Correlation between oncogenic mutations and parameter sensitivity of the apoptosis pathway model

Abstract

One of the major breakthroughs in oncogenesis research in recent years is the discovery that, in most patients, oncogenic mutations are concentrated in a few core biological functional pathways. This discovery indicates that oncogenic mechanisms are highly related to the dynamics of biologic regulatory networks, which govern the behaviour of functional pathways. Here, we propose that oncogenic mutations found in different biological functional pathways are closely related to parameter sensitivity of the corresponding networks. To test this hypothesis, we focus on the DNA damage-induced apoptotic pathway--the most important safeguard against oncogenesis. We first built the regulatory network that governs the apoptosis pathway, and then translated the network into dynamics equations. Using sensitivity analysis of the network parameters and comparing the results with cancer gene mutation spectra, we found that parameters that significantly affect the bifurcation point correspond to high-frequency oncogenic mutations. This result shows that the position of the bifurcation point is a better measure of the functionality of a biological network than gene expression levels of certain key proteins. It further demonstrates the suitability of applying systems-level analysis to biological networks as opposed to studying genes or proteins in isolation.

Figure 1. DNA damage-induced apoptotic pathway.

Blue lines indicate dimerization; black lines indicate transformation; green lines indicate transcription or activation. “mono-ub”, mono-ubiquitinated; “poly-ub”, poly-ubiquitinated; “mito-” mitochondrial and “/” refers to a complex. The production and degradation of most components are not drawn but are included in the ODEs. Protein families with similar functions are grouped into one node/variable denoted by their representative members (e.g. Bax stands for Bax and Bak). High and low levels of caspase-3 indicate apoptosis and survival, respectively.

Figure 2. The typical time evolution of the level of total nuclear p53 and caspase3.

Blue and black lines represent p53 concentrations at low- and high-level DNA damage, respectively; Green and red lines represent caspase-3 concentrations at low- and high-level DNA damage, respectively.

Figure 3. Bifurcation diagram for nuclear p53 and caspase3 for apoptosis.

(A) The bifurcation diagram for nuclear p53 using DNA damage as the control parameter. (B) The bifurcation diagram for caspase3 using DNA damage as the control parameter (black dots). (C) Comparison of bifurcation point with an increase in the parameter kf5. Black, without increase; green, 1.9-fold increase; red, 4.2-fold increase.

Figure 4. Parameter sensitivity analysis.

(A) The change of the saddle-node bifurcation point in response to a 20% increase or decrease in each parameter of the apoptosis pathway. (B) The change in the steady-state concentration of caspase3 in response to a 20% increase or decrease in each parameter of the apoptosis pathway.

Figure 5. The correspondence between parameter sensitivities and the cancer gene mutation spectrum.

(A) The correspondence between parameters linked to sensitivity of the bifurcation point (yellow bar) or caspase3 (blue bar) and high-frequency mutation genes. (B) The correspondence between insensitive parameters and low-frequency mutation genes. (C) The inconsistency between parameter sensitivity and gene mutation frequency. The numbers in the frame indicate the number of occurrences in the mutation spectrum of the gene that relates to the corresponding parameters.

Figure 6. Comparison of parameters linked to sensitivity of caspase3 levels and gene mutations.

The numbers in the frame indicate the number of occurrences in the mutation spectrum of the gene relating to the corresponding parameters. Magenta bar, change in the steady-state concentration of caspase3; Green bar, change in the critical point of bifurcation. gpre-casp, the basal generation rate of pre-caspase; dcaspase, the degradation rate of caspase3.

Figure 7. Extended DNA damage-induced apoptotic pathway.

Blue lines indicate dimerization; black lines indicate transformation; green lines indicate transcription or activation. “mono-ub”, mono-ubiquitinated; “poly-ub”, poly-ubiquitinated; “mito-”, mitochondrial; “/” stands for complex.

Figure 8. Parameter sensitivity analysis and its correspondence with mutations in the extended pathway.

(A) The change in the saddle-node bifurcation point in response to a 20% increase or decrease of each parameter of the extended apoptosis pathway. Yellow and green bars indicate parameters that cause a large or small percentage change in the bifurcation points, respectively. (B) The change in the steady-state concentration of caspase-3 in response to a 20% increase or decrease in each parameter of the extended apoptosis pathway. Magenta and blue bars indicate parameters that cause a large or small change in the steady-state concentration of caspase3, respectively. (C) The correspondence between parameters linked to sensitivity of the bifurcation point (yellow bar) or caspase3 (blue bar) and high-frequency mutation genes. (D) The correspondence between insensitive parameters and low-frequency mutation genes. (E) The inconsistency between parameter sensitivity and gene mutation frequency. The numbers in the frame indicate the number of occurrences in the mutation spectrum of the gene that relates to the corresponding parameters.