Team:SCUT-China B/Apoptosis
Mitochondria-dependent apoptosis:
We apply the mitochondria-dependent apoptosis model previously published by E.Z.Bagci. It shows that the state of cell is estimated by the caspase-3 steady-state concentration whose concentration of the order of nanomolars can be considered to lead to apoptosis, whereas cell survival refers to vanishingly small concentration. The mitochondria-dependent apoptosis model built by standard mass action laws, we take the factors of E.Z.Bagci previous model, however, we focus on the caspase-3 activation relative to transcription rate of bax and bcl-2.
Cyt C Release from Mitochondria to Cytoplasm
tBid translocates to the mitochondria, and forms a complex with Bax to initiate Bax oligomerization and channel (Bax2) formation. Cyt c is then released through the channel.
Inhibition of Bax by Bcl-2
Bcl-2 and Bax can form heterodimer, thus Bax is inhibited.
Apoptosis Complex Formation
The apoptosome complex (apop) is a multimeric assembly composed of seven Apaf-1 seven cyt c molecules.
Caspase-9 Activation
Proaspase-9(pro9) is bound to the apoptosome complex, forming the complex apop-pro9 and then apop-(pro9)2.
And the cleavage of bound procaspases yields the holoenzyme apop-(casp9)2, which finally leads to caspase-9.
Activation of Caspase-3 by Caspase-9
The complexation of caspase-9 with the pro3, and the succeeding cleavage of pro3 to yield the active caspase-3 molecule.
Results
Figure 1:Bax steady state concentration relative to its transcription rate.
Figure 2:Bcl-2 steady state concentration relative to its transcription rate.
Sensitivity Analysis
We analyze the activation of caspase-3 while increasing the transcription rate of bax from 2 times to 20 times, and also the activation of caspase-3 while reducing the transcription of bcl-2 form 2 times to 20 times.
Figure 3:Caspase-3 activation relative to the upregulation of bax transcription rate.
Figure 4:Caspase-3activation relative to the downregulation of bcl-2 transcription rate
Experienced formula of apoptosis index:
The activation of caspase-3 causes series of biological response, finally lead to apoptosis. In our project, we use Annexin/PI double stainning to detect the apoptosis index, and this method mainly bases on the membrane permeability.
The apoptosis index we detected relative to the caspase-3 concentration, but it is hard to consider the pilot process. Therefore, we create an experience formula using radial basis function neural network to predict the apoptosis index from the activation of caspase-3.
The Radial Basis Function neural network:
1.Introduction
By simulating the biological neural topology to solve problems,the neural network was created by mathematician Walter H Pits and biologist Warren S McCulloch firstly. The Radial Basis Function neural network has many advantages i.e. the solid mathematical background.The Radial Basis Function neural network can fit any nonlinearity function accurately,which can deal with the work of analyzing the regularity of the system and has a good generalization ability.Its fast learning convergence rate is often praised.And It has been successfully applied to many field i.e. pattern recognition and system modeling so far.
2.Problem
Now we wish to know the accurate formula about the apoptotic rate and caspase-3 concentration.But it’s really hard to analyze the complex system of caspase-3 concentration as input and the apoptotic rate as output.What’s more,the experiments are of great cost for us.Fortunately,we got the experiments data in the same circumstances we studied from reference.Naturally,we use the method of the RBFnn to solve this problem.
3.Solution
Let
be the caspase-3 concentration and let
be the apoptotic rate.We need find a solution
to the optimization problem
whereis the sample number of the data.
As RBFnn,what needs to be calculated is
and the fomula is as follows.
where
and
is the number of Neurons which shows in the picture.
By training constantly with gradient descent method, the optimization target would be better until the result is satisfactory for us.
Figure A:Apoptosis index relative to the caspase-3 activation
