A mechanistic mathematical model of initiation and malignant transformation in sporadic vestibular schwannoma

Vestibular schwannoma (VS), a relatively rare, benign tumor of the eighth cranial nerve, is often associated with *NF2* gene alterations. Existing mathematical models of schwannoma incidence haven't accounted for specific gene alterations or distinguished between nonsense mutations and LOH. This study addresses these limitations by developing a mechanistic model that links parameters to specific genes and biological processes in Schwann cells. The model aims to describe the incidence of sporadic VS, derive new estimates for biological parameters from existing experimental data, estimate the lifetime risk of malignant transformation, and model the excess risk of malignancy following radiation. Understanding these processes is crucial due to the rarity of malignant schwannoma and the lack of clarity regarding its pathogenesis and the relationships between genomic features, clinical course, and epidemiology. The rarity of malignant transformation, coupled with the availability of detailed tumour growth measurements and histories in cases of malignant transformation, provides a unique opportunity to build a mechanistic model. A previous mechanistic model connected parameters to cell populations and biological processes, determining several key parameters directly from gene sequences. This work extends that approach, focusing on sporadic VS and somatic *NF2* variants, aiming to improve parameter estimation and offer insights into malignancy risk and radiation effects.

The majority of sporadic VS cases involve pathogenic variants in the *NF2* gene and at least one additional genetic hit. Age-related risk is well-described by a three-hit multistage model. While VS is almost always benign, malignant transformation occurs in approximately 0.2% of cases. A study on familial neurofibromatosis type II patients suggested an association between radiotherapy and malignant transformation, but a quantitative estimate of the excess risk was impossible due to the small sample size. The pathogenesis of malignant schwannoma remains unclear, highlighting the need for a model connecting genomic data to clinical observables. Existing models have limitations, such as not accounting for specific genes or different types of mutations. This research aims to overcome these limitations by developing a mechanistic model that links parameters directly to biological processes and genetic alterations, using existing experimental data to improve parameter estimates.

The study uses a three-hit model to describe sporadic VS incidence, focusing on somatic *NF2* loss-of-function mutations. The model considers three distinct sets of mutations that could lead to VS: 1) single-copy inactivation of *NF2* → LOH on 22q → gain of function in GFX (a hypothetical oncogene); 2) single-copy inactivation of *NF2* → mutation on the second *NF2* allele → gain of function in GFX; 3) single-copy inactivation of *NF2* → LOH on 22q → *SMARCB1* single-copy inactivation. The model explicitly accounts for the different orders in which these hits can occur, represented as pathways through a network. A mean-field approximation is used to track the mean subpopulation in each state. The model involves parameters such as the base population of progenitor cells, mutation rates for each gene (*NF2*, *SMARCB1*, GFX), the rate of LOH on chromosome 22, and selective advantages. The mutation rate for each gene is determined by the error rate per replication per base pair, the cell replication rate, and the number of sensitive locations on that gene. Parameter estimation is achieved by combining incidence data with experimental measurements of the frequencies of LOH on 22q and pathogenic *SMARCB1* variants. The model is then extended to include malignant transformation by considering additional mutations in a hypothetical tumor suppressor gene, TSX, within the growing tumor. The probability of malignancy is modeled as a function of tumor volume. Finally, a model for the excess risk of malignancy following radiation is developed, considering the induction and misrepair of double-strand breaks (DSBs) and incorporating cell survival rates following irradiation. Both unfractionated and fractionated radiotherapy scenarios are analyzed, considering cell-cycle times and the possibility of tumor cell recovery between fractions.

The model successfully describes the incidence of sporadic VS, providing new estimates for the base-pair mutation rate (μ = 4.48 × 10⁻¹⁰) and the rate of LOH (2.03 × 10⁻⁵/yr) in Schwann cells. The number of sensitive sites on the hypothetical oncogene GFX was estimated to be 2002, suggesting potential genetic diversity. The model predicts a linear relationship between the risk of spontaneous malignant transformation and tumor volume. The estimated number of sensitive sites on the hypothetical tumor suppressor TSX (1245) suggests potential genetic diversity or involvement of multiple tumor suppressors. The model predicts that radiotherapy should have a negligible excess risk of malignancy for sporadic VS at therapeutic doses, except possibly for rapidly growing tumors. A study of at least 15 malignant schwannoma samples is suggested to investigate LOH patterns and further constrain the model. The model suggests that poorly administered hyperfractionated therapy (with fractions spaced too far apart) might show a significantly increased risk of malignancy compared to single-dose treatments.

The mechanistic model successfully explains the observed incidence of sporadic VS and provides new insights into the genetic mechanisms underlying both tumor initiation and malignant transformation. The high estimate for the number of sensitive sites on both GFX and TSX suggests potential genetic heterogeneity or the involvement of multiple genes. The negligible excess risk of malignancy associated with radiotherapy at therapeutic doses is reassuring, supporting current clinical practice. However, careful consideration should be given to rapidly growing tumors. The model's limitations, such as assumptions about the homogeneity of the dose and the nature of cell survival curves, highlight areas for future investigation. Further research focusing on the identification of the genes responsible for both initiation and malignant transformation is crucial.

This study provides a comprehensive mechanistic mathematical model of sporadic vestibular schwannoma initiation and malignant transformation, offering new parameter estimates and insights into the impact of radiotherapy. Future work should focus on refining the model by incorporating additional genes (e.g., LZTR1), investigating the genetic diversity of both initiation and malignant transformation, and conducting experimental studies to validate the model's predictions. The development of more accurate cell survival curves and the investigation of the impact of inhomogeneous dose distributions on multifocal tumor clusters would also enhance the model’s capabilities.

The model's accuracy depends on the accuracy of the input parameters, some of which were estimated from relatively small sample sizes, leading to uncertainties. The model simplifies the complex biological processes involved in tumorigenesis and assumes that only one gene is responsible for malignancy, which might be an oversimplification. The model also makes certain assumptions about the dynamics of cell division and DNA repair that may not fully reflect the complexity of these processes. The absence of information on transition/transversion frequencies in schwannoma could affect the accuracy of mutation rate estimations. Finally, the study does not consider familial NF2 cases.