ࡱ > J L I 5 bjbjRR 0 0 0 + W
c c c c c w w w w 8 K , w S- w : S S S " " " , , , , , , , . 1 | , c " " " " " , % c c S S \
- % % % " c S c S R( % " , % % ' c c ' `Pn w I% v ' ( 4 #- 0 S- ' , 3 % 3 ' % ' c ( " " "
) :
Choice of activation and repression term in Eq. (5) in the main text
Transcription of the kaiBC mRNA is based on simple activation and simple repression showcased in Table 1 from Bintu et al. ADDIN EN.CITE Bintu200542824282428217Bintu, L.Buchler, N. E.Garcia, H. G.Gerland, U.Hwa, T.Kondev, J.Phillips, R.Physics Department, Brandeis University, Waltham, MA 02454, USA.Transcriptional regulation by the numbers: modelsCurr Opin Genet DevCurr Opin Genet Dev116-241522005/03/31*Gene Expression RegulationHumans*Models, Theoretical*Thermodynamics*Transcription, Genetic2005Apr0959-437X (Print)
0959-437X (Linking)15797194http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=15797194S0959-437X(05)00030-4 [pii]
10.1016/j.gde.2005.02.007eng[1]. We further assume that the transcriptional activator and the transcriptional repressor have opposite effects on kaiBC expression and they, therefore, do not compete for the same binding site upstream of the kaiBC promoter. Bintu et al. explain transcriptional control from a thermodynamic point of view such that interactions of activators, repressors, RNA polymerase and protein-protein interactions regulating gene expression are described by a single regulation factor (Freg). Simple activation can thus be described through the mathematical form of expected fold-change of gene expression
EMBED Equation.DSMT4 .
The parameters are the effective in vivo dissociation constant (KA) between the activator and a promoter region and the enhancement factor ((), which characterizes the degree of stimulation in transcription.
In this study, the simple activation involves a phospho-state of KaiC (U, T, D or S) from the hexamer pool, CH (see Methods). Case 2 in Table 1 ADDIN EN.CITE Bintu200542824282428217Bintu, L.Buchler, N. E.Garcia, H. G.Gerland, U.Hwa, T.Kondev, J.Phillips, R.Physics Department, Brandeis University, Waltham, MA 02454, USA.Transcriptional regulation by the numbers: modelsCurr Opin Genet DevCurr Opin Genet Dev116-241522005/03/31*Gene Expression RegulationHumans*Models, Theoretical*Thermodynamics*Transcription, Genetic2005Apr0959-437X (Print)
0959-437X (Linking)15797194http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=15797194S0959-437X(05)00030-4 [pii]
10.1016/j.gde.2005.02.007eng[1] gives the mathematical form of the expected fold-change with
EMBED Equation.DSMT4
and X = HU, HT, HD, HS, HP.
For simplicity, KA was set to 1 resulting in
EMBED Equation.DSMT4 .
The mathematical form for simple repression is given by
EMBED Equation.DSMT4
with
EMBED Equation.3 and Y = HU, HT, HD, HS, HP, BU, BT, BD, BS, BP.
Here, the simple repression involves a phospho-state of KaiC (U, T, D or S) from the hexamer pool, EMBED Equation.3 , and from the KaiBC pool, CB (see Methods).
The dissociation constant KR was set to 1 as well resulting in
EMBED Equation.3 .
Activators and repressors function at different times. Defining now that k1bc and k3bc are the transcription rate and degradation rate, respectively, transcription of kaiBC mRNA can be written as
EMBED Equation.DSMT4 ,
which is identical to equation (5) of the manuscript.
