Lecture 1

• 13:30: “Proteins are built as machines that can transition between states”
• E coli changes its composition according to its environment, how does it compute when to make a protein?

  • RNAp binds, transcribes to mRNA, which is translated into a protein.

  • Proteins called transcription factors represent the external environment internally to the cell.

  • transcription factors regulate transcription

  • “the cell has 300 degrees of freedom”

  • transcription factors have specific binding sites and when they bind, it “increases the probability” that the RNAp will do its thing.

    We use \(X \to Y\) to symbolize this entire interaction.

• This happens across several orders of magnitude in terms of timescales. The binding of a transcription factor to an environmental trigger is µs, TF to binding site is seconds, translation and transcription is minutes and finally, making it to “functional volume” is hours.
• The transcription factor binding site can, in humans, have as many as 20 TFs bound there, and the result of the binding is a probabilistic logic program.
• 31:40 “When you collect all the arrows, you get a graph.” GRN: Gene Regulation Network
• 34:42 “Evolution didn’t go to engineering school, but it still has understandable features”
  • In this he was talking about how when engineers build a system, they build it out of small parts that they understand. Apparently evolution did the same thing, regardless of its need to be understandable post facto. This was commentary on the fact that the parts are the same, designed for reuse across most species. This seems profound on its face, but the truth is that it is really that they are descendant from the same ancestors—single celled organisms, literal prototypes—of the massively complex multicellular organisms of today.
  • E coli’s order is ~4500, while \(|E|\) is ~10,000.
• The input function plots, given an \(X \to Y\), the rate of \(Y\) production given a certain \(X^*\) concentration?
  • \(X^*\) denotes the “activated” version of \(X\), \(\beta\) is max value / concentration, \(K\) is 50% activity / concentration and \(n\) is the “steepness” of the hill function, when \(N = 1\), this function is linear, when it’s \(\infty\), it’s a step function.
  • \(n\) is typically between 1 and 4.

\[ \cfrac{\beta (X^{*})^n}{K^n+(X^{*})^n} \]

• When a gene is bound by two TFs, it is a product of hill functions, but works like a AND or OR gate. Apparently we don’t know how to “systematically look at them”.
• Synthetic biology
• “circuits”—subgraphs of the larger network within a cell.
• A proteasome cuts a protein back up into amino acids.

\[ \cfrac{dy}{dt} = \beta - \alpha y \]

• This is for a function \(x \to y\), where \(\beta\) is the rate of production of \(x\), i.e., “signal”, and \(\alpha\) is the rate of degradation. This can be done via dilution or by direct degradation, via proteasomes.
  • In a steady state, \(\cfrac{dy}{dt}\) is \(0\), so \(\beta - \alpha y = 0\), so you have \(\cfrac{\beta}{\alpha}\)—production over removal.
• response time is dependent only on removal rate, there is math to explain this but I don’t understand it yet. He uses \(e\) in the equations and mentions an eigenvalue, but I don’t know what that is.
  • High response time is given by high removal, but this is expensive.
  • production of half the steady state of proteins is 1 generation, meaning that the cell reach steady state only to divide to give those proteins to its descendants. This problem will be the topic of the next lecture.