Molecular BioSystems View Article Online
Published on 22 February 2016. Downloaded by LA TROBE UNIVERSITY on 01/03/2016 19:55:57.
PAPER
Cite this: DOI: 10.1039/c6mb00044d
View Journal
Stabilization of epigenetic states of CpG islands by local cooperation Giulia Sormani, Jan O. Haerter, Cecilia Lo ¨ vkvist and Kim Sneppen* DNA methylation of CpG sites is an important epigenetic mark in mammals. Active promoters are often associated with unmethylated CpG sites, whereas methylated CpG sites correlate with silenced promoters. Methylation of CpG sites must be generally described as a dynamical process that is mediated by methylation enzymes, such as DNMT1 and DNMT3a/b. However, there are several models of how CpG sites can be protected from methylation and thereby remain unmethylated. In this paper we examine the combination of both: the positive feedbacks of DNA methylation and a short range
Received 19th January 2016, Accepted 17th February 2016
counterpart which in turn protects—and thereby maintains—the unmethylated state. The emergent
DOI: 10.1039/c6mb00044d
cooperative protection of one CpG site by another in favor of unmethylated CpG sites. Our results
www.rsc.org/molecularbiosystems
suggest that this synthesis of mechanisms provides equally robust maintenance of both the unmethylated and methylated states of CpG islands.
dynamics is provided by collaborative, re-enforcing feedbacks in favor of methylated CpG islands and
1 Introduction Epigenetics is the phenomenon of cells persistently maintaining different states of gene expression, in spite of otherwise identical DNA exposed to the same environment.1,2 In physics terms this means bistable gene expression, where stability of both expression states is found to be sufficiently robust to be maintained across cell divisions. In physics terms this means that the expression pattern of a genetic system can be in two different and well-separated states, i.e. the genetic regulatory system is bistable. Epigenetics further implies that the bistability is sufficiently robust to maintain the uniqueness of each of these states across cell divisions. trans-Mediated epigenetics is typically maintained by diffusing transcription factors. cis-Mediated epigenetics, in contrast, refers to the subset of epigenetic systems that are able to maintain their distinct states using only a localized region on the genome. cis-Mediated epigenetics thereby relies on positive feedback mechanisms that act within a relatively short region of DNA.3 An example of a cis-mediated epigenetic system is one that is mediated through read–write enzymes that act on nucleosomes, which in turn recruit these read–write enzymes to influence other nucleosomes.4–10 A nucleosome is a protein complex that packages eukaryotic DNA, typically a stretch of approximately 200 base pairs (bp). Nucleosomes can change their epigenetic state: while one state prevents the associated genomal region from gene transcription, another state may allow transcription. Center for Models of Life, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark. E-mail: [email protected]
This journal is © The Royal Society of Chemistry 2016
For example, when nucleosomes are methylated at the amino acid position H3K9, DNA transcription is repressed. In contrast, for acetylated nucleosomes, transcription is not repressed.11,12 Another cis-acting epigenetic mechanism is tied to the particular states of the cytosine–phosphate–guanine dinucleotide sequence, termed as the CpG site. Methylation of a given CpG site along the DNA results from a methyl group being attached to both cytosine nucleotides of the two complementary CpG pairs. Thus a CpG site in fact consists of two complementary base pairs CG and GC. For CpG sites on the DNA surrounding promoters13 which are dominantly methylated, promoter activity is silenced, whereas promoters covered by persistently unmethylated CpG sites tend to be transcriptionally active.14–18 The methylation patterns are maintained and restored throughout cell generations even though the methylated DNA is replicated and new initially unmethylated DNA-strands are synthesized and hemimethylated double stranded DNA is formed in both daughter strands. (A fully methylated CpG site has both strands methylated, whereas a hemimethylated CpG site only has one of the two cytosines methylated.) CpG sites are distributed intermittently on the DNA, either within CpG islands (CGIs), where CpG sites are typically densely spaced (E10 bp apart), or in larger genomic regions outside CGIs—termed as open sea—where site separation is typically an order of magnitude larger.19,20 While CpG sites in the open sea are mostly methylated, those within CpG islands are often either completely methylated or completely unmethylated.21,22 Methylation is found to be anti-correlated with CpG density: higher density means lower methylation.14,23 In fact, analyzing all CGIs in the human genome, we recently found that small CGIs, i.e. those containing
Mol. BioSyst.
View Article Online
Published on 22 February 2016. Downloaded by LA TROBE UNIVERSITY on 01/03/2016 19:55:57.
Paper
less than ten CpG sites, are persistently methylated, whereas large CGIs with more than 40 sites are predominantly unmethylated.24 Intermediate CGIs, those with 15–40 sites, were found in either of the two extremal states, but rarely in a mixed configuration of some methylated and some unmethylated sites. Importantly, the typical methylation status of a CGI was dependent on the distances between the CpG sites within the island. A modeling framework to analyse DNA-methylation has to be modest due to the humbling complexity of this interacting system. Besides the known contributing factors, many others presumably also affect the methylation status of a given CpG island. The state of CpG sites is influenced by the local genome status such as transcription factors, modifications on nearby nucleosomes as well as possible activity of transcribing RNA polymerase.25 DNA-methylation may in turn also influence other sub-systems. For instance, CpG sites may recruit factors that modify nucleosomes. The key players involved in maintaining and introducing methylation are methyltransferases DNMT1 and DNMT3a/b. How precisely the unmethylated state can be persistently protected against methylation is still under discussion. The discovery of the ten-eleven translocation protein Tet126 made it clear that Tet1 plays a role in demethylation. It is known that Tet1 enables the conversion of methylated to hydroxymethylated cytosine. The processes that then convert the intermediate hydroxymethylated to the final unmethylated state are as yet not convincingly established. The hydroxymethylated cytosine could either be passively converted to cytosine by replication or actively by additional enzymes.27,28 Tet1 is a main player during early development but is also present in adult mammals.27 In this work we analyse a theoretical model for DNA methylation which reproduces the bistable behaviour of CGIs. In particular, we focus on how unmethylated CpG islands retain their collective state across many cell generations, while also having the ability to persistently maintain the alternative methylated state. We explore the possibility of a short range cooperative binding between DNA associated proteins that favor unmethylated CpG sites. In fact, we simplify the description of this mechanism as to view a passively DNA-binding protein to bind cooperatively to unmethylated CpG sites and protect nearby CpG sites from becoming methylated.29 Combining this mechanism with the collaborative read–write activity of the methylases, we obtain CpG islands that can be robustly maintained in two distinct states. The model further provides the remarkable ability to differentiate between CpG sites inside an island, and CpG sites outside the island. The CpG island retains the ability to exist in two different epigenetic states, while the open sea of surrounding CpG sites remains predominantly methylated—in considerable agreement with the experimental data.
