dissertation proposal: a multi-scale, physics engine-based ... · 2014-12-05 · outline research...

OutlineResearch Motivation

Research ScopeDesign of the ToolResearch Schedule

Dissertation Proposal: A Multi-Scale, PhysicsEngine-Based Simulation of Cellular Migration

Terri A. Grosso

CUNY Graduate Center

December 5, 2014

Terri A. Grosso Dissertation Proposal: A Multi-Scale, Physics Engine-Based Simulation of Cellular Migration



Overall Research Goal

To model the molecular interactions between cells and theirenvironment, in order to study macro-level emergent behaviors.




Research Motivation

Research Scope

Design of the ToolThe Physics EngineModeling the CellModeling the BondsModeling Trafficking and Protein InteractionsModeling the Environment

Research Schedule




Biological Motivation - Cellular Migration

I Embryogenesis

I Wound-Healing

I Immune responses

I Cancer metastasis




Importance of Simulation

I System is very complex

I Experiments are time-consuming

I Supplies are expensive

I Difficult to isolate variables




Research Issues

Challenge Approach

Multiple moving objects Physics Engine

Physical bonds and constraints Physics Engine

Complex shapes Triangular Mesh

Hetergenous cell surface Triangular Mesh

Surface protein trafficking Differential equations

Developing concentration gradients Partial differential equations

Visualization Rendering Engine

Extensibility User-defined parameters




Research Scope




Specific Goals

I Clearly represent the interactions between the cell and itsenvironment

I Interactions happen at the cell membrane

I Demonstrate how ligand binding affects the trafficking ofsurface proteins

I Show how that trafficking leads to cells moving




Research Scope

I Building around work with Retinal Progenitor Cell migration inMicrofluidic Channels at the Redenti Lab at Lehman College

I Mouse RPG cells

I Long, closed, narrow channel (13mm by 95µ diameter) withlaminin-coated walls

I Generates a stable gradient of ligand across the channel

I Can take pictures of cells and track them as they migrate




The Microfluidic Channel

Figure: Microfluidic Channel Design [1]




The Physics EngineModeling the CellModeling the BondsModeling Trafficking and Protein InteractionsModeling the Environment

Designing the Tool

I The Physics and Rendering Engines

I Modeling the Cells

I Modeling Protein Interactions

I Modeling Surface Protein Trafficking and Protein Interactions

I Modeling the Environment





The Use of the Physics Engine

Advantages:

I Designed for video games

I Supplies motion, forces, collision detection and constraintresolution

I Works in real time

I Using the JBullet Physics Engine

I Binds to OpenGL for rendering





Rendering the Channel





Migrating Cells Have Complex Shapes

Figure: Mesenchymal and Amoeboid Migration[2]





Modeling with a Triangular Mesh

I Data structure composed of a set of triangles in 3D spacethat share edges and vertices

I Used frequently to represent very complex shapes in videogames

I Use is optimized in physics and rendering engines

I Allows characteristics of an object to be represented at finergranularities





Different Levels of Granularity





The Heterogenous Cell Membrane

I Distribution of surface proteins and internal proteins differfrom one triangle segment of the cell to another

I How that distribution changes over time also differs across thecell

I Can use the triangular mesh to represent these distributions ata fine granularity

I Can visualize these differences with different shades of color





Visualizing Variability Across the Cell





Binding to a Surface

I Surface binding is necessary for cell migration

I Binding happens between receptors and surface proteins

I Do not model each individual molecular bond - too many ofthem

I Each constraint represents a group of molecular bonds (100molecules here)





The Lifetime of a Bond

I Bonds break probabilistically based onI ageI the force being applied

I When first formed, they can easily break

I Over time bonds become focal adhesions - large, stable, hardto break

I Eventually focal adhesions are degraded

I Forces applied to bonds help to break them

I Bond flexibility also age-dependent





Change in Concentration of Surface Proteins

I Receptors are secreted to the surface at a specific rate

I Some receptors bind to ligand in the environment

I Empty receptors are internalized at a different rate

I Bound receptors are internalized at still another rate

I Movement of membrane proteins in and out of cell calledtrafficking





Schematic Representation of Trafficking

[3]





Mathematical Description of Surface Membrane Turnover

Differential equations describing the changes in membrane proteinsover time:

Changes in the number of unbound receptors:

dRdt = −konRL + koff C − ktR + QR

Changes in the number of bound receptors:

dCdt = konRL − koff C − keC [3]





Localized Turnover of Surface Proteins

I Each triangle membrane segment has its own rates for eachrepresented protein

I Rate of secretion to the surfaceI Rate at which unbound receptor is internalizedI Rate at which bound receptor is internalized

I Changes to these rates affect the number of receptors on themembrane surface





Proteins Affect Each Other

Defining Protein Interactions

I Receptor and Target

I Number of bound Receptor molecules determines affect onthe Target protein

I Binding of Receptor can affect any of the trafficking rates ofthe Target protein

I Receptor of one Interaction can be the Target of another





Walls

I Can simply use a set of rigid boxes

I Represent the surface concentration of a protein with a singlevalue if we assume it is constant

I Can represent a wall as a triangular mesh to represent varyingamounts of surface ligands

I Can set them to be invisible for visualization





Ligand Gradients

I Ligand concentration modeled continuously using partialdifferential equations

I Dependent on the experimental set-up

I Visualized on screen





Walls and Gradients - Example





Some Example Videos

Here are some example videos.




Current Progress

Challenge Status

Multiple moving objects Implemented

Physical bonds and constraints Partially implemented

Complex shapes Next Steps

Hetergenous cell surface Implemented

Surface protein trafficking Implemented

Developing concentration gradients Implemented

Visualization Implemented

Extensibility Partially implemented




Next Steps - Changing Cell Shape

I Shapes of the cells need to change in response to theenvironment

I Vertices should move relative to each other

I New vertices form at bond positions

I Vertices may also be removed if no longer necessary




Next Steps - Simulation Analysis

I Computational Efficiency - how does changing number ofcells, triangles and proteins affect the speed of computation?

I Parameter Estimation - which parameters give results similarto those found in the lab?

I Sensitivity Analysis - how do parameter ranges affect theoutput?




Future Research

I An XML interface for user-defined objects and parameters

I Implement other assays and compare to published research




References

Qingjun Kong, Robert J Majeska, and Maribel Vazquez.Migration of connective tissue-derived cells is mediated byultra-low concentration gradient fields of egf.Exp. Cell Res., 317(11):1491–502, 2011.

K Pankova, D Rosel, M Novotny, and Jan Brabek.The molecular mechanisms of transition between mesenchymaland amoeboid invasiveness in tumor cells.Cell. Mol. Life Sci., 67(1):63–71, 2010.

Harish Shankaran, Haluk Resat, and H Steven Wiley.Cell surface receptors for signal transduction and ligandtransport: a design principles study.PLoS Comput. Biol., 3(6):e101, 2007.




The End

Thank you for your time and support!Questions?


dissertation proposal: a multi-scale, physics engine-based ... · 2014-12-05 · outline research...

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