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1 Journal Club Jacqueline Barnes Mentors: Dr. Joel Stiles Dr. Markus Dittrich (

2 Hourglass Model for a Protein-Based Circadian Oscillator Eldon Emberly and Ned S. Wingreen

3 Background Cyanobacteria Circadian Rhythms Other Biological Oscillators

4 Cyanobacteria Early earth inhabitant Produced oxygen in the atmosphere Ancient life form, simple model ( ons/ser/snapshot-lake-waterqualitynov06/html/images/cyanobacteri a.jpg) (

5 Circadian Oscillators (Rhythms) Many organisms possess internal biochemical clocks, known as circadian oscillators, which allow them to regulate their biological activity with a 24-hour period. This was needed to adjust early life to the daily activity of sunlight. Now evolved, most are the result of negative feedback of DNA transcription (

6 Biological Oscillators Biochemical events are intrinsically stochastic, and this tends to desynchronize oscillating protein populations. (can be synched with something else) Bio. Oscillations are a rhythm or fairly regular fluctuation in some measure of activity. What do all of these have in common? Common example: Neural oscillations (movement and most sensory systems)

7 The Model The circadian oscillator of cyanobacteria is able to function in a test tube with only three proteins, KaiA, KaiB, and KaiC, and ATP. KaiC monomers are the main player. KaiA accelerates its phosphorylation while KaiB inhibits this phosphorylation. ATP binds to KaiC for the KaiC to form hexamers. It is used for energy.

8 Two sites of phosphorylation (two hands)

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10 KaiC Phosphorylation Cycle Two possible phosphorylation sites. MO monomers have both sites unphosphorylated (WHITE). MP monomers (GREY) have one site phosphorylated. M2P monomers (BLACK) have both sites phosphorylated. The monomers form hexamer rings. These rings exchange monomers and then form clusters when mostly phosphorylated.

11 KaiC Phosphorylation Cycle Rates of Phosphorylation/ Dephosphorylation KaiA/KaiB have no effect in clusters

12 Thesis of The Paper The Quantitative Hourglass Model Day night cycle behavior how how do the stochastic phosphorylations of the monomers form one clock? During the day, the KaiC hexamers exchange monomers (this is very fast, and necessary for robust oscillations). Formation of clusters which autodephosphorylate throughout the night, eventually breaking up, back into hexamers (and the clusters are necessary).

13 The Math dm0(t)/dt = 2αM0 + γmp + (NoNc Pmin)(Pmin+1)γCPmin+1 dmp(t)/dt = 2αM0 + 2γM2P αmp γmp +Pmin(Pmin+1)γCPmin+1 dm2p(t)/dt () = αmp 2γM2P NoNcβ [(m2p)^no*of]^nc dc2nonc(t)/dt = β(m2p)noofnc 2NoNcγC2NoNc dci(t)/dt = iγci + (i+1)γci + 1, i=pmin + 1,, 2NoNc 1

14 Change in Unphosphorylated dm0(t)/dt = Monomers 2αM0 + γmp + (NoNc Pmin)(Pmin+1)γCPmin+1

15 Change in Singly Phosphorylated dmp(t)/dt = Monomers 2αM0 + 2γM2P αmp γmp +Pmin(Pmin+1)γCPmin+1

16 Change in Doubly Phosphorylated dm2p(t)/dt = Monomers αmp 2γM2P NoNcβ *[(m2p)^no*of]^nc

17 Methods Mathematical model Test the equations Relate them to known biological i l behavior. (this does produce biologically accurate behavior..oscillations with a period of ~20h). Insensitive to protein concentration (this varies in cells). KaiA/KaiB KaiB appear to saturate. t

18 Results (Emberly, Wingreen, 2006)

19 Oligomer Size/Cluster Size (Emberly, Wingreen, 2006)

20 Conclusions/Future Research? Importance of collective assembly/disassembly of proteins in biochemical networks. Applications to other biological oscillators Question the evolution of oscillation? (where did DNA/RNA transcription come into play?)

21 ..My Research From these equations (and given rates, not shown), I determine the reactions and reaction rates involved in this model. Put those reactions and rates into Mcell. Check rates, find a way to put in a time dependent rate. Model the results in Dreamm, or plot concentrations, to determine oscillation. Change parameters to manipulate the oscillation?

22 Questions? Thank you Reference: Emberly, Eldon, Ned S. Wingreen. Hourglass Model for a Protein-Based Circadian Oscillator. Physical Review Letters January 27; 96(3):