sigma}{N}\frac{\partial\ln Z}{\partial \widetilde{s}} \end{equation} The helicity degree for long chains is: \begin{equation} \label{DegreeofHelZBsolventLongFinal} \theta(\sigma,\widetilde{s})=\frac{\widetilde{s}+\sigma}{1+\widetilde{s}+\sqrt{(1-\widetilde{s})^2+4\sigma\widetilde{s}}} \left(1+\frac{2\sigma-1+\widetilde{s}}{\sqrt{(1-\widetilde{s})^2+4\sigma\widetilde{s}}}\right). \end{equation} To pass to the Hamiltonian representation of Zimm-Bragg model in order to include solvent effects, we need to replace Zimm-Bragg model's \(\sigma\) and \(\widetilde{s}\) parameters: \begin{equation} \sigma=\frac{1}{Q} \end{equation} \begin{equation}\label{renorm-param-s} \widetilde{s}(t,t_0,h,h_{ps},Q,q)=\frac{1}{Q}\left[\left(e^{-\frac{h}{R(t-t_{0})}}+\frac{e^{\frac{h_{ps}-h}{R(t-t_0)}}-e^{-\frac{h}{R(t-t_{0})}}}{q}\right)^{-2}-1\right], \end{equation} The final expression for heat capacity is [5]: \begin{equation}\label{heat-capacity-with-solvent} C_V=-2Nh\frac{\partial\theta}{\partial T}+\frac{2Nh_{ps}^2 e^{h_{ps}/T}(q-1)}{T^2\left(q+e^{h_{ps}/T}-1\right)^2}(1-\theta)+\frac{2Nh_{ps} e^{h_{ps}/T}}{\left(q+e^{h_{ps}/T}-1\right)}\frac{\partial\theta}{\partial T}. \end{equation} The fitting parameters and their units are in the following table: \begin{array} {|c|c|}\hline t_0 & h & h_{ps} & Q \\ \hline K & J/mol & J/mol & 1 \\ \hline \end{array}