Cell-based models of morphogenesis in normal and pathogenic development - Continued Maria Audi Byrne September 21 st 2007 Mathbiology and Statistics Seminar University of South Alabama

Presentation Outline 1.Morphogenesis 2.Model of normal development: myxobacteria fruiting body development 3.Model of pathogenic development: tumorigenesis in the prostrate duct

Modeling of Paracrine Signaling Project 2: Aim 3

Core B: Image Fusion Gore Core C: Biomath & Bioinformatics Shyr Project 3: Bone metastasis Mundy Vanderbilt-Ingram Cancer Center Mouse Models of Human Cancer Consortium Vanderbilt Integrative Cancer Biology Center Prostate Center Center for Bone Biology VU Institute for Imaging Sciences Breast SPORE BioMathematics Small animal imaging Proteomics Core A: Protein collection & Proteomics Caprioli Biostatistics Project 1: Breast Cancer Moses Matrisian TGF  effectors Vanderbilt University Tumor Microenvironment Network VUTMEN Project 2: Prostate Cancer Hayward & Bhowmick

Paracrine Signaling A cell or tissue produces a factor which acts upon an adjacent tissue. Examples include many growth factors during development, adult homeostasis and in cancer.

TGF  as a master regulator of host:tumor interactions Bierie and Moses, Cytokine Growth Factor Reviews, 2006

Preliminary Model: Static Model of Paracrine Interactions in Prostate

What is the Prostate? From Wikipedia: The prostate is an exocrine gland of the male mammalian reproductive system.exocrine gland mammalianreproductive system The main function of the prostate is to store and secrete fluid that constitutes 10-30% of the volume of the seminal fluid. seminal fluid

Prostate Cancer Again from Wikipedia: Prostate cancer is one of the most common cancers affecting older men in developed countries and a significant cause of death for elderly men (estimated by some specialists at 3%). Regular rectal exams are recommended for older men to detect prostate cancer early. Many men never know they have prostate cancer. Autopsy studies of men who died of other causes have found prostate cancer in thirty percent of men in their 50s, and in eighty percent of men in their 70s. [Breslow et al, 1977]

Modeling Problem: Non-linear effect of stroma on epithelium Tissue Recombination Project – Normal stromal cells were mixed with altered stromal cells. – The altered stromal cells were unable to respond to TGF- beta. – Effect on epithelial cells was observed. In experiments intermediate levels of altered stroma yield the worst epithelial changes. – 0% AS: Normal epithelial tissue – 50% AS: Proliferative and invasive epithelial tissue. –100% AS: Proliferative epithelial tissue. Drs. Neil Bhowmick and Hal Moses

Mathematical modeling of epithelial-stromal interactions Modeling Goal How can we define epithelial and stromal cell rules that (1) are biologically motivated, (2) model correct proliferative behavior, (3) model correct invasive behavior? Method: Hypothesize a set of simplified biologically motivated rules and use computer simulations to check if they are sufficient to yield expected cell behaviors. Warning: If successful, we identify rules that are sufficient to explain experimental observations. Discourse between model predictions and further experiments are needed to further validate/refine the model.

Proliferation is controlled by a diffusing morphogen secreted by the altered stroma that acts on the normal epithelium (e.g., HGF). Simplified Biological Assumptions

Altered Stroma Normal Epithelium Proliferative Epithelium Invasive Epithelium HGF

Proliferation is controlled by a diffusing morphogen secreted by the altered stroma that acts on the normal epithelium (e.g., HGF). Migration is controlled by a diffusing morphogen secreted by the normal stroma that acts on proliferative epithelium (e.g., SDF1). Simplified Biological Assumptions

Normal Stroma Normal Epithelium Proliferative Epithelium Invasive Epithelium SDF1

Normal Stroma Altered Stroma Normal Epithelium Proliferative Epithelium Invasive Epithelium HGF SDF

Normal Stroma Altered Stroma Normal Epithelium Proliferative Epithelium Invasive Epithelium HGF SDF 0% Altered Stroma  Normal Epithelium

Normal Stroma Altered Stroma Normal Epithelium Proliferative Epithelium Invasive Epithelium HGF SDF 100% Altered Stroma  Proliferative Epithelium

Normal Stroma Altered Stroma Normal Epithelium Proliferative Epithelium Invasive Epithelium HGF SDF 50% Altered Stroma  Invasive Epithelium

ABC TGF  Schematic describing how TGF  can be simultaneously tumor repressive and promoting. Developmental Model Hypothesis

LGCA lattice gas cellular automata Particles are modeled as points with a defined “interaction neighborhood”. Each particle is assigned a “state” corresponding to the particle “channel” (orientation). Important exclusion rule: only one cell per channel. Computationally efficient updating with a 2-step transition rule at every time step: (1) Interaction step: Cells are assigned new velocities based on neighborhood interactions. (2) Transport step: All cells are transported simultaneously along velocity channels.

