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This study introduces dynamical matrices to unify cancer mutation statistics like site frequency spectra (SFS) and mutational burden distributions (MBD). The new framework reveals how cell division distributions (DD) impact tumor evolution and mutation accumulation.

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Area of Science:

  • Computational Biology and Bioinformatics
  • Cancer Genomics
  • Evolutionary Dynamics

Background:

  • Genetic mutations serve as indicators of cancer evolution and provide insights into tumor growth dynamics.
  • Tumor mutation accumulation is quantified by statistics like site frequency spectra (SFS), division distributions (DD), and mutational burden distributions (MBD).
  • While SFS and DD are well-studied, MBD is gaining attention with single-cell sequencing, yet an integrated understanding is lacking.

Purpose of the Study:

  • To develop novel mathematical tools for an integrated understanding of tumor evolutionary dynamics.
  • To introduce dynamical matrices for analyzing and unifying SFS, DD, and MBD.
  • To derive recurrence relations for the expectations of these distributions and explore their interconnections.

Main Methods:

  • Development and application of dynamical matrices to analyze tumor mutation statistics.
  • Derivation of recurrence relations for the expectations of SFS, DD, and MBD.
  • Mathematical modeling to approximate distributions in the presence of cell death.

Main Results:

  • The dynamical matrix framework successfully recovers known results for SFS and DD in pure-birth models.
  • A novel expression for MBD is derived, and approximations for SFS, DD, and MBD are obtained when cell death is included.
  • A direct link between SFS and single-cell MBD is demonstrated, and MBD is shown to be reproducible through DD.

Conclusions:

  • Dynamical matrices provide a unified approach to understanding diverse tumor mutation statistics.
  • The study highlights that single-cell MBD is primarily influenced by stochasticity in cell division distributions (DD), not mutation number stochasticity.
  • This framework offers enhanced insights into the ecological and evolutionary dynamics of tumors, crucial for cancer research.