2 Results Our model (Fig. 1A) builds on a minimal model proposed previously,30 in the sense that it includes positive feedback from methylated (m) and hemimethylated (h) CpG sites, upon
Mol. BioSyst.
Molecular BioSystems
Fig. 1 Model and methylation dynamics. (A) Model with recruitment and protection from a DNA-binding protein. Protection state marked as u* (dark blue), a normal unmethylated CpG site marked as u (blue), hemimethylated CpG marked as h (blue/red) and methylated CpG as m (red). Reactions that are repressed by the u*-state are confined to closely positioned nearest neighbors (within the B10 bp distances found between CpG sites in CpG islands). The red arrows mark non-local methylation recruitment-reactions acting between distant CpG sites. (B) Example of CpG sites that are in the protected state (u*) such that the methylation of neighboring CpG sites is repressed (to the left of the four u*-sites). Methylation is possible if the CpG sites are not protected (to the right, due to the greater distance). (C) Simulation of methylation dynamics of the CpG island consisting of 15 CpG sites. Initial conditions: all CpG sites methylated. (D) As (C) but with all CpG sites initially unmethylated. The parameters in (C) and (D) are: b = m = 0.02, c = 0.1.
increasing methylation of other CpG sites. Biologically, this positive feedback is now believed to be mediated by a methyl binding domain (MBD) protein that binds specifically to methylated CpGs. It can then change the methylation status of nearby nucleosomes to H3K9met, which in turn recruit DNMT3a/b. The activity of the resulting DNMT3a/b enzymes closes the feedback loop by further methylating other, previously unmethylated, CpG sites in the vicinity of the nucleosomes.31–33 The model in Fig. 1A explores the consequences of a protein that binds cooperatively to DNA with unmethylated CpG sites. A possible candidate for such a protein is the CpG-binding protein Cfp1. This protein is found to bind unmethylated CGIs and coincides with the histone mark H3K4me3 (a mark that is found to repress DNMT3a/b during early development).29,33 The protein in the model is further assumed to repress changes to the methylation status of nearby CpG sites. We add a fourth state, u*, to the model in Haerter et al.,30 where unmethylated
This journal is © The Royal Society of Chemistry 2016
View Article Online
Molecular BioSystems
Paper
sites (u) passively convert to u* which in turn protect against methylation of neighboring CpG sites.
Published on 22 February 2016. Downloaded by LA TROBE UNIVERSITY on 01/03/2016 19:55:57.
Methylation dynamics We assume that all active recruitment reactions (red lines in Fig. 1) have unit strength. The model behavior is then examined in terms of three parameters: the rates b and m as well as the parameters c which quantify cooperative interactions and protection associated with the unmethylated state, respectively (see Table 1). The simulation uses a Gillespie updating scheme for attempted reactions.34 The procedure is summarized as follows. Initially, set time T = 0. At each update step: (1) Assign an update time for each of the potential reactions outlined in Fig. 1A and B. For any given rate p these update times are sampled from an exponential probability distribution with mean 1/p, i.e. the probability density function of update times of reaction p is P(t) B exp( pt). In practice, this is accomplished by selecting a random number r A [0,1] uniformly and evaluating tp = ln(r)/p, with ln being the natural logarithm. For clarity we summarize all rates in Table 1. The parameter p can then take any of the values in the second column of the table. (2) Select the reaction corresponding to the smallest time ti. Select a target CpG site x randomly. If the reaction involves recruitment (see Table 1), then also select another CpG site y randomly. If x and y are not compatible with the selected reaction, no update of x takes place. Considering Table 1, the reaction types can only be carried out if x is in the initial state of the reaction, e.g. for u - h, site x must be in state u. If a further condition is indicated (third row in Table 1), site y must fulfil that condition. For example if the selected reaction is 3, 4 or 5 (Table 1) and the state of x is m, h and u, respectively, the corresponding update is done. Additionally, protection by state u* against methylation of surrounding CpG sites is implemented, i.e. the state u* at a given site prevents (further) methylation at neighboring sites in the u or h state. This is the case for reactions 1, 2, 7, 8, and 9 in Table 1. Given that site x (and y if recruitment is required) allows the change, the state of the neighboring CpG sites is also
checked. If one of these neighboring sites is in the u* state, the reaction does not take place. Similarly, to remove u* from a selected site x, (reaction 6 in Table 1), the state of the two neighboring sites is again considered and the transition u* - u is performed with probability cn, with n A 0, 1, 2 being the number of nearest neighbors of x in state u*. This condition in itself allows the u* state to aggregate along the DNA site (implicitly assuming that closely spaced non-methylated CpG sites are available). (3) Update the time T - T + ti. Cell division When the simulation time reaches the cell generation time Td, i.e. T 4 Td, cell division takes place. For any simulation we set Td such that the reaction with the smallest average rate (from reaction 1–9) is expected to occur once for each CpG site. Upon cell division, each CpG site in the h state is converted to u with probability 1/2. All CpG sites in state m are converted to h, and all u* states are converted to u (Table 1). The time is reset, i.e. T = 0, and the procedure is repeated. Fig. 1C and D demonstrate the model’s ability to persistently preserve the predominantly methylated, respectively, and unmethylated states for a CpG-island of 15 sites over many generations, i.e. once set, even cell replication cannot alter the fidelity of the island-specific epigenetic mark. The figure shows us that the model is fully able to support alternative epigenetic states over several cell generations. In particular, compared to the earlier model of ref. 30, it is demonstrated that one could indeed maintain epigenetic states without relying on read–write recruitment processes of Tet-like proteins.