Biological LGCA Coined by Edelstein-Keshet and Ermentrout, 1990 May relax exclusion principle or include novel modeling elements

Lattice-based Computational Model Cell-Based Each lattice node may be occupied by a cell No more than 1 cell per node A lattice node is about 5 x 5  m Each cell has a “state” Different cell states correspond to different cell types Each cell state has its own set of rules that define the behavior of that cell type Simulation-based The lattice at time step t+1 is a function of the lattice at time step t A “simulation” is an arbitrary number of time steps Mathematical modeling of epithelial-stromal interactions

5 cell types in model: Normal Stroma Altered Stroma Normal Epithelia Transformed Epithelia Type 1: proliferative phenotype Type 2: invasive phenotype Mathematical modeling of epithelial-stromal interactions

Cell Rules for Each State Normal Stroma secretes SDF: SDF(i,j,t+1) = SDF(i,j,t+1) + 1 Altered Stroma secretes Wnt: Wnt(i,j,t+1) = Wnt(i,j,t+1) + 1 Normal Epithelial Phenotype Transforms at threshold levels of Wnt if Wnt(i,j)>5, state changes from normal to proliferative Proliferative Epithelial Phenotype Transforms at threshold levels of SDF: if SDF(i,j)>3, state changes from proliferative to invasive Invasive Epithelial Phenotype for each cell located at the node (i,j)

Molecules / morphogen units are discrete. Molecules are secreted by cells. Molecules diffuse over the lattice by random walk (at a diffusion rate specified for each molecule. Model keeps tracks of how many of each type of molecule are at each node at each time-step. Interactions can occur between cells and molecules and between molecules. Model of diffusing molecules (paracrine interaction)

Cell Rules for Each State Normal Stroma secretes SDF: SDF(i,j,t+1) = SDF(i,j,t+1) + 1 Altered Stroma secretes Wnt: Wnt(i,j,t+1) = Wnt(i,j,t+1) + 1 Normal Epithelial Phenotype Transforms at threshold levels of Wnt if Wnt(i,j)>5, state changes from normal to proliferative Proliferative Epithelial Phenotype Transforms at threshold levels of SDF: if SDF(i,j)>3, state changes from proliferative to invasive Invasive Epithelial Phenotype for each cell located at the node (i,j)

Diffusion At each time-step, cells, activator molecules and inhibitor molecules diffuse by either: resting at their current node with probability p s (or ) moving right, up, left or down with probability (1- p s )/4. As the probability of resting p s increases, the diffusion rate of the particle decreases. Model Particles: Cells, Activator, Inhibitor, and Fibronectin

Initial cell positions are taken from an experimental image. Blue: Normal fibroblasts Cyan: Altered fibroblasts Black: Normal epithelia

Altered stroma secretes Wnt that diffuses to the epithelium and causes epithelial cells to transform. Stage 1: Transformation of Epithelium from Normal to Proliferative

Wnt Production and Diffusion after 10 time steps - from altered stromal cells only -

Wnt Production and Diffusion Over 100 Time Steps

Blue: Normal fibroblasts Cyan: Altered fibroblasts Black: Normal epithelia Red: Transformed epithelia

Blue: Normal fibroblasts Cyan: Altered fibroblasts Black: Normal epithelia Red: Transformed epithelia

Stage 1: Transformation of Epithelium from Normal to Proliferative Altered stroma secretes Wnt that diffuses to the epithelium and causes epithelial cells to transform. –The amount of Wnt increases with time. –The amount of Wnt increases with the fraction of altered stroma. –The number of transformed epithelial cells increases with time, fraction of altered stroma.

Stage 2: Transformation of Epithelium from Proliferative to Invasive Normal stroma secretes SDF that diffuses to the epithelium and causes transformed epithelial cells to transform further. –The amount of SDF increases with the fraction of normal stroma. –Recall, the number of transformed epithelial cells (stage 1) increases with the fraction of altered stroma. –What fraction of altered stroma will yield the greatest number of invasive epithelial cells? What can we learn about SDF dynamics from the dependence of the number of invasive cells upon the fraction of altered stroma?

Model Results For Different Parameters Error bars show average and standard deviation of five simulations.

Model Results For Different Parameters Error bars show average and standard deviation of five simulations.

Future Directions Incorporating experimental data (quantitative data will specify some parameters). Investigating what limits the total number of invasive cells in the case of 50% altered stroma. (What limits available levels of SDF?) - spontaneous exponential decay of SDF? (current model) - limited cell receptors for SDF? - ECM reservoirs of SDF? Developing a dynamic model based on normal prostate duct development that allows cell division (proliferation) and cell movement (migration). Systematically explore parameter space and form simulation-based predictions that will inform us about the consequences of the model assumptions.

Thanks! The End

Proliferation is controlled by a diffusing morphogen secreted by the altered stroma that acts on the normal epithelium (e.g., HGF). 1.Normal stroma does not produce HGF because HGF is suppressed by TGF-beta. 2.Altered stroma are resistant to TGF-beta and do produce HGF. 3.HGF diffuses from the stroma to the epithelia. 4.Threshold levels of HGF transform normal epithelia to a proliferative phenotype. Simplified Biological Assumptions for Proliferation

FIGURE 1. Cellular relationships. From the following article: Cancer: Dangerous liaisons Allan Balmain and Rosemary J. Akhurst Nature 428, (18 March 2004) doi: /428271aCancer: Dangerous liaisons

Migration is controlled by a diffusing morphogen that is secreted by normal stromal cells and acts upon proliferative epithelial cells (e.g. SDF-1/CXCL12 via AKt pathway). 1. Normal fibroblasts produce SDF1. 2. Altered fibroblasts do not produce SDF1. 3. Normal epithelia cells do not have SDF receptor CXCR4. 4. Proliferative epithelial cells up-regulate CXCR 4 (TGFB dependent). 5. Epithelial cells with CXCR4 respond to SDF1 by becoming invasive. Simplified Biological Assumptions for Migration