Welcome to the q-bio Summer School and Conference!

Cancer Dynamics, 2016

From Q-bio

In this theme we will address a number of biological and mathematical issues related to modeling of evolution of cancer. Lectures will cover topics spanning many time- and length-scales, from the fundamental issues of cell proliferation and mutation dynamics, to molecular events affecting specific pathways in cells, to 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 (kimmel@rice.edu) and Rosemary Braun (rbraun@northwestern.edu) -- please contact us if you have any questions!

Instructors

Lecturers

Project Mentors

General Research Lectures

These general research seminars will present state-of-the-art research in cancer dynamics topics.

Breast Cancer: Deterministic Modeling of Tumor Progression Based Upon Clinical Histopathology Data

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

8:30-9:30, Tues 12 July, Scott 229

Abstract: This research seminar will present an ODE/compartment model of breast cancer. For an outline and list of relevant references, please see File:Q-bio Schedule & Topics & Refs Axelrod 070616.docx

Colon Cancer: Stochastic Modeling of Stem Cell Dynamics to Improve Treatment and Prevention

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

8:30-9:30, Weds 13 July, Scott 209

Abstract: This research seminar will present a stochastic agent-based model of colon cancer stem cell dynamics and therapy. For an outline and list of relevant references, please see File:Q-bio Schedule & Topics & Refs Axelrod 070616.docx

"Hearing the Shape" of Complex Disease

Rosemary Braun, Northwestern University, rbraun@northwestern.edu

14:00-15:00, Thur 14 July, Scott 229

Abstract: (fill me in!)

Kimmel Research Seminar (title TBA)

Marek Kimmel, Rice University, kimmel@rice.edu

14:00-15:00, Fri 15 July, Scott 229

Abstract: (fill me in!)

Corey Research Seminar (title TBA)

Seth Corey, Virginia Commonwealth University, coreylab@yahoo.com

8:30-9:30, Thur 21 July, Scott 229

Abstract: (fill me in!)

The role of cell location and spatial gradients in the evolutionary dynamics of the intestinal crypt

Alexandra Jilkine, Notre Dame, ajilkine@nd.edu

8:30-9:30, Fri 22 July, Scott 229

Abstract: The intestinal crypt is an important model system for adult stem cell proliferation and differentiation. We develop a spatial stochastic model to study the rate of somatic evolution in a normal intestinal crypt, focusing on the production of two-hit mutants that inactivate a tumor suppressor gene. We investigate the effect of cell division pattern along the crypt on mutant production, assuming that the division rate of each cell depends on its location. We find that higher probability of division at the bottom of the crypt, where the stem cells are located, leads to a higher rate of double-hit mutant production. The optimal case for delaying mutations occurs when most of the cell divisions happen at the top of the crypt. We further consider an optimization problem where the "evolutionary" penalty for double-hit mutant generation is complemented with a "functional" penalty that assures that fully differentiated cells at the top of the crypt cannot divide. The trade-off between the two types of objectives leads to the selection of an intermediate division pattern, where the cells in the middle of the crypt divide with the highest rate. This matches the pattern of cell divisions obtained experimentally in murine crypts.

Cancer Dynamics Breakout Sessions

These course-specific didactic sessions are targeted to students in the Cancer Dynamics track, but are open to all.

Cancer Biomedical Background (13-14 July)

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

This two-part series will present the basic biomedical background of cancer. For an outline and detailed list of relevant references, please see File:Q-bio Schedule & Topics & Refs Axelrod 070616.docx

Cancer Biomedical Background, Part 1 (15:15-17:30, Weds 13 July)

  • Intro, concepts, assumptions
  • Vocabulary to talk with experimental cancer biologists, pathologists, clinicians
  • Why hasn’t the cancer problem been solved?
  • Definition
  • Challenges
  • Opportunities
  • Benign and Malignant Neoplasms
  • Clonal Origin of Cancer
  • Tumor Progression
  • Invasion and Metastasis

Cancer Biomedical Background, Part 2 (15:15-17:30, Thur 14 July)