Table 1 Reaction types, rates and conditions for all reactions in Fig. 1. E.g. for the parameter b, the update time tb = ln(r)/b. Note that, as indicated in the third column of the table, several of the rates are dependent on the methylation state of another CpG site. The reactions d1–d3 apply only upon cell division, i.e. when the typical division time Td is exceeded (T 4 Td)
Reaction type
Rate
Condition
1 2 3 4 5 6 7 8 9
u-h h-m m-h h-u u - u* u* - u u-h h-m h-m
b b m m 1 1 1 1 1
None None None None None None m-state CpG m-state CpG h-state CpG
d1 d2 d3
m-h h-u u* - u
1 1/2 1
None None None
This journal is © The Royal Society of Chemistry 2016
Fig. 2 Parameter sampling for sustainable states. Testing of parameter combinations which allow for the long-term maintenance of both epigenetic states of an isolated CpG island containing 15 sites. For simulations with model B (blue), the parameter c = 0.1. For simulations with model A (red), the recruitments toward the u-state were attempted with a variety of strengths of the recruitment rate t A [0,1] (uniformly distributed). For simplicity, all recruitment reactions are assumed to occur between sites irrespective of the spacing between these sites in the island (which is in any case short, i.e. less than the length of a nucleosome of approximately 200 bp). The requirement for accepting a parameter was a lifetime of more than 500 generation of each joint epigenetic state, i.e. the island remained predominantly methylated, respectively unmethylated during this period.
Mol. BioSyst.
View Article Online
Published on 22 February 2016. Downloaded by LA TROBE UNIVERSITY on 01/03/2016 19:55:57.
Paper
To explore the range of parameters where passive protection could be a key player in keeping the CpG island demethylated, we examine the robustness of the mechanisms in terms of the range of working rate constants (Fig. 2). We maintain all recruitment rates equal, as favored by,30 and thus only vary the non-recruited conversions (b and m) of CpG sites. The figure compares the epigenetic ability to the model proposed in ref. 30 where the u* state was not implemented, but recruited demethylation reactions were used instead. The comparison shows that the introduction of a protected unmethylated state allows for much larger rates of reactions that are independent of the state of the CpG-island: protection by cooperative binding increases robustness to the maintenance of epigenetic states. The model robustness against larger values of non-recruited methylation also gives robustness against long range perturbations from methylation reactions caused by recruitment from methylated CpG sites outside the CpG island. This is explored further in Fig. 3 where we assume that mutual protection
Molecular BioSystems
between unmethylated neighbouring CpG sites vanishes outside the CGI. The motivation for implementing this difference is that the CpG–CpG distances are longer outside the islands, and therefore there should be no protection and no cooperativity between proteins binding at these outside CpG sites. We observe that the model thereby easily distinguishes regions of the DNA where CpG sites are closely spaced from those where they are more sparse. The model can sustain alternative bistable states in a dense CpG island surrounded by many sparsely spaced CpG sites that mostly remain methylated. In the simulation the distances between CpG sites outside the island are assumed to be 100 bp, which is 10 times larger than the 10 bp used for CpG sites within the island. For the recruited reactions the collaborative site is chosen from a distance of x bp with a probability of 1/(x + a) (we use a = 200 bp to mimic the DNA stiffness over short distances). The main feature of the present model is its sensitivity to the cooperativity of the u* state, which allowed the u* to form a longer filament along the closely spaced and unmethylated CpG sites inside the island. If this stretch of cooperativity can be broken more easily, for example, by increasing distances between CpG sites within the island, then the unmethylated state of the island will be destabilized. This may be part of the explanation for the fact that CpG islands with longer CpG–CpG spacing tend to be more methylated.
3 Conclusions
Fig. 3 Simulation results. Model simulation with a dense 15-site CpG island surrounded by 50 widely-spaced CpG sites on either side. Parameters: b = 0.01, m = 0.025 and c = 0.1 (compare with Table 1); the simulated spacing of CpG-sites within (outside) the island was 10 (100) bp. These distances influence the strength of the assumed read–write processes, and systematically reduce the impact of the outside on the inside of the CpG island. (A) Time series of the simulation showing the number of CpG sites in each state for each generation. (B) Space-time plot of a region of the system simulated with u in blue, m in red and h in yellow. The CpG island is located between the 50 and 65 sites. (C) Histogram of the distribution of methylated CpG sites.
Mol. BioSyst.
Epigenetic states, encoded in the pattern of DNA methylation within CpG islands, show remarkable stability against noise and cell-replication. A growing body of experimental evidence now points towards the existence of feedback reactions, partially mediated by histone modifications, which help maintain a given extremal methylation configuration, i.e. either a dominantly methylated or a dominantly unmethylated state of the island.31–33 While previous work has largely focused on active feedbacks, here we have introduced and analyzed a protective reaction as a potential extension of the minimal model for the maintenance of epigenetic states of CpG islands.30 The extension focused on the potential role of an additional cooperative step involving a transition to a u* state. Our new model produces bistable CpG islands that remain unmethylated respectively methylated for many cell generations. The model is robust and less sensitive to parameter changes compared to previous models.30 By further assuming the additional cooperative step to be sensitive to the distance between the CpG sites, our model provides high methylation of CpG sites outside CpG islands, while maintaining bistability within islands. Our results support local cooperation within the unmethylated state as a strong mechanism in support of bistability. A given CpG island can alter between two extremal states, however, the states are very stable. A transcription factor or some external protein that influences the methylation dynamics is needed in order to switch from one state to the other. We are not aware of any robust experimental evidence for the existence of a u* state, the CpG binding protein Cpf1 that binds to unmethylated CpG sites and
This journal is © The Royal Society of Chemistry 2016
View Article Online
Published on 22 February 2016. Downloaded by LA TROBE UNIVERSITY on 01/03/2016 19:55:57.
