Mathematical Oncology: Using Mathematics to Enable Cancer Discoveries

Jackson, Trachette L.; Komarova, Natalia L.; Swanson, Kristin R.

doi:10.4169/amer.math.monthly.121.09.840

Cited by 26 publications

(16 citation statements)

References 67 publications

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“…Moreover, they could improve clinical care of patients by increasing the use of tools from applied mathematics and incorporating such approaches into biomedical models of disease (see e.g. the reviews [3][4][5][6][7][8][9][10][11][12]).…”

Section: Cancer and Mathematics: Some Factsmentioning

confidence: 99%

“…This paper does not intend to be a review of the accomplishments in the mathematical description of cancerrelated phenomena. There are excellent recent reviews and books on that [3][4][5][6][7][8][9][10][11][12]22,32]. Instead, our goal is more 'philosophical', as we will try to describe why mathematics has had so limited impact in oncology, what can be expected from applied mathematics in the war on cancer and how we can close the gap between mathematics and oncology.…”

Section: Cancer and Mathematics: Some Factsmentioning

confidence: 99%

See 1 more Smart Citation

Applied mathematics and nonlinear sciences in the war on cancer

Pérez-Garcı́a

Fitzpatrick

Pérez-Romasanta

et al. 2016

Applied Mathematics and Nonlinear Sciences

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Applied mathematics and nonlinear sciences have an enormous potential for application in cancer. Mathematical models can be used to raise novel hypotheses to test, develop optimized treatment schedules and personalize therapies. However. this potential is yet to be proven in real-world applications to specific cancer types. In this paper we discuss how we think mathematical knowledge may be better used to improve cancer patients’ outcome.

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Section: Cancer and Mathematics: Some Factsmentioning

confidence: 99%

Section: Cancer and Mathematics: Some Factsmentioning

confidence: 99%

Applied mathematics and nonlinear sciences in the war on cancer

Pérez-Garcı́a

Fitzpatrick

Pérez-Romasanta

et al. 2016

Applied Mathematics and Nonlinear Sciences

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“…where α 0 ðtÞ, α 1 ðtÞ ≠ 0 to be chosen in place of α 0 ðXÞ and α 1 ðXÞ, respectively, and G = GðβÞ satisfies Equation (1).…”

Section: Solution Of the Generalized Zakharov-kuznetsov Equationmentioning

confidence: 99%

“…The mathematical models are important as it impacts every aspects of our daily life (see [1]). The study of exact solutions of such mathematical models is the most exciting area of research investigation.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Mohanty

Dev

Sahoo³

et al. 2023

Advances in Mathematical Physics

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In this investigation, the exact solutions of variable coefficients of generalized Zakharov-Kuznetsov (ZK) equation and the Gardner equation are studied with the help of an extended generalized G ′ / G expansion method. The main objective of this study is to establish the closed-form solutions and dynamics of analytical solutions to the generalized ZK equation and the Gardner equation. The generalized ZK equation and the Gardner equation govern the behavior of nonlinear wave phenomena in the presence of magnetic field in plasma dynamics, turbulence, bottom topography, and quantum field theory. We construct innovative solutions to the models under consideration using various computing tools and a recently developed extended generalized G ′ / G expansion technique. The extended generalized G ′ / G expansion technique is a well-defined and simple technique which is based on the initial assumed solutions of the polynomial of G ′ / G . The derived solutions for both the equations are the hyperbolic, trigonometric, and rational functions. The obtained solutions have shock/kink waves and multisoliton, which depict the dynamical representations of the acquired solutions through the three-dimensional surface plots and the contour plots.

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“…Mathematical models in oncology can help to understand the mechanisms of oncogenesis, cancer progression, and optimal treatment [2]. Computational models have revealed extensive pairwise epistasis among germline variants and among gene knockdowns [3, 4], and approaches have been applied to identify sets of variants that are sufficient to cause cancer [5].…”

Section: Introductionmentioning

confidence: 99%

Pairwise and higher-order epistatic effects among somatic cancer mutations across oncogenesis

Alfaro-Murillo

Townsend

2022

Preprint

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Cancer occurs as a consequence of multiple somatic mutations that lead to uncontrolled cell growth. Mutual exclusivity and co-occurrence of mutations imply---but do not prove---that they can exert synergistic or antagonistic epistatic effects on oncogenesis. Knowledge of these interactions, and the consequent trajectories of mutation and selection that lead to cancer has been a longstanding goal within the cancer research community. Recent research has revealed mutation rates and scaled selection coefficients for specific recurrent variants across many cancer types. However, estimation of pairwise and higher-order effects---essential to estimation of the trajectory of likely cancer genotoypes---has been a challenge. Therefore, we have developed a continuous-time Markov chain model that enables the estimation of mutation origination and fixation (flux), dependent on somatic cancer genotype. Coupling the continuous-time Markov chain model with a deconvolution approach provides estimates of underlying rates of mutation and selection across the trajectory of oncogenesis. We demonstrate computation of fluxes and selection coefficients in a somatic evolutionary model for the four most frequently variant driver genes (TP53, LRP1B, KRAS and STK11) from 585 cases of lung adenocarcinoma. Our analysis reveals multiple antagonistic epistatic effects that reduce the possible routes of oncogenesis, and inform cancer research regarding viable trajectories of somatic evolution whose progression could be forestalled by precision medicine. Synergistic epistatic effects are also identified, most notably in the somatic genotype TP53+LRP1B for mutations in the KRAS gene, and in somatic genotypes containing KRAS or TP53 mutations for mutations in the STK11 gene. Large positive fluxes of KRAS variants were driven by large selection coefficients, whereas the flux toward LRP1B mutations was substantially aided by a large mutation rate for this gene. The approach enables inference of the most likely routes of site-specific variant evolution and estimation of the strength of selection operating on each step along the route, a key component of what we need to know to develop and implement personalized cancer therapies.

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Mathematical Oncology: Using Mathematics to Enable Cancer Discoveries

Cited by 26 publications

References 67 publications

Applied mathematics and nonlinear sciences in the war on cancer

Applied mathematics and nonlinear sciences in the war on cancer

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method

Pairwise and higher-order epistatic effects among somatic cancer mutations across oncogenesis

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Mathematical Oncology: Using Mathematics to Enable Cancer Discoveries

Cited by 26 publications

References 67 publications

Applied mathematics and nonlinear sciences in the war on cancer

Applied mathematics and nonlinear sciences in the war on cancer

Exact Solutions of the Generalized ZK and Gardner Equations by Extended GeneralizedG′/G-Expansion Method

Pairwise and higher-order epistatic effects among somatic cancer mutations across oncogenesis

Contact Info

Product

Resources

About

Exact Solutions of the Generalized ZK and Gardner Equations by Extended Generalized $(G^{'} / G)$ -Expansion Method