Equations for Wg-like diffusion

$\displaystyle \dot{m}_{\mathrm{EM}}=$	$\displaystyle D^{m}_{\mathrm{EM}} \Delta {m}_{\mathrm{EM}}$	$\displaystyle - \delta^{m}_{\mathrm{EM}} {m}_{\mathrm{EM}} + \beta \frac{{m}_{\... ...rm{EM}} - {m}_{\mathrm{EM}} d_{\mathrm{mem}}}{d_{\mathrm{EM}}+d_{\mathrm{mem}}}$
$\displaystyle \dot{m}_{\mathrm{mem}}=$		$\displaystyle - \delta^{m}_{\mathrm{mem}} {m}_{\mathrm{mem}} - \beta \frac{{m}_... ...rm{EM}} - {m}_{\mathrm{EM}} d_{\mathrm{mem}}}{d_{\mathrm{EM}}+d_{\mathrm{mem}}}$
		$\displaystyle - \alpha_{f} r_\mathrm{free} m_{\mathrm{mem}} + \alpha_{r} r_\mathrm{bound}$
$\displaystyle \dot{d}_{\mathrm{EM}}=$		$\displaystyle - \delta^{d}_{\mathrm{EM}} {d}_{\mathrm{EM}} + \gamma n d_{\mathrm{mem}}$
$\displaystyle \dot{d}_{\mathrm{mem}}=$		$\displaystyle - \delta^{d}_\mathrm{{mem}} {d}_{\mathrm{mem}} - \gamma n d_{\mathrm{mem}} + \sigma_{d}$
$\displaystyle \dot{n}=$	$\displaystyle D_{n} \Delta {n}$	$\displaystyle - \delta_{n} n + \sigma_{n}$
$\displaystyle \dot{r}_\mathrm{free}=$		$\displaystyle - \delta^{r}_{\mathrm{free}} r_\mathrm{free} - \alpha_{f} r_\mathrm{free} m_{\mathrm{mem}} + \alpha_{r} r_\mathrm{bound}+ \sigma_{r}$
$\displaystyle \dot{r}_\mathrm{bound}=$		$\displaystyle - \delta^{r}_{\mathrm{bound}} r_\mathrm{bound} + \alpha_{f} r_\mathrm{free} m_{\mathrm{mem}} - \alpha_{r} r_\mathrm{bound}$
$\displaystyle \frac{\partial m_{\mathrm{EM}}}{\partial x} \left( x=0 \right) =$		$\displaystyle - \nu$
$\displaystyle {d}_{\mathrm{mem}}(t=0)=$		$\displaystyle \sigma_d/\delta^{d}_\mathrm{mem}$
$\displaystyle {r}_\mathrm{free}(t=0)=$		$\displaystyle \sigma_r/ \delta^{r}_\mathrm{free}$

Unspecified boundary conditions are zero-flux conditions, and unspecified initial conditions are 0.