Molecular BioSystems
coincides with H3K4 methylation, however, is one potential explanation. Another possible justification for u* is that a 15-site CpG island may be covered by one or two nucleosomes with H3K4 methylation, which has been found to exclude DNMT3a/b and DNMTL and thereby cause the CpG island to remain unmethylated.35 We speculate on a further possibility, where our u*-state is interpreted as a parametrization of sets of transcription factors that may bind the nucleosome depleted regions close to promoters, keeping it free from nucleosomes and consequently circumventing recruitment of DNMT3A/b.25,36,37 Thereby, the number and strength of cooperative interactions that facilitate the u* state may vary between promoters, and allow for context dependent states of CpG islands. Our simple model (Fig. 2b) provides bistability for an intermediately sized CpG island with a preference for residing both in the methylated and unmethylated states. However, a majority of the larger-sized CpG islands is found to be predominantly unmethylated.24 Our model lacks long-ranged cooperativity of demethylation reactions that would favor the unmethylated state of larger islands. The model would hence provide weaker preference for large islands to predominantly remain unmethylated. However our model lacks long-range recruitment reactions that direct demethylation reactions, and would hence be unable to reproduce the finding that large islands in the genome of mammals are predominantly unmethylated.24 As shown experimentally, Tet1 is transiently recruited to unmethylated CpG sites by its CXXC domain and is further known to initiate demethylation reactions.26,38 This evidence could provide an argument for long-ranged cooperative demethylation and thereby a mechanism for the unmethylated status of large CpG islands. An alternative model is that recruited methylation reactions are mediated through nucleosomes that surround the CpG island. The finite methylation capacity of this small number of nucleosomes would then make it difficult to methylate the big number of CpG sites in large islands. This paper focused on detectable features of short-ranged cooperative protection of the unmethylated state. The aim of the presented model is to emphasize the important role of cross-talk between the spatial distribution of the CpG sites and the methylation state of CpG sites, both in islands and open sea regions. In summary, this paper emphasizes the merit of short-ranged binding-cooperativity to favour a robust bistability of CpG islands, providing at the same time independence of the CpG-island state from that of the surrounding CpG sites.
References 1 G. Felsenfeld, Cold Spring Harbor Perspect. Biol., 2014, 6, a018200. 2 A. Bird, Nature, 2007, 447, 396–398. 3 R. Bonasio, S. Tu and D. Reinberg, Science, 2010, 330, 612–616. 4 M. Grunstein, Cell, 1998, 93, 325–328. 5 B. Turner, Cell. Mol. Life Sci., 1998, 54, 21–31. 6 G. Felsenfeld and M. Groudine, Nature, 2003, 421, 448–453.
This journal is © The Royal Society of Chemistry 2016
Paper
7 C. Jiang and B. F. Pugh, Nat. Rev. Genet., 2009, 10, 161–172. 8 I. B. Dodd, et al., Cell, 2007, 129, 813–822. 9 A. Angel, J. Song, C. Dean and M. Howard, Nature, 2011, 476, 105–108. 10 S. Mukhopadhyay, V. H. Nagaraj and A. M. Sengupta, BioSystems, 2010, 102, 49–54. 11 F. Fuks, Curr. Opin. Genet. Dev., 2005, 15, 490–495. `re, C. Sawan and Z. Herceg, Mutat. Res., Rev. Mutat. 12 T. Vaissie Res., 2008, 659, 40–48. 13 Z.-X. Chen and A. D. Riggs, Biochem. Cell Biol., 2005, 448, 438–448. 14 A. Bird, Genes Dev., 2002, 16, 6–21. 15 S. Saxonov, P. Berg and D. L. Brutlag, Proc. Natl. Acad. Sci. U. S. A., 2006, 103, 1412–1417. 16 F. Larsen, G. Gundersen, R. Lopez and H. Prydz, Genomics, 1992, 13, 1095–1107. 17 D. Takai and P. A. Jones, Proc. Natl. Acad. Sci. U. S. A., 2002, 99, 3740–3745. ¨beler, M. C. Lorincz, D. M. Cimbora, A. Telling, 18 D. Schu Y.-Q. Feng, E. E. Bouhassira and M. Groudine, Mol. Cell. Biol., 2000, 20, 9103–9112. 19 F. Antequera, eLS, 2007. 20 J. Shen, S. Wang, Y.-J. Zhang, H.-C. Wu, M. G. Kibriya, F. Jasmine, H. Ahsan, D. P. Wu, A. B. Siegel and H. Remotti, et al., Epigenetics, 2013, 8, 34–43. 21 F. Antequera, J. Boyes and A. Bird, Cell, 1990, 62, 503–514. 22 A. P. Bird, Trends Genet., 1987, 3, 342–347. 23 R. A. Rollins, F. Haghighi, J. R. Edwards, R. Das, M. Q. Zhang, J. Ju and T. H. Bestor, Genome Res., 2006, 16, 157–163. ¨vkvist, I. B. Dodd, K. Sneppen and J. O. Haerter, Nucleic 24 C. Lo Acids Res., 2016, gkw124. 25 P. A. Jones, Nat. Rev. Genet., 2012, 13, 484–492. 26 K. Williams, J. Christensen, M. T. Pedersen, J. V. Johansen, P. A. Cloos, J. Rappsilber and K. Helin, Nature, 2011, 473, 343–348. 27 A. Jeltsch and R. Z. Jurkowska, Trends Biochem. Sci., 2014, 39, 310–318. 28 M. R. Branco, G. Ficz and W. Reik, Nat. Rev. Genet., 2012, 13, 7–13. 29 J. P. Thomson, P. J. Skene, J. Selfridge, T. Clouaire, J. Guy, S. Webb, A. R. Kerr, A. Deaton, R. Andrews, K. D. James, D. J. Turner, R. Illingworth and A. Bird, Nature, 2010, 464, 1082–1086. ¨vkvist, I. B. Dodd and K. Sneppen, Nucleic 30 J. O. Haerter, C. Lo Acids Res., 2013, gkt1235. 31 E. Ballestar and A. P. Wolffe, Eur. J. Biochem., 2001, 268, 1–6. 32 F. Fuks, P. J. Hurd, D. Wolf, X. Nan, A. P. Bird and T. Kouzarides, J. Biol. Chem., 2003, 278, 4035–4040. 33 H. Cedar and Y. Bergman, Nat. Rev. Genet., 2009, 10, 295–304. 34 D. T. Gillespie, J. Phys. Chem., 1977, 81, 2340–2361. 35 S. Feng, S. E. Jacobsen and W. Reik, Science, 2010, 330, 622–627. 36 C.-K. Lee, Y. Shibata, B. Rao, B. D. Strahl and J. D. Lieb, Nat. Genet., 2004, 36, 900–905. 37 L. Bai, A. Ondracka and F. R. Cross, Mol. Cell, 2011, 42, 465–476. 38 C. Frauer, A. Rottach, D. Meilinger, S. Bultmann, ¨der, M. Wang, W. Qin, J. So ¨ding K. Fellinger, S. Haseno and F. Spada, et al., PLoS One, 2011, 6, e16627.
