The authors have declared that no competing interests exist.
Conceived and designed the experiments: HWK AF SPNS. Performed the experiments: MC GN HWK. Analyzed the data: HWK AF SPNS. Contributed reagents/materials/analysis tools: MF SPNS. Wrote the paper: HWK AF SPNS. Provided lung tumor tissues for the PCR experiments: MF. Provided EGFR mutant lung cancer cell lines and Gefitinib: MG.
Lung cancer is the leading cause of cancerrelated deaths worldwide. Lack of early detection and limited options for targeted therapies are both contributing factors to the dismal statistics observed in lung cancer. Thus, advances in both of these areas are likely to lead to improved outcomes. MicroRNAs (miRs or miRNAs) represent a class of noncoding RNAs that have the capacity for gene regulation and may serve as both diagnostic and prognostic biomarkers in lung cancer. Abnormal expression patterns for several miRNAs have been identified in lung cancers. Specifically, let7 and miR9 are deregulated in both lung cancers and other solid malignancies. In this paper, we construct a mathematical model that integrates let7 and miR9 expression into a signaling pathway to generate an in silico model for the process of epithelial mesenchymal transition (EMT). Simulations of the model demonstrate that EGFR and Ras mutations in nonsmall cell lung cancers (NSCLC), which lead to the process of EMT, result in miR9 upregulation and let7 suppression, and this process is somewhat robust against random input into miR9 and more strongly robust against random input into let7. We elected to validate our model in vitro by testing the effects of EGFR inhibition on downstream MYC, miR9 and let7a expression. Interestingly, in an EGFR mutated lung cancer cell line, treatment with an EGFR inhibitor (Gefitinib) resulted in a concentration specific reduction in cMYC and miR9 expression while not changing let7a expression. Our mathematical model explains the signaling link among EGFR, MYC, and miR9, but not let7. However, very little is presently known about factors that regulate let7. It is quite possible that when such regulating factors become known and integrated into our model, they will further support our mathematical model.
Lung cancer is the leading cause of cancerrelated deaths worldwide. In the U.S. the number of new occurrences is approximately
microRNAs (miRs or miRNAs) represent a class of noncoding RNAs that have the capacity for gene regulation and may serve as diagnostic and prognostic biomarkers in lung cancer. Abnormal expression patterns for miRNAs have been identified in lung cancers. Specifically, let7 and miR9 are deregulated in both lung cancers and other solid malignancies. Takamizawa et al. (2004) and Nicoloso et al. (2009) demonstrated that let7 is downregulated in nonsmall cell lung cancers (NSCLC)
Given the fact that a single miRNA may regulate tens to hundreds of genes, understanding the importance of an individual miRNA in cancer biology can be challenging. This is further complicated by observations that the dysregulation of several miRNAs is often required to cause a given phenotype. To date, few models exist to elucidate the mechanisms by which multiple miRNAs contribute both individually and in tandem to promote tumor initiation and progression. Applying mathematical modeling to miRNA biology provides an opportunity to understand these complex relationships. In the current study, we have developed for the first time a mathematical model focusing on miRNAs (miR9 and let7) in the context of lung cancer as a model system; however, our model system could be applicable to miRNA biology in both malignant and benign diseases. For simplicity, we have integrated these miRNAs into a signaling pathway to generate an in silico model for the process of EMT. Herein, we include the EGFEGFR complex and associated downstream signaling culminating in matrix metalloproteinase (MMP) expression. Other components of our pathway include SOS, Ras, ERK, MYC,ECadherin, miR9, and let7.
We have simulated the model under several scenarios of gene mutations that may lead to lung cancer and determined, in each scenario, that miR9 was upregulated and let7 downregulated. We have also shown that the process leading to EMT is somewhat robust against random input into miR9 and more strongly robust against random input into let7.
A pathway from EGFEGFR complex to MMP, which includes miR9 and let7, is given in (A) and a simplified pathway is shown in (B).
MYC controls many fundamental cellular processes, and aberrant MYC expression is known to be associated with cancer. For example, Frenzel et al. (2010) observed that MYC is usually activated in many cancers
Investigators have also identified a link between MYC and miRNAs that also play a significant role in cancer. Rinaldi et al. (2007) showed that both MYC and the miRNA cluster miR1792 are amplified in human mantle cell lymphoma
Our proposed pathway is based on several lines of investigation. Similar to breast cancer, let7 is downregulated in NSCLC
Roberts and Der (2007) used an EGFRRasRafMEKERK pathway to explain that 10% of NSCLC arise from EGFR mutations and that 30% of NSCLC arise from mutations in Ras
We introduce a system of ordinary differential equations that describe a signaling pathway of EMT (represented by the level of MMP mRNA) induced by MYC through miR9 and let7 as shown in
Notation  Description 

