# ๐ Cortassa 2012

Contents

Computational modeling of mitochondrial function

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## Introduction

- biochemistry, cellular, and molecular biology
- thermodynamic models: agreement with the fundamental principles, lack of mechanistic details
- Stoichiometric models: large networks of biological processes without any possibility of transient behavior or regulatory interactions
- Kinetic models: kinetic mechanisms, many parameters to find
- Modular building of models (piece by piece), each module represents the known or hypothesized kinetic scheme available for that process
- Allows zooming in and out in a network of processes
- Spatio-temporal organization

- The reliability of a computational model
- sound physicobiochemical basis
- ability to reproduce qualitative and quantitative experimental data
- provision of meaningful explanation of the simulated experimental behavior
- predictive power

## Materials

### Basic biochemical information

- KEGG: http://www.genome.jp/kegg/
- BRENDA: http://www.brenda-enzymes.org/

### Repository databases

- biomodels https://www.ebi.ac.uk/biomodels/
- CellML repo http://models.cellml.org/cellml
- ModelDB (Neurons) https://senselab.med.yale.edu/ModelDB/

### Experimental data

- to constrain the modulesโ kinetics

### Computational tools

- Matlab , Mathematica, Maple, C++, Python, JAVA, Julia, …

## Methods

- Clear identification of
*the level*of organization (molecular, (sub)cellular, (multi)cellular) => SDE, ODE, PDE, ABM, … - Identification of the set of processes of interest along with observables (
*experimental variables*) - Choice of the kinetic expressions
- GoldmanโHodgkinโKatz voltage equation (membrane potential)
- Fickโs laws (non-charged simple diffusion)
- (Not mechanistic) power-law formalism, fractal (non-integer) kinetics

- Using your favorite program to represent the kinetic behaviors to code

### Choosing the right set of *parameters*

- first hint about parameter values can be obtained from experimental data or literature
- may need some
*adjustment*since the conditions in which they have been measured may not correspond to physiological ones

### The sensitivity of the curve to substrate or effector

- provide information about ways to modify a module behavior in the fully assembled model when the simulated output differs from experimental data

### individual behavior of a module should be compared with experimental data obtained in vitro

- in vivo experimental data can be obtained for some biological processes,

### The modules may be assembled once their individual behavior is proved satisfactory according to the above criteria 1โ6

- which of the variables participating in the equations will become
*state variables*, and which will be*adjustable parameters* - Rate of change = rate of production +/- rate of transport - rate of consumption
- the rate in ODEs may be subjected to scaling factors to account for volume or buffering effects
- the format with which to write the differential equations
- the choice of the integration algorithm
- Time scale: ms ~ secs
- Stiff ODE solvers

- Simulate short term first: To watch is whether some state variables take negative or extreme (unphysiological) values. Will provide key insights into which and how (extent and direction of change: increasing or decreasing) parameters may be adjusted to render reasonable simulations of the model behavior.
- run a model simulation till it reaches a steady state (dx/dt < tolerance), may take a while
- comparing the model output with experimental data (e.g., steady-state values of variables, or fluxes). => fine-tuning of parameters
- a model is able to predict if it can simulate a behavior that has not yet been observed. Oscillatory behavior of reduced glutathione, GSH, was first observed in the model, and later confirmed experimentally

## Footnotes

- the physical unit
- in vitro condition provides an initial guess rather than an accurate figure of a parameter value
- control analysis to know if the process in question exerts control over the fluxes in the network of interest
- Or, test by model simulations which consequences bring about a parameter variation representing that activity

## Reference

Cortassa S, Aon MA. Computational modeling of mitochondrial function. Methods Mol. Biol. 2012;810:311-326. doi:10.1007/978-1-61779-382-0_19. PMC3350335. ↩︎