Mol. BioSyst.
Published on 22 February 2016. Downloaded by LA TROBE UNIVERSITY on 01/03/2016 19:55:57.
PAPER
Cite this: DOI: 10.1039/c6mb00044d
View Journal
Stabilization of epigenetic states of CpG islands by local cooperation Giulia Sormani, Jan O. Haerter, Cecilia Lo ¨ vkvist and Kim Sneppen* DNA methylation of CpG sites is an important epigenetic mark in mammals. Active promoters are often associated with unmethylated CpG sites, whereas methylated CpG sites correlate with silenced promoters. Methylation of CpG sites must be generally described as a dynamical process that is mediated by methylation enzymes, such as DNMT1 and DNMT3a/b. However, there are several models of how CpG sites can be protected from methylation and thereby remain unmethylated. In this paper we examine the combination of both: the positive feedbacks of DNA methylation and a short range
Received 19th January 2016, Accepted 17th February 2016
counterpart which in turn protects—and thereby maintains—the unmethylated state. The emergent
DOI: 10.1039/c6mb00044d
cooperative protection of one CpG site by another in favor of unmethylated CpG sites. Our results
www.rsc.org/molecularbiosystems
suggest that this synthesis of mechanisms provides equally robust maintenance of both the unmethylated and methylated states of CpG islands.
dynamics is provided by collaborative, re-enforcing feedbacks in favor of methylated CpG islands and
1 Introduction Epigenetics is the phenomenon of cells persistently maintaining different states of gene expression, in spite of otherwise identical DNA exposed to the same environment.1,2 In physics terms this means bistable gene expression, where stability of both expression states is found to be sufficiently robust to be maintained across cell divisions. In physics terms this means that the expression pattern of a genetic system can be in two different and well-separated states, i.e. the genetic regulatory system is bistable. Epigenetics further implies that the bistability is sufficiently robust to maintain the uniqueness of each of these states across cell divisions. trans-Mediated epigenetics is typically maintained by diffusing transcription factors. cis-Mediated epigenetics, in contrast, refers to the subset of epigenetic systems that are able to maintain their distinct states using only a localized region on the genome. cis-Mediated epigenetics thereby relies on positive feedback mechanisms that act within a relatively short region of DNA.3 An example of a cis-mediated epigenetic system is one that is mediated through read–write enzymes that act on nucleosomes, which in turn recruit these read–write enzymes to influence other nucleosomes.4–10 A nucleosome is a protein complex that packages eukaryotic DNA, typically a stretch of approximately 200 base pairs (bp). Nucleosomes can change their epigenetic state: while one state prevents the associated genomal region from gene transcription, another state may allow transcription. Center for Models of Life, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark. E-mail: [email protected]
This journal is © The Royal Society of Chemistry 2016
For example, when nucleosomes are methylated at the amino acid position H3K9, DNA transcription is repressed. In contrast, for acetylated nucleosomes, transcription is not repressed.11,12 Another cis-acting epigenetic mechanism is tied to the particular states of the cytosine–phosphate–guanine dinucleotide sequence, termed as the CpG site. Methylation of a given CpG site along the DNA results from a methyl group being attached to both cytosine nucleotides of the two complementary CpG pairs. Thus a CpG site in fact consists of two complementary base pairs CG and GC. For CpG sites on the DNA surrounding promoters13 which are dominantly methylated, promoter activity is silenced, whereas promoters covered by persistently unmethylated CpG sites tend to be transcriptionally active.14–18 The methylation patterns are maintained and restored throughout cell generations even though the methylated DNA is replicated and new initially unmethylated DNA-strands are synthesized and hemimethylated double stranded DNA is formed in both daughter strands. (A fully methylated CpG site has both strands methylated, whereas a hemimethylated CpG site only has one of the two cytosines methylated.) CpG sites are distributed intermittently on the DNA, either within CpG islands (CGIs), where CpG sites are typically densely spaced (E10 bp apart), or in larger genomic regions outside CGIs—termed as open sea—where site separation is typically an order of magnitude larger.19,20 While CpG sites in the open sea are mostly methylated, those within CpG islands are often either completely methylated or completely unmethylated.21,22 Methylation is found to be anti-correlated with CpG density: higher density means lower methylation.14,23 In fact, analyzing all CGIs in the human genome, we recently found that small CGIs, i.e. those containing
Mol. BioSyst.
View Article Online
Published on 22 February 2016. Downloaded by LA TROBE UNIVERSITY on 01/03/2016 19:55:57.
Paper
less than ten CpG sites, are persistently methylated, whereas large CGIs with more than 40 sites are predominantly unmethylated.24 Intermediate CGIs, those with 15–40 sites, were found in either of the two extremal states, but rarely in a mixed configuration of some methylated and some unmethylated sites. Importantly, the typical methylation status of a CGI was dependent on the distances between the CpG sites within the island. A modeling framework to analyse DNA-methylation has to be modest due to the humbling complexity of this interacting system. Besides the known contributing factors, many others presumably also affect the methylation status of a given CpG island. The state of CpG sites is influenced by the local genome status such as transcription factors, modifications on nearby nucleosomes as well as possible activity of transcribing RNA polymerase.25 DNA-methylation may in turn also influence other sub-systems. For instance, CpG sites may recruit factors that modify nucleosomes. The key players involved in maintaining and introducing methylation are methyltransferases DNMT1 and DNMT3a/b. How precisely the unmethylated state can be persistently protected against methylation is still under discussion. The discovery of the ten-eleven translocation protein Tet126 made it clear that Tet1 plays a role in demethylation. It is known that Tet1 enables the conversion of methylated to hydroxymethylated cytosine. The processes that then convert the intermediate hydroxymethylated to the final unmethylated state are as yet not convincingly established. The hydroxymethylated cytosine could either be passively converted to cytosine by replication or actively by additional enzymes.27,28 Tet1 is a main player during early development but is also present in adult mammals.27 In this work we analyse a theoretical model for DNA methylation which reproduces the bistable behaviour of CGIs. In particular, we focus on how unmethylated CpG islands retain their collective state across many cell generations, while also having the ability to persistently maintain the alternative methylated state. We explore the possibility of a short range cooperative binding between DNA associated proteins that favor unmethylated CpG sites. In fact, we simplify the description of this mechanism as to view a passively DNA-binding protein to bind cooperatively to unmethylated CpG sites and protect nearby CpG sites from becoming methylated.29 Combining this mechanism with the collaborative read–write activity of the methylases, we obtain CpG islands that can be robustly maintained in two distinct states. The model further provides the remarkable ability to differentiate between CpG sites inside an island, and CpG sites outside the island. The CpG island retains the ability to exist in two different epigenetic states, while the open sea of surrounding CpG sites remains predominantly methylated—in considerable agreement with the experimental data.
