Rationale for modeling and modeling tools

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Understanding a biological system

What does it mean to understand something?

  • A theoretical description that captures broad principles but can also be applied in many specific instances.
    • For example, physical laws
      • Newton’s laws of motion
      • Einstein's General Theory of Relativity
  • Simplifications possible in many physical systems:
    • Can separate one "layer" of description from another
      • For example: center of mass of a ball is sufficient to describe its trajectory in response to an applied force; can initially ignore its molecular composition
  • What is the reason that it is difficult to do this for biological systems?
    • Multiple levels of description:
      • Molecular level
      • Cellular level
      • Organ level
      • Organismal level
      • Population level
        • Example: Sickle cell anemia
          • Single mutation, changes a glutamic acid to a valine (a different amino acid)
          • Under low oxygen conditions, the hemoglobin aggregates, causing red blood cells to take on a sickle shape
          • Having a double dose of the mutation is lethal; a single dose improves resistance to malaria, so the mutation persists
          • Note that understanding the disease requires understanding the system at the molecular, cellular, organismal and population levels
    • Variability
      • This is an intrinsic feature of biological systems.
      • Darwin's revolution: variation is the signal, not noise; there is no such thing as an "ideal" species.
      • This variation makes it hard to be sure that a description of an "average" individual captures essential information.
      • For example, in the future, medical treatments may be tailored to a particular individual.
    • Differential Penetrance
      • Sometimes, small changes can have a major impact.
      • At other times, large changes can have very little impact.
      • Physical example: predict whether adding a grain of sand to a sand pile will trigger an avalanche or not.
      • Importance of mechanistic and "level crossing" models

Rationale for modeling biological systems

  • Why bother making a model if you can do an experiment?
  • Mastering complexity
    • Imagine a ball on a spring hanging from the ceiling, and assume that it is initially at rest
    • What would happen if you pulled the ball down?
    • We can "run this experiment in our heads"
    • Now imagine that the room was filled with balls and springs, all interconnected
    • Could you predict what would happen next?
    • If a system is sufficiently complicated, may not be able to "run it in your head"; models become critical
    • Note the vital role that modeling plays in engineering disciplines - designing a plane, a space ship, or a bridge
  • Resource limitations
    • May not be feasible to run an experiment (time, cost, number of subject);
    • A model allows us to try many "what if" scenarios much more quickly
  • Ethical considerations
    • Cannot determine infectiveness of an agent by infecting a population of people; but can explore this in a model

Approaches to modeling biological systems

  • Importance and value of qualitative understanding
    • Value: "A feeling for the organism"; deep insights into how it works, basis for design of ingenious experiments
    • Limitations of qualitative approach: No quantitative predictions; may be possible to "fudge" explanations, especially if values are close
  • Importance and value of quantitative understanding
    • Ability to predict outcome of specific experiments (example of placebo effect - is effect significant or not?)
    • Limitations: Problem if model is as complicated as original system
  • Importance and value of mathematical understanding
    • Ability to prove theorems; broad application to any phenomenon with the same underlying mathematical structure
    • Limitations of mathematical approach: analytical tractability may require sacrifice of details that matter for quantitative predictions about an actual system

Modeling tools

  • Programming languages
    • Pro: Full control
    • Con: Overhead for setting up interface
  • General purpose modeling tools
    • Examples: Matlab, Mathematica, Maple
    • Pro: Useful built-ins; can prototype quickly; platform independence
    • Con: May be slower than programming language
  • Special purpose modeling tools
    • Pro: These tools make it very easy to set up simulations in specific area
    • Cons: May be harder to modify; May be extremely hard to use it for something it was not designed to do

Publication of a Model Developed in Dynamics of Biological Systems

  • Priscilla Ambrosi took the course in Spring 2012.
  • She chose to replicate a model of embryonic development in Drosophila.
  • She was working in Dr. Claudia Mizutani's lab, and Dr. Mizutani realized that the model could help studies of embryonic size in different Drosophila species.
  • Priscilla therefore extended the model so that it could deal with the different geometries of different species of embryos.
  • She found that features of the Toll signaling gradient interacted with the cell numbers and sizes to generate the different sized embryos.
  • Priscilla's paper can be found here.