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Cancer Dynamics, 2015

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In this theme we will address a number of biological and mathematical issues related to modeling of evolution of cancer, organized in three core lectures, which will cover the fundamental issues of cell proliferation and mutation dynamics, molecular events affecting specific pathways in cells and the population genetics effects (see the abstracts further on)

This section of the summer school will include a number of instructor-suggested group projects, in which students will apply various numerical techniques to formulate, identify and solve stochastic models of cancer evolution. Students will then apply these tools to model experimental and clinical data. This section of the summer school is organized by Marek Kimmel. Please address all questions about this section of the summer school to its organizer.

Core Instructors

  • Marek Kimmel, Rice, kimmel@rice.edu (Course Leader)
  • Jaroslaw Smieja, Silesian University of Technology, jaroslaw.smieja@polsl.pl

Course-specific Instructors

  • David E. Axelrod, Rutgers University, axelrod@dls.rutgers.edu
  • Seth Corey, Northwestern U., coreylab@yahoo.com
  • Rosemary Braun, Northwestern U., rbraun@northwestern.edu

Core lectures

Modeling mutations and genomic transformations in cancer

Marek Kimmel, Rice University, kimmel@rice.edu

Contents (tentative, to be updated)

  • Lecture 1 (Chalk talk): Introduction. Elements of the theory of Markov Chains. Stochastic models of population genetics and population dynamics: Moran model and branching process models. Fixation of a mutant in Moran model. [Additional advanced topics and some mathematical derivations at 1 or 2 evening sessions for those interested.]
  • Lecture 2: (Chalk talk) Branching process model of emergence of drug resistance. Modeling driver mutations in secondary myelodysplastic syndrome using Moran model and branching process (exploration of mathematical properties of the model in search of a setup for the biological process.
  • Lecture 3: (Breakout session). Literature examples of stochastic models of proliferation and mutation in cancer including spatial effects.

References (idiosyncratic and ad hoc)

  • Kimmel, Marek, and David E. Axelrod. "Branching Processes in Biology” (2nd ed. updated and extended). Springer New York 2015.

Modeling cell cycle kinetics of normal and cancer cells and anti-cancer therapy

Jaroslaw Smieja, Silesian University of Technology, jaroslaw.smieja@polsl.pl

Lecture contents:

  • Lecture 1 - Introduction:
    • Motivation for modeling of cancer dynamics
    • Sample clinincal & modeling results
    • Compartmental models
    • Modeling of cancer cell population growth with treatment
    • Phase-specific chemotherapy models
  • Lecture 2 - Treatment as a control problem
    • More on phase-specific chemotherapy models
    • Drug resistance modeling
    • Antiangiogenic treatment model
    • Combined therapies
    • Immunotherapy
    • Other
    • A peek at optimization
  • Lecture 3. – Therapy optimization/ introduction to optimization theory (chalk talk, theoretical)
    • Control system structure (open loop vs closed loop, sampled data systems)
    • Formulation of optimization problem (performance indices, feasible controls, additional constraints)
    • Necessary conditions in unconstrained and constrained optimization problems
    • Solutions for free and fixed final points; transversality conditions
    • Some remarks on sufficient conditions
    • Pontryagin maximum principle
    • bang-bang control
    • gradient methods for finding optimal switching times
    • singular arcs
  • Lecture 4. – Infinite dimensional model of drug resistance
    • Model development
    • Analysis of model dynamics
    • Transforming model description
    • Treatment optimization
  • Special evening session (research):
    • Modeling of molecular processes dynamics and cancer
    • Some issues in deterministic modeling of signaling pathways
    • Crosstalk between heat-shock and NFkB pathways

Course-specific lecture sequences

Cancer Biomedical Background

David E. Axelrod, Rutgers University, axelrod@dls.rutgers.edu

  • 1 Introduction to Cancer
    • Pathology of Neoplasia
    • Territorial Expansion of a Mutant Clone (M. Greaves)
    • Tumor Growth Models
    • The Mathematical Challenge
      • Diagnosis, Prognosis, Therapy, Prevention
  • 2 Cancer Evolution
    • Initiation, Invasion, Progression, Metastasis
    • Tumor Heterogeneity
    • Successful Molecular Therapies
    • Rate Limiting Step for Chemoprevention
    • Opportunities for Modeling Cancer Evolution and Progression
  • 3 Cancer Stem Cells
    • Stem Cells in Development
    • Stem Cells in Colon Crypts, Evidence and Stochastic Models
    • Cancer Stem Cell Assays
    • Models of Stochastic and Hierarchical Cancer Stem Cell Dynamics Evidence from Breast Cancer and Melanoma
  • 4 Tumor-Host Interaction
    • Tumor Microenvironment
    • Intra-tumor cooperation
    • Cell-cell interactions
      • Prostate Cancer Associated Fibroblasts
      • Glioblastoma Ligands and Receptors
    • Opportunities for Modeling Cell-cell Interactions

Networks in cancer

Rosemary Braun, Northwestern U., rbraun@northwestern.edu

  • Network analysis of genomic data
  • Identifying aberrant network dynamics in cancer


Seth Corey, Northwestern U., coreylab@yahoo.com

Course-specific lectures

  • TBA