2 Results Our model (Fig. 1A) builds on a minimal model proposed previously,30 in the sense that it includes positive feedback from methylated (m) and hemimethylated (h) CpG sites, upon
Mol. BioSyst.
Molecular BioSystems
Fig. 1 Model and methylation dynamics. (A) Model with recruitment and protection from a DNA-binding protein. Protection state marked as u* (dark blue), a normal unmethylated CpG site marked as u (blue), hemimethylated CpG marked as h (blue/red) and methylated CpG as m (red). Reactions that are repressed by the u*-state are confined to closely positioned nearest neighbors (within the B10 bp distances found between CpG sites in CpG islands). The red arrows mark non-local methylation recruitment-reactions acting between distant CpG sites. (B) Example of CpG sites that are in the protected state (u*) such that the methylation of neighboring CpG sites is repressed (to the left of the four u*-sites). Methylation is possible if the CpG sites are not protected (to the right, due to the greater distance). (C) Simulation of methylation dynamics of the CpG island consisting of 15 CpG sites. Initial conditions: all CpG sites methylated. (D) As (C) but with all CpG sites initially unmethylated. The parameters in (C) and (D) are: b = m = 0.02, c = 0.1.
increasing methylation of other CpG sites. Biologically, this positive feedback is now believed to be mediated by a methyl binding domain (MBD) protein that binds specifically to methylated CpGs. It can then change the methylation status of nearby nucleosomes to H3K9met, which in turn recruit DNMT3a/b. The activity of the resulting DNMT3a/b enzymes closes the feedback loop by further methylating other, previously unmethylated, CpG sites in the vicinity of the nucleosomes.31–33 The model in Fig. 1A explores the consequences of a protein that binds cooperatively to DNA with unmethylated CpG sites. A possible candidate for such a protein is the CpG-binding protein Cfp1. This protein is found to bind unmethylated CGIs and coincides with the histone mark H3K4me3 (a mark that is found to repress DNMT3a/b during early development).29,33 The protein in the model is further assumed to repress changes to the methylation status of nearby CpG sites. We add a fourth state, u*, to the model in Haerter et al.,30 where unmethylated
This journal is © The Royal Society of Chemistry 2016
View Article Online
Molecular BioSystems
Paper
sites (u) passively convert to u* which in turn protect against methylation of neighboring CpG sites.
Published on 22 February 2016. Downloaded by LA TROBE UNIVERSITY on 01/03/2016 19:55:57.
Methylation dynamics We assume that all active recruitment reactions (red lines in Fig. 1) have unit strength. The model behavior is then examined in terms of three parameters: the rates b and m as well as the parameters c which quantify cooperative interactions and protection associated with the unmethylated state, respectively (see Table 1). The simulation uses a Gillespie updating scheme for attempted reactions.34 The procedure is summarized as follows. Initially, set time T = 0. At each update step: (1) Assign an update time for each of the potential reactions outlined in Fig. 1A and B. For any given rate p these update times are sampled from an exponential probability distribution with mean 1/p, i.e. the probability density function of update times of reaction p is P(t) B exp( pt). In practice, this is accomplished by selecting a random number r A [0,1] uniformly and evaluating tp = ln(r)/p, with ln being the natural logarithm. For clarity we summarize all rates in Table 1. The parameter p can then take any of the values in the second column of the table. (2) Select the reaction corresponding to the smallest time ti. Select a target CpG site x randomly. If the reaction involves recruitment (see Table 1), then also select another CpG site y randomly. If x and y are not compatible with the selected reaction, no update of x takes place. Considering Table 1, the reaction types can only be carried out if x is in the initial state of the reaction, e.g. for u - h, site x must be in state u. If a further condition is indicated (third row in Table 1), site y must fulfil that condition. For example if the selected reaction is 3, 4 or 5 (Table 1) and the state of x is m, h and u, respectively, the corresponding update is done. Additionally, protection by state u* against methylation of surrounding CpG sites is implemented, i.e. the state u* at a given site prevents (further) methylation at neighboring sites in the u or h state. This is the case for reactions 1, 2, 7, 8, and 9 in Table 1. Given that site x (and y if recruitment is required) allows the change, the state of the neighboring CpG sites is also
checked. If one of these neighboring sites is in the u* state, the reaction does not take place. Similarly, to remove u* from a selected site x, (reaction 6 in Table 1), the state of the two neighboring sites is again considered and the transition u* - u is performed with probability cn, with n A 0, 1, 2 being the number of nearest neighbors of x in state u*. This condition in itself allows the u* state to aggregate along the DNA site (implicitly assuming that closely spaced non-methylated CpG sites are available). (3) Update the time T - T + ti. Cell division When the simulation time reaches the cell generation time Td, i.e. T 4 Td, cell division takes place. For any simulation we set Td such that the reaction with the smallest average rate (from reaction 1–9) is expected to occur once for each CpG site. Upon cell division, each CpG site in the h state is converted to u with probability 1/2. All CpG sites in state m are converted to h, and all u* states are converted to u (Table 1). The time is reset, i.e. T = 0, and the procedure is repeated. Fig. 1C and D demonstrate the model’s ability to persistently preserve the predominantly methylated, respectively, and unmethylated states for a CpG-island of 15 sites over many generations, i.e. once set, even cell replication cannot alter the fidelity of the island-specific epigenetic mark. The figure shows us that the model is fully able to support alternative epigenetic states over several cell generations. In particular, compared to the earlier model of ref. 30, it is demonstrated that one could indeed maintain epigenetic states without relying on read–write recruitment processes of Tet-like proteins.