EGFEGFR complex (constant) 

active SOS concentration 

active Ras concentration 

active ERK concentration 

MYC protein concentration 

miR9 concentration 

let7 concentration 

ECadherin concentration 

MMP mRNA concentration 
A large number of NSCLC cases arise from EGFR mutations
Simulations of the model equations were performed using Matlab. We used an ode solver, ode15 s, to solve a system of ordinary differential equations numerically. To solve a system of stochastic differential equations with random inputs in miR9 or let7 numerically, we developed a code using an Euler scheme. All initial values are taken to be those of healthy normal cells, namely,
If
When the negative feedback of ERK to SOS is weakened as a result of possible mutations in ERK, the parameter
In
It would be interesting to study the effect of a ‘background’ on miR9 and let7, namely, the genes with whom these miRNAs interact. Such interactions however, are not reported in the literature. We therefore model such interactions by a random input.
For (A–D)
For (A–D)
For (A–D)
For (A–D)
We conclude that mean MMP concentrations and standard deviations from the means are stable (robust) to small perturbations in miR9, i.e. when
Since we are focusing on miR9 upregulation and let7 downregulation as potential biomarkers for lung cancer, we wanted to determine how the quotient
Scatter plots are drawn for statistically significant parameters (pvalue
Name  Description  Value used  References 

concentration of EGFEGFR complex 


(constant)  

total concentration of SOS 



total concentration of Ras 



total concentration of ERK 



Steadystate concentration of active SOS 

estimated 

Steadystate concentration of active Ras 

estimated 

Steadystate concentration of active ERK 

estimated 

Steadystate concentration of MYC protein 



Steadystate concentration of miR9 

estimated 

Steadystate concentration of let7 



Steadystate concentration of ECadherin 



Steadystate concentration of MMP mRNA 



Saturation of inactive SOS on active SOS 



Saturation of active SOS on inactive SOS 



Saturation of inactive Ras on active Ras 



Control of let7 on Ras 

estimated 

Saturation of active Ras on inactive Ras 



Saturation of inactive ERK on active ERK 



Saturation of active ERK on inactive ERK 



Saturation of MYC on miR9 

estimated 

Control of MYC on let7 

estimated 

Control of MYC on ECadherin 

estimated 

Control of ECadherin on MMP mRNA 

estimated 

Catalytic production rate of active SOS 



Catalytic production rate of active Ras 



Catalytic production rate of active ERK 



Catalytic production rate of MYC 

estimated 

Catalytic production rate of miR9 

estimated 

Catalytic production rate of let7 

estimated 

Catalytic production rate of ECadherin 

estimated 

Catalytic production rate of MMP 

estimated 

Degradation rate of active SOS 



Degradation rate of active Ras 



Degradation rate of active ERK 



Degradation rate of MYC protein 



Degradation rate of miR9 



Degradation rate of let7 



Degradation rate of ECadherin 



Degradation rate of MMP mRNA 


Parameter  Range  PRCC 










































Among the
In an initial attempt to validate our mathematical model, we treated an EGFR mutant lung cancer cell line with several concentration of the clinically used EGFR inhibitor Gefitinib. We then assessed treated cells for miR9, let7a and cMYC expression by QRTPCR. As shown in
Statistical significance is defined as *
Lung cancer is the leading cause of cancerrelated deaths worldwide. The majority of cases are diagnosed at later stages thus limiting therapeutic options and contributing to poor outcome. As a result, investigators have sought to identify lung cancer specific biomarkers that may be utilized for early detection and to better understand the metastatic process. Such biomarkers may significantly improve prognosis and reduce mortality. In this paper, we have proposed a mathematical model that integrates the miRNAs let7 and miR9 into the process of EMT. miR9 has been shown to be significantly upregulated and let7 downregulated in NSCLC.
Based on the experimental literature, we introduced a signaling pathway from the EGFEGFR complex to MMP expression which involves SOS, Ras, ERK, MYC, the miRNAs miR9 and let7, ECadherin, and MMP. Recent studies have demonstrated elevated MMP9 in NSCLC
We correspondingly developed a mathematical model including a system of differential equations and used the model to compute the level of miR9 overexpression and let7 downexpression in the setting of EGFR mutations and Ras mutations. We showed that such mutations upregulate the level of miR9 and downregulate the level of let7. The
To the best of our knowledge, the present paper is the first one that develops a model for lung cancer and miRNA in terms of differential equations. The model is based on a signaling pathway that includes miR9 and let7. Simulations of the model demonstrate how mutations that are detected in NSCLC include upregulation of miR9 and downregulation of let7. The mathematical model could be further extended by including additional signaling pathways, specifically involving let7, that are associated with lung cancer. However, an important next step in this line of investigation is to determine how deregulation of miR9 and let7 may jointly contribute to lung cancer progression and may be used as reliable biomarkers. In order to address this challenge mathematically, additional clinical investigation will be required.
In this model, we assume that the EGFEGFR complex is at steady state and set it as a constant. Brown et al. (2004) modeled EGFR signaling with negative feedback of ERK to SOS
We denote by
Using the fact that the EGFEGFR complex activates SOS and that ERK represses active SOS, we replace
The parameters of
We denote by
According to Brown et al. (2004)
Since EGF and EGFR are located on the cell surface, we need to compute the cell surface area; we assume that the cells have spherical shape with radius
Converting the number of molecules of
Let
The initial concentration of SOS (all inactive) was
Let
For total Ras concentration, we convert the total number of Ras molecules in a cell obtained from
Let
We convert the total number of ERK molecules, consisting of active and inactive ERK in a cell to concentration, using the volume of the cytoplasm in a HeLa cell, and set
Following Rudolph et al. (1999), there are
Halflife of cMYC protein is
In steady state in
We compute a solution of
Since the miR9 copy number in the normal lung cell is very small
Based on the fact that miR9 expression in the NSCLC tissues is about
Halflife of let7 after TAM treatment is
Taking
Using the total ECadherin concentration in Chaplain (2011)
Taking
According to Safranek et al. (2009), the number of MMP9 mRNA in human lung tissue is
Halflife of MMP9 mRNA is
For our experiments shown in
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