  • Tumor Microenvironment
  • Cancer Stem Cells
  • Cancer Therapy
  • Cancer Prevention

References

Network Analysis of *Omic Data (15 & 19 July)

Rosemary Braun, Northwestern University, rbraun@northwestern.edu

The cellular proliferation, migration, and invasion characteristics that are the hallmarks of cancer are due to aberrant signaling in the regulatory networks that ordinarily control growth and apoptosis. These pathways can be compromised in a variety of ways, both in terms of the affected molecules and in terms of the mechanism (eg, by mutation or by altered transcription). Today, modern high-throughput assays yield genome-wide profiles of sequence variation, transcription factor binding, methylation, and expression for each sample of interest, and this exquisitely detailed information provides an unprecedented opportunity to characterize the molecular mechanisms governing malignant transformation. At the same time, the high dimensionality of the data presents analytical challenges. Mathematical models of regulatory networks are essential for identifying pathological signaling processes in cancer cells. In these lectures, we will discuss various approaches for the systems-level analysis of high-throughput data.

Part 1: Pathway analysis of genomic data (15:15-17:30, Fri 15 July)

  • Introduction to basic statistical and bioinformatic analysis of genome-wide profiling data, including popular non-network approaches
  • Incorporating pathway network topology into the analysis,
  • Introduction to graph theory
  • Approaches to analyze experimental data in the context of networks derived from expert-knowledge pathway databases
  • Comparison of methods & discussion of open challenges

Part 2: Inferring network topology and identifying aberrant networks in cancer (15:15-16:30, Tue 19 July)

  • Methods for reconstructing regulatory network structure from experimental data
  • Overview of probabilistic graphical models
  • Overview of partial correlation/partial least squares regression
  • Graph-theoretic (SPaTO, PDM) and information-theoretic (ARACNe) network reconstruction techniques

Evolutionary Models for Cancer Genomics (18-20 July)

Andrzej Polanski and Marek Kimmel, kimmel@rice.edu

Coalescent theory is a widely used tool for statistical inference on genetic parameters and structures of populations and scenarios of evolution of populations. The standard coalescent model, which assumes populations of constant size was generalized to cover scenarios of population growth. General coalescent model with arbitrary history of population size change has many applications since majority of real populations undergo changes in their sizes.

This series of three lectures will present the methodology of coalescent theory and its application to cancer genomics.

Part 1: Coalescent modeling (15:15-17:30, Mon 18 July)

  • Wright-Fisher model of reproduction
  • Discrete and continuous-time coalescent
  • Probability distributions of times in the coalescent model
  • Coalescent with mutations; infinite sites model
  • Pairwise comparisons; estimators of scaled mutation rate parameter

Part 2: General coalescent model with non-constant population size (16:30-17:30 AND 19:30-20:30, Tues 19 July)

  • Allelic frequencies of mutations in the general coalescent model.
  • Exponential growth model.
  • Probability distributions of times in the general coalescent model.
  • Derivation of the Griffiths-Tavare formula for joint pdf of coalescence times.* Marginal distributions and expectations of times in the coalescent model.
  • Estimation of the product parameter of population growth.

Part 3: Cancer genomics sequencing (CGS) data. (15:15-17:30, Weds 20 July)

  • Specificity of cancer genomics data.
  • Formats of CGS data.
  • Tools for processing CGS data, and for searching for somatic mutations.
  • Driver and passenger somatic mutations.
  • Scenarios of tumor growth.
  • Somatic and intra-somatic mutations.
  • Fitting the model of exponential growth to allelic frequencies of intra-somatic mutations.

References:

  1. Hein J., Schierup M.H., Wiuf C., (2005), Gene genealogies variation and evolution, Oxford University Press.
  2. Griffiths R.C., S. Tavare, (1998), The Age of a Mutation in a General Coalescent Tree, Stochastic Models, 14: 273-295.
  3. Hudson R.R., (1991) Gene genealogies and the coalescent process. Oxford Surveys in Evolutionary Biology 7: 1–44.
  4. Polanski A., Kimmel M., (2003), New Explicit Expressions for Relative Frequencies of SNPs with Application to Statistical Inference on Population Growth, Genetics, vol. 165, pp. 427-436.