Table 1 Reaction types, rates and conditions for all reactions in Fig. 1. E.g. for the parameter b, the update time tb = ln(r)/b. Note that, as indicated in the third column of the table, several of the rates are dependent on the methylation state of another CpG site. The reactions d1–d3 apply only upon cell division, i.e. when the typical division time Td is exceeded (T 4 Td)
Reaction type
Rate
Condition
1 2 3 4 5 6 7 8 9
u-h h-m m-h h-u u - u* u* - u u-h h-m h-m
b b m m 1 1 1 1 1
None None None None None None m-state CpG m-state CpG h-state CpG
d1 d2 d3
m-h h-u u* - u
1 1/2 1
None None None
This journal is © The Royal Society of Chemistry 2016
Fig. 2 Parameter sampling for sustainable states. Testing of parameter combinations which allow for the long-term maintenance of both epigenetic states of an isolated CpG island containing 15 sites. For simulations with model B (blue), the parameter c = 0.1. For simulations with model A (red), the recruitments toward the u-state were attempted with a variety of strengths of the recruitment rate t A [0,1] (uniformly distributed). For simplicity, all recruitment reactions are assumed to occur between sites irrespective of the spacing between these sites in the island (which is in any case short, i.e. less than the length of a nucleosome of approximately 200 bp). The requirement for accepting a parameter was a lifetime of more than 500 generation of each joint epigenetic state, i.e. the island remained predominantly methylated, respectively unmethylated during this period.
Mol. BioSyst.
View Article Online
Published on 22 February 2016. Downloaded by LA TROBE UNIVERSITY on 01/03/2016 19:55:57.
Paper
To explore the range of parameters where passive protection could be a key player in keeping the CpG island demethylated, we examine the robustness of the mechanisms in terms of the range of working rate constants (Fig. 2). We maintain all recruitment rates equal, as favored by,30 and thus only vary the non-recruited conversions (b and m) of CpG sites. The figure compares the epigenetic ability to the model proposed in ref. 30 where the u* state was not implemented, but recruited demethylation reactions were used instead. The comparison shows that the introduction of a protected unmethylated state allows for much larger rates of reactions that are independent of the state of the CpG-island: protection by cooperative binding increases robustness to the maintenance of epigenetic states. The model robustness against larger values of non-recruited methylation also gives robustness against long range perturbations from methylation reactions caused by recruitment from methylated CpG sites outside the CpG island. This is explored further in Fig. 3 where we assume that mutual protection
Molecular BioSystems
between unmethylated neighbouring CpG sites vanishes outside the CGI. The motivation for implementing this difference is that the CpG–CpG distances are longer outside the islands, and therefore there should be no protection and no cooperativity between proteins binding at these outside CpG sites. We observe that the model thereby easily distinguishes regions of the DNA where CpG sites are closely spaced from those where they are more sparse. The model can sustain alternative bistable states in a dense CpG island surrounded by many sparsely spaced CpG sites that mostly remain methylated. In the simulation the distances between CpG sites outside the island are assumed to be 100 bp, which is 10 times larger than the 10 bp used for CpG sites within the island. For the recruited reactions the collaborative site is chosen from a distance of x bp with a probability of 1/(x + a) (we use a = 200 bp to mimic the DNA stiffness over short distances). The main feature of the present model is its sensitivity to the cooperativity of the u* state, which allowed the u* to form a longer filament along the closely spaced and unmethylated CpG sites inside the island. If this stretch of cooperativity can be broken more easily, for example, by increasing distances between CpG sites within the island, then the unmethylated state of the island will be destabilized. This may be part of the explanation for the fact that CpG islands with longer CpG–CpG spacing tend to be more methylated.
3 Conclusions
Fig. 3 Simulation results. Model simulation with a dense 15-site CpG island surrounded by 50 widely-spaced CpG sites on either side. Parameters: b = 0.01, m = 0.025 and c = 0.1 (compare with Table 1); the simulated spacing of CpG-sites within (outside) the island was 10 (100) bp. These distances influence the strength of the assumed read–write processes, and systematically reduce the impact of the outside on the inside of the CpG island. (A) Time series of the simulation showing the number of CpG sites in each state for each generation. (B) Space-time plot of a region of the system simulated with u in blue, m in red and h in yellow. The CpG island is located between the 50 and 65 sites. (C) Histogram of the distribution of methylated CpG sites.
Mol. BioSyst.
Epigenetic states, encoded in the pattern of DNA methylation within CpG islands, show remarkable stability against noise and cell-replication. A growing body of experimental evidence now points towards the existence of feedback reactions, partially mediated by histone modifications, which help maintain a given extremal methylation configuration, i.e. either a dominantly methylated or a dominantly unmethylated state of the island.31–33 While previous work has largely focused on active feedbacks, here we have introduced and analyzed a protective reaction as a potential extension of the minimal model for the maintenance of epigenetic states of CpG islands.30 The extension focused on the potential role of an additional cooperative step involving a transition to a u* state. Our new model produces bistable CpG islands that remain unmethylated respectively methylated for many cell generations. The model is robust and less sensitive to parameter changes compared to previous models.30 By further assuming the additional cooperative step to be sensitive to the distance between the CpG sites, our model provides high methylation of CpG sites outside CpG islands, while maintaining bistability within islands. Our results support local cooperation within the unmethylated state as a strong mechanism in support of bistability. A given CpG island can alter between two extremal states, however, the states are very stable. A transcription factor or some external protein that influences the methylation dynamics is needed in order to switch from one state to the other. We are not aware of any robust experimental evidence for the existence of a u* state, the CpG binding protein Cpf1 that binds to unmethylated CpG sites and
This journal is © The Royal Society of Chemistry 2016
View Article Online
Published on 22 February 2016. Downloaded by LA TROBE UNIVERSITY on 01/03/2016 19:55:57.
