Intracellular regulation of cell signaling cascades: how location makes a difference

Abstract

Organelles such as endosomes and the Golgi apparatus play a critical role in regulating signal transmission to the nucleus. Recent experiments have shown that appropriate positioning of these organelles within the intracellular space is critical for effective signal regulation. To understand the mechanism behind this observation, we consider a reaction-diffusion model of an intracellular signaling cascade and investigate the effect on the signaling of intracellular regulation in the form of a small release of phosphorylated signaling protein, kinase, and/or phosphatase. Variational analysis is applied to characterize the most effective regions for the localization of this intracellular regulation. The results demonstrate that signals reaching the nucleus are most effectively regulated by localizing the release of phosphorylated substrate protein and kinase near the nucleus. Phosphatase release, on the other hand, is nearly equally effective throughout the intracellular space. The effectiveness of the intracellular regulation is affected strongly by the characteristics of signal propagation through the cascade. For signals that are amplified as they propagate through the cascade, reactions in the upstream levels of the cascade exhibit much larger sensitivities to regulation by release of phosphorylated substrate protein and kinase than downstream reactions. On the other hand, for signals that decay through the cascade, downstream reactions exhibit larger sensitivity than upstream reactions. For regulation by phosphatase release, all reactions within the cascade show large sensitivity for amplified signals but lose this sensitivity for decaying signals. We use the analysis to develop a simple model of endosome-mediated regulation of cell signaling. The results demonstrate that signal regulation by the modeled endosome is most effective when the endosome is positioned in the vicinity of the nucleus. The present findings may explain at least in part why endosomes in many cell types localize near the nucleus.

Appendix: Normalization of the model

The reaction-diffusion equations for the signaling cascade in Fig. 1 are given as follows (Munoz-Garcia et al. 2009):

$$\begin{aligned} \begin{aligned} {\partial C_1 \over \partial t}&= D\frac{\partial ^2 C_1}{\partial x^2}-V^{phos}_1+\epsilon \delta P_{1}(x,t),\\ {\partial C_n \over \partial t}&= D\frac{\partial ^2 c_n}{\partial x^2}+V^{kin}_n-V^{phos}_n+\epsilon \delta P_{n}(x,t)\quad \mathrm{for}\,\, n=2,3,\ldots ,N \end{aligned} \end{aligned}$$

(28a)

with boundary conditions,

$$\begin{aligned} \begin{aligned} D\frac{\partial C_1}{\partial x}\Big |_{x=0}&=-V^{kin}_1, \frac{\partial C_1}{\partial x}\Big |_{x=L}=0,\\ \frac{\partial C_n}{\partial x}\Big |_{x=0}&= \frac{\partial C_n}{\partial x}\Big |_{x=L}=0\quad \mathrm{for}\,\, n=2,3,\ldots ,N, \end{aligned} \end{aligned}$$

(28b)

where the reaction terms are given as

$$\begin{aligned} V_1^{kin}&= V_{max,1}^{kin}\frac{C_1^{tot}-C_1}{K_1^{kin}+ {C_1^{tot}-C_1}}\Big |_{x=0}, \nonumber \\ V_n^{kin}&= k_{cat,n}^{kin}\frac{C_{n-1} (C_n^{tot}-C_n)}{K_n^{kin}+C_n^{tot}-C_n}\quad \mathrm{for}\,\, n=2,3,\ldots ,N, \\ V_n^{phos}&= V_{max,n}^{phos}\frac{C_n}{K_n^{phos}+C_n}\quad \mathrm{for}\,\, n=1,2,\ldots ,N.\nonumber \end{aligned}$$

(29)

Here, $k_{cat,n}^{kin}$ is the catalytic constant (turnover number), $V_{max,1}^{kin}$ the maximal rate for the kinase at the cell membrane, $V_{max,n}^{phos}$ the maximal rate for the phosphatase at level n of the cascade, $K_n^{kin}$ the Michaelis constant for the kinase at level n, and $K_n^{phos}$ the Michaelis constant for the phosphatase at level n. Normalization of Eq. (1) by $C_{tot}$ leads to the normalized reaction terms as in Eq. (4), where $v_n^{kin}=V_1^{kin}/C_{tot}$ and $v_n^{phos}=V_n^{phos}/C_{tot}$ for all $n$. The apparent first-order rate constants in Eq. (4) are readily obtained as:

$$\begin{aligned} \begin{aligned} k_{1}^{a}&=\frac{V_{max,1}^{kin}}{K_1^{kin}},~k_n^a= \frac{k_{cat,n}^{kin}C_{n-1}^{tot}}{K_{n}^{kin}}\quad \mathrm{for}\,\, n=2,3,\ldots ,N, \\ k_n^i&=\frac{V_{max,n}^{phos}}{K_{n}^{phos}}\quad \mathrm{for}\,\, n=1,2,3,\ldots ,N. \end{aligned} \end{aligned}$$

(30)

Similarly, the normalized (dimensionless) Michaelis constants in Eq. (4) are given as:

$$\begin{aligned} m_n^a=\frac{K_n^{kin}}{C_n^{tot}},~m_n^i=\frac{K_n^{phos}}{C_n^{tot}}\quad \mathrm{for}\quad n=1,2,3,\ldots ,N. \end{aligned}$$

(31)