Model base and main assumptions
As described in Background, our model is a simplification of the in vivo viral system, in the sense that it only involves promoter control by two transcriptional factors, EBNA-1 and Oct-2, with co-factors. The premise is that other regulatory factors documented in the literature, are less important as concerns the basic properties of the switch.
Regarding DNA binding of transcription factors to DNA, particularly to the FR region, the model assumes independent binding of both EBNA-1 and Oct-2. Moreover, bound proteins exclude only other bindings at that specific site, but do not affect neighbouring sites The octamer sites found in FR suggests a monomer binding of Oct-2, which we assume in our model, although the possibility of dimer bindings cannot be ruled out. The system is modelled with one kinetic equation, describing the dynamics of EBNA-1, coupled with thermodynamic equilibrium probabilities for transcription factor binding, to estimate transcription rates from Cp and Qp. As no regulation of Oct-2 levels by viral factors is known, Oct-2 level are essentially an external parameter to the model. The dynamics is modelled deterministically, disregarding noise in the transcription and translation (see Discussion). Details concerning parameter estimates are discussed in the following section.
Parameters
It is evident that all modelling results depend on the parameters used, resulting in a demand for exact parameters, or good estimates based on experimental studies. In Table 1 we list the parameters used in this study. These include the EBNA-1 dimerization constant, DNA binding dissociation constants, steady state level of EBNA-1 in latency III together with EBNA-1 half-life time, cell division time and the volume of the system.
Of central importance in this model are the binding affinities for our transcription factors to the FR region and Qp sites. The dissociation constant for EBNA-1 binding to FR and the relative dissociation constant for the Qp sites was determined by Ambinder et al., 1990. Their experimental results give a dissociation constant, K
dEFR
, for EBNA-1 from FR that is 15 pM and a K
dQ
from the Qp binding sites that is 14 times higher [39]. Regarding EBNA-1 dimerization, EBNA-1 is known to be in dimer form in solution and bind DNA as a dimer [40], but the exact dimerization constant has however not been experimentally determined. We have used a K
dE
value of 1 nM as reference value, but varied this parameter to examine its impact on the system.
Oct-2 belongs to the POU family of proteins, which share two distinct DNA-binding subdomains; a POU-specific domain and a POU homeodomain. The ATGC half of the octamer sites is recognized by the POU-specific domain, and the homeodomain binds to the AAAT half [41]. Oct proteins therefore bind octamer sites as monomers, although they are able to form dimers and bind to similar palindromic sites known as MORE and PORE. In the FR region, the binding sites present are octamer-like; hence Oct-2 is assumed to bind as a monomer. The Oct-2 dissociation constant for the consensus octamer site, ATGCAAAT is known to be 2.5 nM [41]. The octamer sites in FR are however not perfect, and most sites noticeably have an A6G variant in the last half of the sequence, and at least two base exchanges in the first half. From published mutational analyses of Oct-2 and Oct-1 octamer sites we can however deduce that the homeodomain generally has a higher binding affinity that the POU-specific domain, and that an A6G mutation does not dramatically affect the affinity [41, 42]. The dissociation constant of the Oct-2+Grg/TLE complex to sites within FR, K
dOFR
, is therefore here assumed to be 2.5 M but the effects of a higher dissociation constant was also tested.
The transcription rates for Cp and Qp and the translation rate for EBNA-1 transcripts are not experimentally known. As our model does not describe the transcription and translation steps individually but uses a total production rate, we incorporate both rates into one. Estimation of this production rate comes from experimentally determined steady state levels of EBNA-1 in latency III cell lines. Sternås et al. measured these EBNA-1 levels to range from 25,000 to 44,000 with an approximate mean value around 34,000 [43]. This roughly corresponds to a production of 34,000 new EBNA-1 proteins every cell cycle, when production is balanced by dilution and degradation of EBNA-1.
The exact half-life of EBNA-1, τ
1/2, is not known, but experiments indicate that it is at least 48 hours, probably due to the Gly-Ala repeat domain which inhibits proteasomal degradation [44, 45]. In our study we have hence chosen a half-life of 48 hours, and the cell division time is set to be 24 hours [46]. The model assumes an homogeneous distribution of molecules in the system and does not include spatial movements between different cellular compartments. EBNA-1 is mostly located in the nucleus, due to its functions in transcriptional and translational control [47]. Our system volume therefore corresponds to the nuclear volume of B-cells, a spherical volume with a diameter of 7 μ m [48].
