Non-linear ODEs: Scan Article 03 Conrad, E D, and Tyson, J J. Modeling molecular interaction networks with nonlinear ordinary differential equations. In: System Modeling in Cell Biology: From Concepts to Nuts and Bolts. Z. Szallasi, J. Stelling and V. Periwal, eds. MIT Press, Cambridge, MA. pp 97-123. 2006.
Use for backup of detailed, student explanations of the Sniffers-Buzzers paper.
0. Knew: I knew ODE equations could be used to model molecular interactions in and among cells by estimating the relative abundances of proteins and other participating molecules.
ReplyDelete1. Learned: this answered or addressed some of my questions from sniffers and buzzers.
2. Pressing ??: I'll try and give this another pass before class and see what's left.
3. Presentation: I'd be interested to see how complex these things can get.
4. Thoughts: I didn't like the quick math they used to justify their assumptions. I realize this can be necessary to overcome a glut of variables, but they provided little support for their use. My hangup with such assumptions is that when we accept something as a rule we may overlook the exceptions
0-1) Good
ReplyDelete2) Excellent!
3) They can get very complicated, to the point of not supporting fine-scale mechanistic understanding.
4) Let's check this out...
0: What I knew
ReplyDeleteI have a previously learned some of the biology that is modeled in this paper. For example, I am familiar with Michaelis-Menten kinetics, the biology of protein phosphorylation/synthesis/degradation, and feedback mechanisms in physiology.
1: What I learned
In the conclusion section of this paper, I got the opportunity to glimpse into the core structure/model (for each example) of the sniffers/buzzers paper as well as this one. Through the Dynamical Perspective, I learned how Tyson started with molecular mechanisms, and then derived kinetic equations from biochemical kinetics to describe them. Ultimately, the steady-state solutions of these equations can be understood beyond math through their function in physiology.
2: Pressing Question
When looking at complex biological systems that are regulated by organic/inorganic molecules, proteins, and other factors, how useful are these simplified differential equations in modeling different physiological processes?
3: Presentation Idea
Using molecular wiring diagrams to simplify biological phenomena like apoptosis or the cell cycle
4: Thoughts
I thought this paper was a good tool to further explain each of the different cases presented in the figures we are analyzing in class. There were some shortcuts taken in the figures we look at in class, and this paper clarified some of the questions I had when reading the initial Tyson paper with the figures we are analyzing.
0) Knew: This is kind of an expansion on the '03 sniffers & buzzers paper, so revisiting these concepts with a little more mathematical and biological background is familiar.
ReplyDelete1) Learned: I liked the discussion of assumptions in chapter 6.1. Depending on the time scale or set of macromolecules you are trying to model, the "well-stirred" and "number of molecules" assumptions may not hold true, which can be deterministic of the success of the model. I also appreciated the description of phase planes and vector fields, and how the ODE system follows these based on constants and initial conditions.
2) Question: The positive feedback loop in Figure 6.10 is said to exhibit hysteresis, or irreversibility. But if S is increased past Sc2, then lowered below Sc1, wouldn't X drop back to the lower steady state, allowing S to raise it along the lower curve again?
3) Presentation: I'd like to know how to account for the failure of assumptions like the "well-stirred bioreactor" and availability of molecules in developing these ODEs.
4) Thoughts: This was a good follow-up to Sniffers & Buzzers and helped solidify some of the concepts.
0) What I Already Knew: I have a decent background in these sorts of ODE models as I took a course in biophysics in the spring. The majority of the content we covered involved ODE systems such as these.
ReplyDelete1) What I Learned: I had not seen the delayed feedback oscillation network before. This example was also interesting as it included the levels of phosphatase.
2) Most Pressing Question. I have two actually. First, why is the level of phosphatase included in only the delayed feedback oscillator? Second, how do researchers accurately and precisely determine the kinetic constants for very chaotic systems?
3) Suggestion for Class Discussion: Methods of computationally solving differential equation systems.
4) Thoughts: I really liked this paper. It is very well-written and gives a detailed but not overwhelming overview of ODE modeling of molecular networks.
0) KNEW
ReplyDeleteI knew about general graphs from Sniffers and Buzzers. I had an idea of how the differential equations would play into those graphs. I also knew a bit about the underlying biology of some of the systems. I knew about the general shape of Michaelis-Menten graphs.
1) LEARNED
I came to understand that the nullclines are a product of phase-space. It was helpful to think back to math classes such as Multi-variable calculus and differential equations in order to see how these equations created such graphs. The sign of the derivative (rate of change of the species) determines whether feedback between two species is positive or negative.
2) QUESTION
If cells are constantly going through these wiring diagrams to produce all sorts of activity, I'm curious as to how few of these are necessary for a cell to survive. Do we have any guesses as to which evolved first?
3) PRESENTATION
I think that we could talk about bifurcation events
4) THOUGHTS
Overall, I thought this paper was very helpful in bringing to light a few concepts that I was unsure about after going through Sniffers and Buzzers. Of main importance was seeing how the nullclines and phase space lead to stable and unstable steady states.
0) Knew
ReplyDeleteThe approach of wiring diagrams and mathematical modeling.
1) Learned
Mutual antagonism is fairly unfamiliar to me and section 6.4.5 is a nice brief intro to it.
2) Question
3) Presentation
n/a
4) Thoughts
In a given system, what is the minimal number of participants that allows a continuous treatment using ODEs? What if we wanted to measure a quantity that is discontinuous? For instance, the rate of binding of a particular protein. Or perhaps we don't really care about what the individual participants are doing but rather the bigger scale phenomena...