Optimization process
In order to investigate whether a two-loop feedback model sufficiently explains the data we fitted each model to the measured data points derived from our own image analysis of Figure S2 from Murayama et al. ADDIN EN.CITE Murayama200841894189418917Murayama, Y.Oyama, T.Kondo, T.Division of Biological Science, Graduate School of Science, Nagoya University, Furo-cho 1, Chikusa-ku, Nagoya 464-8602, Japan.Regulation of circadian clock gene expression by phosphorylation states of KaiC in cyanobacteriaJ BacteriolJournal of BacteriologyJ Bacteriol1691-819052008/01/01Bacterial Proteins/*genetics/metabolismBlotting, NorthernBlotting, WesternCircadian Rhythm/*genetics*Gene Expression Regulation, BacterialIsopropyl Thiogalactoside/pharmacologyKineticsPhosphorylationPromoter Regions, GeneticRNA, Messenger/genetics/metabolismSynechococcus/drug effects/*genetics/metabolismTranscription, Genetic2008Mar1098-5530 (Electronic)18165308http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=181653082258689JB.01693-07 [pii]
10.1128/JB.01693-07eng[2], using a least-squares method. The values are given in Table S1. The cost function to be optimized is the sum of the least squares
EMBED Equation.DSMT4 (S1)
with
R = kaiBC mRNA,
U = unphosphorylated KaiC Protein/total KaiC, and
P = total phosphorylated KaiC protein/total KaiC.
Binomial distribution
The following binomial distribution is to show that using homogenous phospho-states of KaiC as responsible for the feedback regulation is a reasonable assumption.
We assume that every hexamer that contains threonine phosphorylated KaiC will contribute to the transcriptional feedback. (This is analogous for double phosphorylated, serine phosphorylated and unphosphorylated KaiC hexamers.) The probability for a hexamer EMBED Equation.DSMT4 T-KaiC and EMBED Equation.DSMT4 U-kaiC, D-KaiC or S-KaiC is a binomial distribution (special version of Eq. S16 in ADDIN EN.CITE Brettschneider201042184218421817Brettschneider, C.Rose, R. J.Hertel, S.Axmann, I. M.Heck, A. J.Kollmann, M.Institute for Theoretical Biology, Humboldt Universitat zu Berlin, Berlin, Germany.A sequestration feedback determines dynamics and temperature entrainment of the KaiABC circadian clockMol Syst BiolMol Syst Biol38962010/07/162010Jul 131744-4292 (Electronic)
1744-4292 (Linking)20631683http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=206316832925524msb201044 [pii]
10.1038/msb.2010.44eng[3])
EMBED Equation.DSMT4 (S2)
We further assume that i T-phosphorylated KaiC lead to an i-fold binding affinity in comparison to a hexamer containing one T-phosphorylated KaiC. This expectation value of a binomial distribution reduces to
EMBED Equation.DSMT4 . (S3)
We therefore conclude that the binding affinity to the promoter is proportional to EMBED Equation.DSMT4 .
Simulations of kai mutants
In Figure 4 in the main text, overexpression of the kaiA gene induced at time of minimal kaiBC expression was simulated. For example, we have modeled an oxkaiA mutant by a 10-fold higher transcriptional rate
EMBED Equation.DSMT4
EMBED Equation.DSMT4 .
We have further introduced the heaviside function:
EMBED Equation.DSMT4
EMBED Equation.3
The KaiC translational rate k2bc(t) has been simulated analogously (Figures 5, S11).
References
ADDIN EN.REFLIST 1. Bintu L, Buchler NE, Garcia HG, Gerland U, Hwa T, et al. (2005) Transcriptional regulation by the numbers: models. Curr Opin Genet Dev 15: 116-124.
2. Murayama Y, Oyama T, Kondo T (2008) Regulation of circadian clock gene expression by phosphorylation states of KaiC in cyanobacteria. J Bacteriol 190: 1691-1698.
3. Brettschneider C, Rose RJ, Hertel S, Axmann IM, Heck AJ, et al. (2010) A sequestration feedback determines dynamics and temperature entrainment of the KaiABC circadian clock. Mol Syst Biol 6: 389.
PAGE \* MERGEFORMAT10[Text S1 Hertel et al.]
Text S1 Hertel et al.
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