This is my final night at CSHL CCB this summer. I’ve greatly enjoyed my sojourn with this community of computational cell biologists.
I’ll be here from 7:00 PM through 10:00 PM tonight (Thursday) if anyone wants to discuss how to begin the process of translating their favorite biological system into a model.
Some modelers find it more natural and more informative to work in the time domain rather than in phase space. When I say the time domain, I mean that we like to see plots of species, and fluxes as functions of time. For those of you who have an affinity for this approach it might be useful to get together to think about modeling from the perspective of real world applications with many, many state variables. Here are some things we could do:
- We could build a Diagram for one or more of YOUR biological problems. We’d talk through the decisions that a modeler makes based on what the experimental biologist says. Watching this process can be amazingly instructive even if the biological system being modeled is not your own.
- We could discuss the important differences between process diagrams and connection diagrams. We’d see why one of them immediately and unambiguously translates to ODEs and the other does not. This is an exercise about my post on a general rule for biological diagrams.
Perhaps the only disadvantage of a course with multiple lecturers is that not everyone uses the same word for the same modeling concept. Following is a list of synonyms you may find helpful in following the modeling thread through the fabric of diverse lectures. I haven’t done this for the phase space/bifurcation lecturers, but I hope one of the TAs or lecturers will do so.
In general, I’ve listed the standard SBML term first:
- Species, State variable, State
- Reaction, Process, Transition
- Compartment, Place, Structure, Location
- Kinetic Law, Rate law, Constitutive relation
If this post can be made publicly editable, everyone should feel free to ADD lines and ADD synonyms.
All my slides (including the ones I did not present this year) are now on the CSHL Courserve server. I also uploaded some of my own papers that represent practical applications of the basic principles discussed in my lectures. I’ll be at CSHL through Thursday night so that you have plenty of opportunity to ask questions.
When writing rate laws (or constitutive relations) involving mass action kinetics, modelers have different preferences for the units of the SBML species (states, state variables).
In my lectures I expressed a preference for abundance units (molecules/cell) rather than concentration units (moles/L or Molar). Another systems biologist whose published models adopt this preference is Upinder Bhalla.
Because nearly all of the theory of biochemical kinetics was developed in well-mixed compartments like test tubes or spectrophotometer cuvettes, it became standard practice to say that the mass action rate law for a second order reaction is
flux = k [A] [B],
where [A] is the concentration of A. This is a correct and widely used rate law.
But it is NOT the only possible rate law, and in many modeling situations the abundance-based rate law has significant advantages.
In terms of abundances, the rate law for a second order reaction is
flux = k’ A B, where A is the abundance of A.
First, convince yourself that neither of these two rate laws is wrong. Perhaps the simplest way to do this is to recognize the the two volumes of distribution (Va for A and Vb for B) are lumped into the k’ of the abundance-based rate law. In other words, A is always proportional to [A] and B is always proportional to [B], so the only difference between the two rate law expressions is the constant of proportionality.
In return for this slightly unconventional approach, you gain significant advantages, especially when your model contains more than one place (or compartment) and some of your processes or reactions involve transport from one place to another.
- The units of all your fluxes are molecules min-1cell-1. This is helpful because mass is conserved and concentration is not conserved when you move from one volume of distribution to another.
- You don’t have to keep track of the changes in volume as you move from one place to another (for example, from cytosol to ER). This alone will prevent headaches.
- You don’t have to pretend you know the volumes of distribution of a species residing in an organelle membrane (for example, a receptor)
- The numerical values of all your state variables are directly comparable
All regulatory interactions (inhibition, activation, etc.) should be indicated as an effect of a species on a reaction. The resulting diagram is called a process diagram and it unambiguously translates to a system of differential equations.
You will recall that an SBML species is a molecule or molecular complex in a place or compartment and a SBML reaction is a process (biochemical, transport, or binding)
I blogged about this a few years ago and the blog post is here:
How many state variables are in the largest model that has ever been analyzed using the tools of phase plane analysis?