Physico-chemical model
The EBNA-1 dynamics is studied with a non-linear differential equation, (Eq. 1) describing production of EBNA-1 (E) from both promoters, Cp and Qp, protein degradation and also dilution, in the case of proliferating cells. The production from Cp is computed as the probability of gene transcription P
c
, times the rate of protein production r
c
(including transcription and translation), and likewise for Qp. Dilution is computed with a continuous dilution rate r
dil
, for cells that are in proliferating state. Degradation is computed with the continuous degradation rate r
deg
. The switch from resting to proliferating state is modelled instantaneously, meaning that the dilution rate is turned on as soon as Cp activity is higher than Qp activity, although in the real cell there is probably some delay. The total number of EBNA-1 molecules, E
tot
, in the system includes the free monomers, E, the dimers, E
d
, and the dimers bound specifically to DNA, E
DNA
, (Eq. 2). E
DNA
is computed as the mean value of bound EBNA-1 dimers and has to be calculated iteratively from the binding probabilities at each time step of a dynamic simulation, since it is dependent on the dimer concentration. The kinetic equation for EBNA-1 then reads;
(1)
where E
tot
is defined as;
E
tot
= 2E
d
+ E + 2E
DNA
Transcriptional probability
The promoter transcription probability is computed from the probability of having a combination of transcription factors bound at the operator that allows for transcriptional activation. Full activation of Cp requires at least eight bound EBNA-1 dimers out of the 20 available sites at FR [14, 15]. The independent binding of EBNA-1 and Oct-2+Grg/TLE means treating the 40 separate sites as 20, where each site can be occupied by either EBNA-1 or Oct-2+Grg/TLE. The transcription activity of Qp is dependent only on the EBNA-1 level, where transcription is blocked when one or two EBNA-1 dimers are bound.
In thermodynamic models, the probability of a certain combination of bound complexes is evaluated from the Boltzmann weight, Z, describing that state normalized with the sum of the weights for all possible states, Z
tot
. For FR, the statistical weight of having n EBNA-1 and k Oct-2+Grg/TLE bound to the N number of sites, Z
nk
, depend on the binding free energies of EBNA-1 and Oct-2+Grg/TLE, E
eFR
and E
o
, to their specific DNA sites, the concentrations of EBNA-1 and Oct-2+Grg/TLE, [E] and [O], and the number of different possible binding combinations that state can occur (Eq. 3). In the case of statistical weights for Q promoter activity, these are computed in the same manner, only dependent on EBNA-1 free energies, E
eQ
, and concentration [E] (Eq. 4). The number of binding sites, N, is 20 for FR and 2 for Qp.
(3)
(4)
Experiments
Western Blot
Protein concentration of nuclear extracts of latency I and III cells was determined by Bio-Rad Dc protein assay (Bio-Rad, Hercules, CA). The same amount of nuclear extract was loaded on every lane. Proteins were fractionated by 9% sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) and transferred to nitrocellulose membranes. After blocking for 1 h at room temperature with 5% milk, made up in PBS- 0.1% Tween 20 (PBST), the membranes were probed overnight at 4°C with the following antibodies at indicated dilutions. Anti Beta-Actin (Sigma) was used as second protein control; Oct-2 (Santa Cruz Biotechnologies, Santa Cruz, Calif.) were used at 1:2000 and anti- EBNA1 used at 1:1000 (OTX-1, a kind gift from Jaap Middeldorp, Amsterdam Free university). The second antibody used was horseradish peroxidase-conjugated (HRP) and bound immunocomplexes were detected by enhanced chemiluminscence (ECL; Amersham Life Science, Little Chalfont, Buckinghamshire, United Kingdom).
Chromatin immunoprecipitation assay (ChIP)
2 * 106 EBV latency type I Rael cell or latency III CBMI-Ral-Sto cell were collected. Proteins were cross-linked to DNA by adding formaldehyde to 1% of culture medium. Cell pellets were collected after 10 min incubation at 37°C. The cell pellets were resuspended in SDS lysis buffer, DNA sheared to 500–1000 bp by sonicating the lysate. The sonicated samples were diluted 10 fold and 2 ug of immunoprecipitating antibody was added respectively: OTiX, mouse monoclonal antibody anti EBNA1, (kindly provided by Dr Jaap Middeldorp, Amsterdam), anti-OCT2 (C-20); rabbit polyclonal antibody, Santa cruz Biotechnology, California; Goat polyclonal antibody Santa cruz Biotechnology, California, and rotated at 4C overnight. 100 ul of salmon sperm DNA/protein A agarose -50% slurry was added to collect antibody/protein/DNA complex. After washes and elution, the complexes were reverse crosslinked by adding sodium chloride to final concentration 0.2 M and kept at 65C for at least 6 hrs. Proteins were digested by proteinase K then DNA was purified by phenol/Chlorofome/ethanol precipitation. PCR primers were FRjz1S: TCCCTCTGGGAGAAGGGTAT and FRjz1A:TTTTCGCTGCTTGTCCTTTT for family of repeats (FR). For control experiments to exclude non-specific binding of antibodies to DNA, the immunopreciptated DNA was analyzed with primers to beta-actin: AC-S:
ATCATGTTTGAGACCTTCAA and AC-A: CATCTCTTGCTCGAAGTCCA. DNA from latency III cell lysate (Mutu III) was immunopreciptated with 4 ug of anti-Oct2 or 4 ug of anti-EBNA1 and amplified by PCR with primers to beta-actin. Water and reaction without antibody was used as negative controls, while cell lysate DNA prior to immunopreciptation was used as positive control.