Team:Purdue/Modeling

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NOTE: We highly suggest you read the project description before venturing into this page. The model description assumes that the reader understands the basic process underlying our system.

Why Model?

A mathematical model of a system can be a useful predictive method for a system. In our case, a spatial-temporal model of the kinetics of microglial activation, tat-GFP production, and tat-GFP diffusion can answer such questions as:

• How long will it take until the GFP is detectable?
• What will be intensity of the resulting CD133+ cells?
• Will the diffusion process be limited by diffusion through the membrane or diffusion in the solution?
• How specific will the system be? (i.e., will many cells besides the CD133+ cells be labeled?)
• Will the promoters used be effective, or will a stronger promoter be necessary?
• Etc.

Assumptions!

Every model contains assumptions. Some assumptions are more valid than others, but in all cases the assumptions simplify the model to make it usable. In our model, we made the following major assumptions as a basic set-up:

• The system lies within a 2-dimensional space

• Our experiments are done in 2-D culture, so any kinetic parameters we measure will apply to the model

• Most processes are simplified into first-order reactions
• Instead of looking at the cell population as a whole, the model generalizes by looking at an "average" cell

• Avoids analyzing the natural cell-to-cell variation
• Uses a single parameter for every cellular process included in the model
• Looking at actual spatial position is unnecessary, as instead we can use the average amount of time to reach a destination

• We will model each distinctly different state of the model as a separate variable, thus eliminating the complexity of looking at the detailed biochemical pathways

Other assumptions concerning each individual step are also made, but these will be detailed later.

The Equations...and what they mean

This mathematical model was constructed using a system of ordinary differential equations. Each equation describes the change in one component over time by summing the effects of other processes on that component (If you don't like math, I promise it's not as complicated as it might look!).

The component names are as follows:

• Mu = "unactivated" microglia
  • These microglia are just sitting around, doing what they do best...grow!
  • They are "far away" from any CD133+ cells -- i.e., they are not interacting with them
• Mg = microglia "near" glioblastoma
  • These microglia are VERY close to the CD133+ glioblastoma cells, but they are not yet touching or interacting
  • This variable allows the model to describe the rate of movement of the microglial cells toward the CD133+ cells without tracking their spatial path
• Ma = "activated" microglia
  • The modified Fc receptors of these microglia have found and bound the CD133 protein, setting off a signal cascade
  • The signal cascade eventually encodes for the production of the tat-GFP construct
• G = CD133+ glioblastoma cells

Below the color-coded equations are explanations of each part of the model.

TEXT

Parameters

We ultimately hope to measure each of the model's parameters ourselves, but for now many of the parameters are estimated based on values found in literature for similar processes.

Put table here?

Results

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