# TMT Thesis Project

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## Contents |

## Thesis Topic

The main objectives of my work is to develop the tools to perform time-dependent stimulation and analysis of signaling pathways, and show that this is more powerful than traditional time-independent or step response analysis. I am using a computational model of the prototype system, the yeast pheromone response pathway, to generate hypotheses about the pathway. In order to test these hypotheses, time-dependent stimuli will be delivered to cells via a microfluidic device, and in vivo fluorescent reporters will be used to observe the system state. In addition to showing the strengths of this new approach to studying biological systems, I would like to use it to further our understanding of the pheromone response pathway.

## Research Goals

My research can be broken down into 4 main goals that follow (for the most part) chronologically.

### Build a model of the pheromone response pathway

- Develop a model of the pheromone response pathway that can be used in conjunction with time-dependent stimulation and analysis of the pathway to propose and test hypotheses. Once completed, this model can be used as a predictive tool for pathway response.
- This model is largely already built (with instances in Matlab and Moleculizer). Also, using BioNetGen2 I have generated an SBML version of my model, which can be read as input by Jacobian, SloppyCell, and the SimBio toolbox in Matlab.
- The model needs to be further refined using data from the literature, and data that I will generate myself.

### Build a microfluidic device for time-dependent stimulation of cells

- Design, build and characterize a device to allow for rapid variation of extracellular conditions for cells fixed in a microfluidic channel.
- This chip has been designed using the technology out of the Quake Lab at Stanford (formerly Caltech). See protocols for more info on chip design. Early versions of the chip (called the Stimulator) have shown great promise. Preliminary tests have shown that I can vary the extracellular environment (with NO cells in the channel) on a sub 100ms timescale. I've also successfully adhered cells to the bottom of the channel, and had them resist detachment under fluid flow, though this needs further characterization. I made a Image:Cells in stimulator.avi with the most recent version showing that I can change the fluid environment of cells in the channel (video in real time, with food dye used to color one of the fluids). Please see the Stimulator page for the latest information.

### Investigate the pathway with time-dependent stimulation

- Examine the frequency filtering characteristics of the pheromone response pathway in order to study the limits of propagation of time-varying signals through the pathway. Use the model to form and test hypotheses generated by studying the response of the pathway to time-dependent stimulation.
- Alternative approach would be to show that using time-varying stimuli increases parameter sensitivity, and that this leads to an improvement in parameter estimation. This is really just a specific instance of hypothesis testing (where the hypothesis is the particular parameter values).

### Identify and apply techniques for non-linear system identification

- Identify and apply tools developed for other fields to the analysis of signaling pathways, particularly with respect to time-dependent stimulation. This can be divided into into two thrusts, parameter estimation and other analysis tools.
- Parameter Estimation
- My first instinct was to try to do parameter estimation using Matlab. This turned out to not be sufficient for my purposes. See my notes on Parameter Estimation in Matlab.
- I settled on using Jacobian for parameter estimation. The current version that I have is still somewhat buggy, but I have been assured by one of the lead guys working on Jacobian that they have corrected all the problems that I identified in the new release which is due out any day now. I'll update on this as soon as I get the new release.

- Model analysis tools
- One basic analysis of a model is parameter sensitivity. Some people think that models should be robust to changes in parameters (reference to be filled in, since it's not cool to just state things and reference it blankly to 'some people'). I'm not so sure that is true, but either way the parameter sensitivity can in the very least tell you to what parameters your model's behavior is sensitive (critically depends on), and to what parameters it is insensitive (does not depend on).
- Another analysis would be to look at parameter identifiability. Essential, just because a simulation (and thus a corresponding experiment) is sensitive to a parameter (as determined by sensitivity analysis), it doesn't mean that you can successfully estimate that parameter from the relevant experimental data. A simple example is that in the steady state, the concentration of a complex is dependent on both the association and dissociation rate constants (k
_{on}and k_{off}), but we can only successfully estimate the dissociation constant (K_{D}= k_{off}/k_{on}).- At ICSB 2005 I discovered this program called SloppyCell written by Ryan Gutenkunst in the Sethna lab at Cornell which addresses parameter identifiability. Basically, SloppyCell calculates the parameter sensitivities, but does so for identifiable parameter groups (which are comprised of weigthed products of the original parameters). More details on this can be found in the original publication of the algorithm, and in my SloppyCell page.
- There are other ways to deal with parameter identifiability. I'm currently looking into methods that incluse linearization of the model followed by model order reduction. When I know more, I'll add details.

- Parameter Estimation

** Relevant questions **

Q. What will determine if using time-varying stimuli is a success?

A. I think that it would be sufficient for me to show that you can get better parameter estimates using time varying stimuli than you can with step increase. When I say better estimate, I mean that we can decrease the error bounds on parameters. This hinges on some intelligent way to put bounds or confidence limits on parameters. This is probably linked to the independence/coupling of paramters topic listed below under Signal Design.

Q. I say that a time varying stimulus can drive a system to a state that it won't normally attain in response to a step increase stimulus. For what types of systems is this true?

A. I think that I can concoct systems that this is true for, but I should try to show that this is indeed true for the pheromone response pathway.