Today’s discussion began by working out some of the confusion surrounding Question 4.2 regarding probabilities and viral genomes and of course a short discussion regarding Mythbusters and mirrors.
Moving onto actual topics we looked into the solution of Equation 4.22 regarding relaxation of concentration jumps. It was stated that anytime a rate of change depends on what is physically present it is an exponential function; examples are radioactive decay or bacterial culture growth. The solution ∆c (t) = ∆c(0) e ^(-t/τ) can be used to calculate concentration differences over time where the concentration jump is an initial condition. The derivation of this solution was supplied by Mitch and if you really want a copy of it let me know. Berg’s textbook was also mentioned as it has an interesting calculation for the number of surface receptors that are required for oxygen saturation in a cell.
We next discussed Figure 4.11b and how a uniform concentration gradient could be maintained (wouldn’t it eventually equilibrate?). The answer was no... If you have a source and sink setup for example a single bacterium (sink) in a lake (infinite oxygen source). In this type of arrangement a constant concentration equals a constant flux. It was stated that entropic forces follow probability and an article was mentioned regarding the derivation of Ficks law and the statistics behind it.
We considered the restraints of dihedral angles, atomic repulsion, etc of proteins when modelling polymers in a random walk, what would happen if you added more constraints and whether a random walk is a good model.
Matt described how it is possible to model a polymer with a random walk. As the atoms themselves ‘jitter’ independently leading to the random movements of a walk. However Mitch stated that a random walk did not account for electrostatics within the polymer, and would thus underestimate how quickly to same-charge atoms would more apart. Seth somewhat settled the debate by stating that the addition of more constraints would change the distribution because you know more about the system. A random walk assumes probability is the only thing that matters whereas a protein will interact with itself. Thus protein folding is not accurately modelled by a random walk. However you can use a random walk with a funnel to be more accurate. But as Calvin pointed out this introduces problems with local minima. If protein folding was a random walk it would be another Levinthals Paradox. This is avoided however in cells because they employ mechanisms to ensure fast, correct folding (such as the addition of sugar molecules to the protein sequence to influence local folds). These mechanisms in turn make secondary structure prediction even harder than just going from sequence to protein. Interestingly many proteins have a 2 state folding. In that they are either unfolded or folded.
During the protein discussion we diverged into how Boltzmann’s distribution is used mainly in terms of temperature and not energy (a dirty trick of thermodynamic reasoning). Explained by the following.
P(E) = e^(-BE)/Z Probability of energy existing
Z = Σe^(-BE) Sum of all possible energies
B= 1/Kb*T Easy to think of Z(B)
It is also evident when thinking of equilibrated systems. If A is in equilibrium with B what is equal is the temperature.
We were introduced to another member of the committee, Ross and some points of the course profile were cleared up. It was decided that the assignment marking for Chapter 1 went to Mitch, Chapter 3 to Matt and Chapter 4 to Heather. The scientific paper discussions will be held in the last week of semester and your paper selection needs to be verified beforehand. In preparation for the final exam we will be given a copy from last year. The problems will be quantitative, involving calculation questions not short answer topics. Also the blog posts can be less of the philosophical questions and more just pointing out important equations and concepts of the text.
Friction of table vs water.
It was decided (after much debate, placing of hands flat out on the table and the mention of cold weather, metal poles and tongues) that it was not necessarily due to van der Waals interactions but mainly that the table is rigid. Meaning that self-diffusion in the table is zero which leads to higher friction.
How long is a long run?
To explain this Central limit theorem was introduced.
Fractional error = 1/sqrt(N)
Therefore 10 runs, 1/sqrt(10) ~ 30% error
The gas law has this built in as you are dealing with 10^23 atoms, however you can’t talk about individuals very accurately.
And ending today’s long report remember: Fluctuations matter in small systems, that is what Biophysics is about.