Fate decisions mediated by crosstalk of autophagy and apoptosis in mammalian cells

Abstract

Autophagy is an important cell activity which is the process of formation of autophagosomes, docking with lysosomes and degradation. The intrinsic pathway of apoptosis involves mitochondrial outer membrane permeabilization (MOMP) and cytochrome c release followed by caspase activation. Many molecules, e.g., Ca²⁺ and mTOR, and different stresses such as endoplasmic reticulum (ER) stress and nutritional stress take part in these two processes. However, the mechanism of how they work together so as to determine cell fate decisions remains to be clarified. Here, we present a computational model for cell fate decisions based on intertwined dynamics with autophagy and apoptosis involving Ca²⁺, mTOR, and both ER stress and nutritional stress. In agreement with experimental observations, the model predicts that both Ca²⁺ and the stresses play critical roles in regulating the choice between autophagy and apoptosis in a combinatorial way. The model presented here might be a good candidate for providing the qualitative mechanism of cell fate decisions mediated by Ca²⁺, mTOR, and two kinds of stress.

Appendix

We briefly describe the mathematical models used to study the crosstalk between the autophagy and apoptosis modules. Such a coupled network can be translated into a set of differential equations that describe how each component in the network changes with time. The rate of change of each component is described by ordinary differential equation based on either the law of mass action or Michaelis-Menten kinetics [5, 7, 14, 15].

1.1 Apoptosis

$$ d\left[ Casp\right]/ dt=\left( kacp+ kacp"\ast \left( Baxt- Baxc\right)\right)\ast \frac{Casp t- Casp}{Jcp+ Casp t- Casp}-\left( kicp+ kcp\ast Bcl2t\right)\ast \frac{Casp}{Jcp+ Casp}, $$

(1)

$$ d\left[ Bcl2\right]/ dt= ksb2-\left( kdb2+ kdb{2}^{\prime}\ast stress+ kdb2"\ast Casp\right)\ast Bcl2, $$

(2)

$$ d\left[ Baxc\right]/ dt= kasbx\ast \left( Baxt- Baxc\right)\ast \left( Bcl2t- Baxc\right)-\left( kdsbx+ kdb2+ kdb{2}^{\prime}\ast stress+ kdb2"\ast Casp\right)\ast Baxc. $$

(3)

Table 1 The parameters of the apoptotic module

Table 2 The parameters of the autophagy module

1.2 Autophagy

$$ d\left[ Bcl2\right]/ dt= ksb2-\left( kdb2+ kdb{2}^{\prime}\ast stress\right)\ast Bcl2, $$

(4)

$$ d\left[ Ca\right]/ dt= kout\ast \left( Cat- Ca\right)- kin\ast Bcl2t\ast Ca, $$

(5)

$$ d\left[ mTOR\right]/ dt=(kamtor)\ast \left( mTORT- mTOR\right)-\left( kimtor+ kimto{r}^{\prime}\ast Ca+ kmtor\ast ns\right)\ast mTOR, $$

(6)

$$ d\left[ Beca\right]/ dt=- kasbc\ast \left( Bcl2t- Becac\right)\ast Beca+\left( kdsbc+ kdb2+ kdb{2}^{\prime}\ast stress\right)\ast Beca c- kiau\ast mTOR\ast Beca, $$

(7)

$$ Becac= Bect- Beca. $$

(8)

1.3 The coupled model

$$ d\left[ Casp\right]/ dt=\left( kacp+ kac{p}^{\prime}\ast Beci+ kac p"\ast \left( Baxt- Baxc\right)+ kac{p}^{\prime \prime \prime}\ast Ca+ kac s\ast ULK1\right)\ast \frac{Caspt- Casp}{Jcp+ Caspt- Casp} $$

(9)

$$ -\left( kicp+ kic{p}^{\prime}\ast Beca\right)\ast \frac{Casp}{Jcp+ Casp},d\left[ Bcl2\right]/ dt= ksb2-\left( kdb2+ kdb{2}^{\prime}\ast stress+ kdb2"\ast Casp\right)\ast Bcl2t, $$

(10)

$$ d\left[ Beca\right]/ dt=- kasbc\ast \left( Bcl2t- Becac- Becic\right)\ast Beca+\left( kdsbc+ kdb2+ kdb{2}^{\prime}\ast stress+ kdb2"\ast Ca\mathrm{s}p\right)\ast Beca c $$

(11)

$$ +\left( kabc+ kab{c}^{\prime}\ast ULK1\right)\ast Beci-\left( kibc+ kib{c}^{\prime}\ast Ca sp+ kiau\ast mTOR\right)\ast Beca,d\left[ Ca\right]/ dt= kout\ast \left( Cat- Ca\right)- kin\ast Bcl2t\ast Ca, $$

(12)

$$ d\left[ Baxc\right]/ dt= kasbx\ast \left( Baxt- Baxc\right)\ast \left( Bcl2t- Baxc\right)-\left( kdsbx+ kdb2+ kdb{2}^{\prime}\ast stress+ kdb2"\ast Casp\right)\ast Baxc, $$

(13)

$$ d\left[ ULK1\right]/ dt= kaulk\ast \left( ULK1t- ULK1\right)-\left( kiulk+ kiul{k}^{\prime}\ast mTOR\right)\ast ULK1, $$

(14)

$$ d\left[ mTOR\right]/ dt=(kamtor)\ast \left( mTORT- mTOR\right)-\left( kimtor+ kimto{r}^{\prime}\ast Ca+ kmtor\ast ns\right)\ast mTOR, $$

(15)

$$ d\left[ Beci\right]/ dt=- kasbc\ast \left( Bcl2t- Becac- Becic\right)\ast Beci+\left( kdsbc+ kdb2+ kdb{2}^{\prime}\ast stress+ kdb2"\ast Casp\right)\ast Beci c $$

(16)

$$ - kabc\ast Beci+\left( kibc+ kib{c}^{\prime}\ast Casp\right)\ast Beca,d\left[ Becac\right]/ dt= kasbc\ast \left( Bcl2t- Becac- Becic\right)\ast Beca-\left( kdsbc+ kdb2+ kdb{2}^{\prime}\ast stress+ kdb2"\ast Casp\right)\ast Beca c $$

(17)

$$ + kabc\ast Becic-\left( kibc+ kib{c}^{\prime}\ast \mathrm{C} asp\right)\ast Becac, Becic= Bect- Beca- Beci- Beca c. $$

(18)

Table 3 The parameters of the coupled model

Table 4 The definition of variables