Mathematical Models of Mutation Acquisition and Time to Cancer

Alexandra Jilkine, Notre Dame, ajilkine@nd.edu

I will cover birth-­‐death processes, and their applications to modeling populations of cancerous cells. Models from population genetics, emphasizing phenomena of genetic drift and clonal extinction, will be used. Effect of fitness and selection on evolutionary dynamics will be covered. These types of models can be used to reconstruct the order in which oncogenic mutations arise, and most likely path to mutation acquisition. Impact of deleterious passengers on cancer progression will be mentioned.

References:

  1. Textbooks:
    1. Linda Allen. An Introduction to Stochastic Processes with Applications to Biology. CRC press, 2nd edition.
    2. Weinberg, Robert. The biology of Cancer. Garland Science, 2nd edition.
  2. Other references
    1. Bozic, Ivana, Tibor Antal, Hisashi Ohtsuki, Hannah Carter, Dewey Kim, Sining Chen, Rachel Karchin, Kenneth W. Kinzler, Bert Vogelstein, and Martin A. Nowak. "Accumulation of driver and passenger mutations during tumor progression." Proceedings of the National Academy of Sciences 107, no. 43 (2010): 18545-­‐18550.
    2. McFarland CD, Korolev KS, Kryukov GV, Sunyaev S, Mirny LA The impact of deleterious passenger mutations on cancer progression. PNAS 2013 110(7).
    3. Ramon Diaz-­‐Uriarte .Inferring restrictions in the temporal order of mutations during tumor progression: effects of passenger mutations, evolutionary models, and sampling. link


Projects

Does colon cancer start “top-down” or “bottom-up”? (David Axelrod)

Agent-based stochastic model of cancer initiation

Evolutionary Models in Cancer, Computer Lab 1 (Andrzej Polanski)

Requires downloading and installing R. Hudson’s program "ms" for coalescent simulations. (Hudson, R. R., 2002, Generating samples under a Wright-Fisher neutral model. Bioinformatics, vol. 18, pp. 337-338.) and writing/using Matlab scripts to read and analyze files created by "ms".

Topics to study/verify:

  • Comparisons of estimators of scaled mutation rate parameters
  • Computing sampling distributions of allele frequencies for different scenarios of population growth. Comparison to theoretical distributions.
  • Estimation of population growth product parameter.

Evolutionary Models in Cancer, Computer Lab 2 (Andrzej Polanski)

Involves the use of pre-prepared cancer genomics sequencing data filtered from the output file of the Mutect program. (K. Cibulskis et al., 2013, Sensitive detection of somatic point mutations in impure and heterogeneous cancer samples, Nature Biotechnology 31/3, 213 – 221).

Topic to study:

  • Fitting the model of exponential growth to data on frequencies of intra-clonal mutations.

Network response to estrogen in ER+ breast cancer (Rosemary Braun)

Here we will use timecourse data of estrogen sensitive, insensitive, and refactory breast cancer cell lines following estrogen exposure to explore the responses of these cells in the context of known signaling pathways. Questions that could be explored include:

  • do high lagged correlations correspond to known pathway edges?
  • how do the [lagged] correlation networks compare between cell types?
  • does the pathway predict the dynamics seen in the data?
  • are graph characteristics (eg, gene degree) associated with differential expression or differential time-course profiles?
  • does the stability of weighted networks (#pos eigvals) differ between phenotypes?
  • does the flexibility (cf http://www.math.uiuc.edu/~rdeville/research/91397.pdf) of the weighted graphs differ?
  • can differences in the timecourse profiles be inferred from the 0-hr data?

Baseline gene expression and drug response (Rosemary Braun)

Here we will use baseline (non time-course) gene expression from a set of 49 breast cell lines and a set of dose-response curves for the same cell-lines when exposed to various therapies. Questions that could be explored include:

  • Can we learn a signature from the baseline expression data that would predict response to a drug?
  • Do the genes associated with drug response cluster on the pathway graphs?

Other projects

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