Molecular BioSystems
coincides with H3K4 methylation, however, is one potential explanation. Another possible justification for u* is that a 15-site CpG island may be covered by one or two nucleosomes with H3K4 methylation, which has been found to exclude DNMT3a/b and DNMTL and thereby cause the CpG island to remain unmethylated.35 We speculate on a further possibility, where our u*-state is interpreted as a parametrization of sets of transcription factors that may bind the nucleosome depleted regions close to promoters, keeping it free from nucleosomes and consequently circumventing recruitment of DNMT3A/b.25,36,37 Thereby, the number and strength of cooperative interactions that facilitate the u* state may vary between promoters, and allow for context dependent states of CpG islands. Our simple model (Fig. 2b) provides bistability for an intermediately sized CpG island with a preference for residing both in the methylated and unmethylated states. However, a majority of the larger-sized CpG islands is found to be predominantly unmethylated.24 Our model lacks long-ranged cooperativity of demethylation reactions that would favor the unmethylated state of larger islands. The model would hence provide weaker preference for large islands to predominantly remain unmethylated. However our model lacks long-range recruitment reactions that direct demethylation reactions, and would hence be unable to reproduce the finding that large islands in the genome of mammals are predominantly unmethylated.24 As shown experimentally, Tet1 is transiently recruited to unmethylated CpG sites by its CXXC domain and is further known to initiate demethylation reactions.26,38 This evidence could provide an argument for long-ranged cooperative demethylation and thereby a mechanism for the unmethylated status of large CpG islands. An alternative model is that recruited methylation reactions are mediated through nucleosomes that surround the CpG island. The finite methylation capacity of this small number of nucleosomes would then make it difficult to methylate the big number of CpG sites in large islands. This paper focused on detectable features of short-ranged cooperative protection of the unmethylated state. The aim of the presented model is to emphasize the important role of cross-talk between the spatial distribution of the CpG sites and the methylation state of CpG sites, both in islands and open sea regions. In summary, this paper emphasizes the merit of short-ranged binding-cooperativity to favour a robust bistability of CpG islands, providing at the same time independence of the CpG-island state from that of the surrounding CpG sites.
References 1 G. Felsenfeld, Cold Spring Harbor Perspect. Biol., 2014, 6, a018200. 2 A. Bird, Nature, 2007, 447, 396–398. 3 R. Bonasio, S. Tu and D. Reinberg, Science, 2010, 330, 612–616. 4 M. Grunstein, Cell, 1998, 93, 325–328. 5 B. Turner, Cell. Mol. Life Sci., 1998, 54, 21–31. 6 G. Felsenfeld and M. Groudine, Nature, 2003, 421, 448–453.
This journal is © The Royal Society of Chemistry 2016
Paper
7 C. Jiang and B. F. Pugh, Nat. Rev. Genet., 2009, 10, 161–172. 8 I. B. Dodd, et al., Cell, 2007, 129, 813–822. 9 A. Angel, J. Song, C. Dean and M. Howard, Nature, 2011, 476, 105–108. 10 S. Mukhopadhyay, V. H. Nagaraj and A. M. Sengupta, BioSystems, 2010, 102, 49–54. 11 F. Fuks, Curr. Opin. Genet. Dev., 2005, 15, 490–495. `re, C. Sawan and Z. Herceg, Mutat. Res., Rev. Mutat. 12 T. Vaissie Res., 2008, 659, 40–48. 13 Z.-X. Chen and A. D. Riggs, Biochem. Cell Biol., 2005, 448, 438–448. 14 A. Bird, Genes Dev., 2002, 16, 6–21. 15 S. Saxonov, P. Berg and D. L. Brutlag, Proc. Natl. Acad. Sci. U. S. A., 2006, 103, 1412–1417. 16 F. Larsen, G. Gundersen, R. Lopez and H. Prydz, Genomics, 1992, 13, 1095–1107. 17 D. Takai and P. A. Jones, Proc. Natl. Acad. Sci. U. S. A., 2002, 99, 3740–3745. ¨beler, M. C. Lorincz, D. M. Cimbora, A. Telling, 18 D. Schu Y.-Q. Feng, E. E. Bouhassira and M. Groudine, Mol. Cell. Biol., 2000, 20, 9103–9112. 19 F. Antequera, eLS, 2007. 20 J. Shen, S. Wang, Y.-J. Zhang, H.-C. Wu, M. G. Kibriya, F. Jasmine, H. Ahsan, D. P. Wu, A. B. Siegel and H. Remotti, et al., Epigenetics, 2013, 8, 34–43. 21 F. Antequera, J. Boyes and A. Bird, Cell, 1990, 62, 503–514. 22 A. P. Bird, Trends Genet., 1987, 3, 342–347. 23 R. A. Rollins, F. Haghighi, J. R. Edwards, R. Das, M. Q. Zhang, J. Ju and T. H. Bestor, Genome Res., 2006, 16, 157–163. ¨vkvist, I. B. Dodd, K. Sneppen and J. O. Haerter, Nucleic 24 C. Lo Acids Res., 2016, gkw124. 25 P. A. Jones, Nat. Rev. Genet., 2012, 13, 484–492. 26 K. Williams, J. Christensen, M. T. Pedersen, J. V. Johansen, P. A. Cloos, J. Rappsilber and K. Helin, Nature, 2011, 473, 343–348. 27 A. Jeltsch and R. Z. Jurkowska, Trends Biochem. Sci., 2014, 39, 310–318. 28 M. R. Branco, G. Ficz and W. Reik, Nat. Rev. Genet., 2012, 13, 7–13. 29 J. P. Thomson, P. J. Skene, J. Selfridge, T. Clouaire, J. Guy, S. Webb, A. R. Kerr, A. Deaton, R. Andrews, K. D. James, D. J. Turner, R. Illingworth and A. Bird, Nature, 2010, 464, 1082–1086. ¨vkvist, I. B. Dodd and K. Sneppen, Nucleic 30 J. O. Haerter, C. Lo Acids Res., 2013, gkt1235. 31 E. Ballestar and A. P. Wolffe, Eur. J. Biochem., 2001, 268, 1–6. 32 F. Fuks, P. J. Hurd, D. Wolf, X. Nan, A. P. Bird and T. Kouzarides, J. Biol. Chem., 2003, 278, 4035–4040. 33 H. Cedar and Y. Bergman, Nat. Rev. Genet., 2009, 10, 295–304. 34 D. T. Gillespie, J. Phys. Chem., 1977, 81, 2340–2361. 35 S. Feng, S. E. Jacobsen and W. Reik, Science, 2010, 330, 622–627. 36 C.-K. Lee, Y. Shibata, B. Rao, B. D. Strahl and J. D. Lieb, Nat. Genet., 2004, 36, 900–905. 37 L. Bai, A. Ondracka and F. R. Cross, Mol. Cell, 2011, 42, 465–476. 38 C. Frauer, A. Rottach, D. Meilinger, S. Bultmann, ¨der, M. Wang, W. Qin, J. So ¨ding K. Fellinger, S. Haseno and F. Spada, et al., PLoS One, 2011, 6, e16627.
Mol. BioSyst.
