The many faces of mathematical modelling in oncology

A Structural Characterisation of the Mitogen-Activated Protein Kinase Network in Cancer

Gene regulatory networks represent collections of regulators that interact with each other and with other molecules to govern gene expression. Biological signalling networks model how signals are transmitted and how activities are coordinated in the cell. The study of the structure of such networks in complex diseases such as cancer can provide insights into how they function, and consequently, suggest suitable treatment approaches. Here, we explored such topological characteristics in the example of a mitogen-activated protein kinase (MAPK) signalling network derived from published studies in cancer. We employed well-established techniques to conduct network analyses, and collected information on gene function as obtained from large-scale public databases. This allowed us to map topological and functional relationships, and build hypotheses on this network’s functional consequences. In particular, we find that the topology of this MAPK network is highly non-random, modular and robust. Moreover, analysis of the network’s structure indicates the presence of organisational features of cancer hallmarks, expressed in an asymmetrical manner across communities of the network. Finally, our results indicate that the organisation of this network renders it problematic to use treatment approaches that focus on a single target. Our analysis suggests that multi-target attacks in a well-orchestrated manner are required to alter how the network functions. Overall, we propose that complex network analyses combined with pharmacological insights will help inform on future treatment strategies, exploiting structural vulnerabilities of signalling and regulatory networks in cancer.

Mathematical model of a personalized neoantigen cancer vaccine and the human immune system

Cancer vaccines are an important component of the cancer immunotherapy toolkit enhancing immune response to malignant cells by activating CD4⁺ and CD8⁺ T cells. Multiple successful clinical applications of cancer vaccines have shown good safety and efficacy. Despite the notable progress, significant challenges remain in obtaining consistent immune responses across heterogeneous patient populations, as well as various cancers. We present a mechanistic mathematical model describing key interactions of a personalized neoantigen cancer vaccine with an individual patient’s immune system. Specifically, the model considers the vaccine concentration of tumor-specific antigen peptides and adjuvant, the patient’s major histocompatibility complexes I and II copy numbers, tumor size, T cells, and antigen presenting cells. We parametrized the model using patient-specific data from a clinical study in which individualized cancer vaccines were used to treat six melanoma patients. Model simulations predicted both immune responses, represented by T cell counts, to the vaccine as well as clinical outcome (determined as change of tumor size). This model, although complex, can be used to describe, simulate, and predict the behavior of the human immune system to a personalized cancer vaccine.

Personalized cancer vaccines have gained attention in recent years due to the advances in sequencing techniques that have facilitated the identification of multiple tumor-specific mutations. This type of individualized immunotherapy has the potential to be specific, efficacious, and safe since it induces an immune response to protein targets not found on normal cells. This work focuses on understanding and analyzing important mechanisms involved in the activity of personalized cancer vaccines using a mechanistic mathematical model. This model describes the interactions of a personalized neoantigen peptide cancer vaccine, the human immune system and tumor cells operating at the molecular and cellular level. The molecular level captures the processing and presentation of neoantigens by dendritic cells to the T cells using cell surface proteins. The cellular level describes the differentiation of dendritic cells due to peptides and adjuvant concentrations in the vaccine, activation, and proliferation of T cells in response to treatment, and tumor growth. The model captures immune response behavior to a vaccine associated with patient-specific factors (e.g., different initial tumor burdens). This model enables the simulation of a complex biological system, the human immune system, by performing in silico experiments that may become the input for further analysis such as the identification of key parameters or mechanisms and/or interpretation of data.