1. A Tale of Three Inferences
Models of transcription and their consequences
Philip Benfey, Ken Birnbaum, Dennis Shasha

2. What is the Logic of Transcription?
Known: transcription factors bind to small subsequences of DNA, perhaps in a statistical mechanical (hence concentration dependent) way.
Controversial: interaction among different transcription factor-binding events.

3. Models of Interaction
Additive (Boolean OR): For promoter P on gene G, if T1 binds to c1 and T2 binds to c2 in an inductive way, then the expression of G will remain the same if the promoter were to have twice the number of c1 and c2 goes to 0.
Boolean AND: Under same conditions, there will be no expression

4. Classical Approach Detailed nature of interaction is unknown.
Find genes whose expressions correlate well with one another.
Infer that common motifs among the promoters of those genes must be the binding cis-elements.

5. Note to ken
Ken, please include a power point slide in which you show how this correlation method is meant to work.

6. Bussemaker, Siggia, et. al
Model: expression of a promoter is:
S coef * number, where coef[j] is the strength of the jth transcription factor-cis-element binding and number[j] is the number of times the cis-element appears.
Additive, Boolean disjunctive model.
No explicit model of transcription factors.

7. Bussemaker Discovery
Consider one experiment consisting of many gene-promoter pairs some of which are expressed.
Best cis-element (largest coefficient) is one that appears in promoters of many expressed genes and few unexpressed genes (inversely weighted by number of appearances per promoter)

8. Bussemaker Example Promoter 1: x, x, x, y. Expression: 1
Promoter 2: x, y. Expression 1.
Promoter 3: x, y, y, y. Expression 3.
Conclude: best hypothesis is that each y contributes to expression with a coefficient of 1. No good model for x.

9. NYU (Birn,Benf,Sha) Model
Transcription factor/cis-elements form a boolean (AND/OR/NOT) model with amplifiers (e.g. TFA & TFB ==> TFC)
Finding these circuits is a multi-stage affair: 1) find cis-element/transcription factor pairs 2) infer boolean circuit by seeing combinations that work.

10. NYU Find TF/Cis-element pairs
Given the knowledge of genes that encode transcription factors and given a sequence of experiments (e.g. different times during sporulation), find cis-elements that correlate best with transcription factors over time.

11. NYU Model Details
Cis-element c expression at time t = sum of expression of genes containing c in their promoter sequence.
Transcription X expression at time t = extent of RNA production at time t.
X binds to c potentially if two time sequences correlate well.

12. Note to Ken
Ken, please put in our experiment with promoters A, B, C such that first promoter has AB, second has AC, and third has BC. First time has TA, TB; second time has TA, TC; and third time has TB, TC.
Gene correlation doesn’t work.
Bussemaker only partly works.