Genetic transcription and regulation
Central dogma of biology DNA codes for DNA DNA codes for RNA RNA codes for proteins not surprisingly, many points for regulation of the process
https://www.youtube.com/ watch?v=2lnxpavug0y DNA codes for DNA replication fork Okazaki fragments - 100-200 nucleotides long in eukaryotes, 10x longer in bacteria! replisome error rate is 1 in 10 8-10 10 bp!
DNA codes for RNA Why the need for a messenger? RNA is more flexible additional regulation RNA polymerase Roger Kornberg received the 2006 Nobel Prize (Chemistry) for structures DNA is sequestered in the nucleus in eukaryotes (protected) and... AMPLIFICATION
DNA codes for RNA Can get MANY copies simultaneously from the same DNA strand
Transcription starts at a promoter promoter is a sequence recognized by the polymerase upstream of the transcription initiation site consensus sequence in bacteria: TATAAT @ -10 bps and TTGACA @ -35 bps (always just a fraction present though!). RNA polymerase is promiscuous, can bind non-specifically but with lower energy. Variation in promoter sequence can lead to strong or weak promoters. Transcription factors are often required for binding p bound = 1 1+ N NS P eβ ϵ pd PBoC 6.1.2
the lac operon operon is just a cluster of genes with one promoter repressor binding site no lactose promoter sequences activator binding site no glucose PBoC 4.4.1
Gene regulation PBoC 4.4.3 genes can be regulated by controlling polymerase access to promoter gene repression gene activation about 10% (1500-3000) of our genes code for transcription factors!
Gene activation instead of two, now have four distinct states also have three relevant interaction energies (P-DNA, A- DNA, P-A) What is pbound for the promoter? p bound = 1 1+[N NS /P F reg (A)]e β ϵ pd F reg (A) = 1+(A/N NS)e β ϵ ad e β ϵ ap 1+(A/N NS )e β ϵ ad PBoC 19.2.2
Genetic switches a genetic switch is a repressor and the gene it controls most interesting are cases where two genes regulate each other s expression in a feedback loop PBoC 19.3.5
Genetic switches p bound (c 1 )= K bc n 1 1+K b c n 1 Hill function - n is cooperativity, i.e., number required for reaction r r(1 p bound (c 1 )) = 1+K b c n 1 r is basal (default) rate in absence of repressor degradation rate basal rate of production dc 1 dt = γc 1 + r 1+K b c n 2 du dt = u + α 1+ν n dc 2 dt = γc 2 + r 1+K b c n 1 due to repression dν dt = ν + α 1+u n PBoC 19.3.5 make dimensionless by change of variables
Genetic switches du dt = u + dν dt = ν + α 1+ν 2 α 1+u 2 assume n = 2 (clever algebra) steady state (u 2 αu +1)(u 3 + u α) =0 switch-like: concentrations are inversely related (u 2 αu +1) two zeroes for α > 2 ν + 1 u =0 uν =1 (u 3 + u α) PBoC 19.3.5 one real zero u = ν not switch-like! (concentrations are always the same)
Stability analysis u u + δu ν ν + δν d dt ( δu δν ) = A ( δu δν ) A = ( 1 f (ν ) f (u ) 1 - f (x) = nαxn 1 (1 + x n ) 2 ) Solution (sum of exponentials) determined by the eigenvalues of A λ 1,2 = 1 ± f (u )f (ν ) if eigenvalues are negative (positive), solution decays (diverges) over time f (u )f (ν ) < 1 required for stability α = rk 1/n b /γ PBoC 19.3.5 α- a combination of basal rate of production, repressor binding constant, and degradation rate - being greater than some critical value determines if switch-like behavior is observed
Stability analysis vectors denote (du/dt, dv/dt) α = r Kb 1/n /γ α = 1 α = 3 filled - stable unfilled - unstable stable Stable equilibrium for α > 2, observe bistable behavior (two dominant states) unstable stable PBoC 19.3.5
Genetic circuits and clocks Synthetic circuit could be used to, e.g., report on concentrations of multiple chemicals in environment Moon, et al. Genetic programs constructed from layered logic gates in single cells. Nature. 491:249-253 (2012). Genetic clock the regulated expression of multiple genes generates ~24h molecular oscillations establishing the circadian rhythm Ko, Takahashi. Molecular components of the mammalian circadian clock. Human Mol. Genetics. 15:R271-277 (2006). 2017 Nobel Prize in Physiology or Medicine awarded to Jeff Hall, Michael Rosbash, & Michael Young