Abstract
The recovery of information from indirect measurements takes different forms depending on the sophistication with which the process being researched can be modelled mathematically. The forms range from (1) the historical and classical inverse problems regularization situation where explicit models which guaranteed existence and uniqueness have been formulated, through (2) situations where model formulation is performed implicitly as a calibration-and-prediction ansatz, to (3) the exploratory (biology) situation where the underlying mechanism is unknown and constraining information about its dynamics is being sought through appropriate experimentation. Each represents a different aspect of the solution of inverse problems. It is the nature of the exploratory form that is discussed in this paper. The focus is the causal modelling of regulated promoter switching experiments performed to understand the dynamics of the genetic control of various biological developmental processes such as vernalization in plants; in particular, regulated promoter switching experiments used to examine the relationship between FLC transcription activity and the associated histone H3 lysine 27 trimethylation at a vernalization-responsive gene in plants. Using a causal representation with Kohlrausch function fading memory, it is shown how such modelling can be used to quantitatively assess the closeness of the linking of one biological process with another, and, in particular, to conclude that the dynamics of FLC transcription and associated H3K27me3 activity are closely linked biologically.
Similar content being viewed by others
References
Anderssen RS, Davies AR, de Hoog FR (2008) On the sensitivity of interconversion between relaxation and creep. Rheologica Acta 47: 159–167
Anderssen RS, Davies AR, de Hoog FR (2008) On the Volterra integral equation relating creep and relaxation. Inverse Probl 24:035009 (p. 13)
Anderssen RS, de Hoog FR, Wesley IJ (2011) Information recovery from near infrared data. In: McLean W, Roberts AJ (eds) Proceedings of the 15th Biennial Computational Techniques and Applications Conference, CTAC-2010, vol 52 of ANZIAM J. pp C333–C348
Anderssen RS, Husain SA, Loy RJ (2004) The kohlrausch function: properties and applications. ANZIAM J. (E) 45: C800–C816
Ashburner M, Ball CA, Blake JA, Botstein D, Butler H, Cherry JM, Davis AP, Dolinski K, Dwight SS, Eppig JT, Harris MA, Hill DP, Issel-Tarver L, Kasarskis A, Lewis S, Matese JC, Richardson JE, Ringwald M, Rubin GM, Sherlock G, Gene Ontology Consortium (2000) Gene ontology: a tool for the unification of biology. Nature Genet 25:25–29
Barnes HA, Hutton JF, Walters K (1989) An introduction to rheology. Elsevier, Amsterdam
Bernstein SN (1928) Sur les functions absolument monotones. Acta Mathematica 52: 1–66
Buzas DM, Robertson M, Finnegan EJ, Helliwell CA (2011) Transcription-dependence of histone H3 lysine 27 trimethylation at the Arabidopsis polycomb target gene FLC. Plant J. 65: 872–881
Craft J, Samalova M, Baroux C, Townley H, Martinez A, Jepson I, Tsiantis M, Moore I (2005) New pOp/LhG4 vectors for stringent glucocorticoid-dependent transgene expression in Arabidopsis. Plant J. 41: 899–918
Desprat N, Richert A, Simeon J, Asnacios A (2005) Creep function of a single living cell. Biophys J 88: 2224–2233
Dodd Ian B, Micheelsen Mille A, Sneppen Kim, Thon Genevive (2007) Theoretical analysis of epigenetic cell memory by nucleosome modification. Cell 129: 813–822
Engl HW, Hanke M, Neubauer A (1996) Regularization of inverse problems. Kluwer, Dordrecht
Ferry J (1980) Viscoelastic properties of polymers. Wiley, New York
Finnegan EJ, Dennis ES (2007) Vernalization-induced trimethylation of histone H3 lysine 27 at FLC is not maintained in mitotically quiescent cells. Curr Biol 17: 1978–1983
Gardner TS, Cantor CR, Collins JJ (2000) Construction of a genetic toggle switch in Escherichia coli. Nature 403: 339–342
Gendall AR, Levy YY, Wilson A, Dean C (2001) VERNALIZATION 2 gene mediates the epigenetic regulation of vernalization in Arabidopsis. Cell 107: 525–535
Grant RP (2011) Taking shape. Scientist 25: 18–20
Helliwell CA, Masumi R, Finnegan EJ, Buzas DM, Dennis ES (2011) Vernalization-repression of Arabidopsis FLC requires promoter sequences but not antisense transcripts. PLOS ONE 6
Heo JB, Sung S (2011) Encoding memory of winter by noncoding RNAs. Epigenetics 6: 544–547
Heo JB, Sung S (2011) Vernalization-mediated epigenetic silencing by a long intronic noncoding RNA. Science 331: 76–79
Kaufman PD, Rando OJ (2010) Chromatin as a potential carrier of heritable information. Curr Opin Cell Biol 22: 284–290
Kim D-H, Doyle MR, Sung S, Amasino RM (2009) Vernalization: winter and the timing of flowering in plants. Annu Rev Cell Dev Biol 25: 277–299
Koornneef M, Hanhart CJ, van der Veen JH (1991) A genetic and physiological analysis of late flowering mutants in Arabidopsis thaliana. Mol Gen Genet 229: 57–66
Macdonald JR (2006) Surprising conductive- and dielectric-system dispersion differences and similarities for two Kohlrausch-related relaxation-time distributions. J Phys Condens Matter 18: 629–644
Michaels SD, Amasino RM (1999) FLOWERING LOCUS C encodes a novel MADS domain protein that acts as a repressor of flowering. Plant Cell 11: 949–956
Osborne BG, Fearn T, Hindle PH (1993) Practical NIR spectroscopy with applications in food and beverage analysis. McGraw-Hill series in higher mathematics. Longman Scientific & Technical, Harlow
Prohaska SJ, Stadler PF, Krakauer DC (2010) Innovation in gene regulation: the case of chromatin computation. J Theor Biol 265: 27–44
Sedighi M, Sengupta AM (2007) Epigenetic chromatin silencing: bistability and front propagation. Phys Biol 4: 246–255
Sheldon CC, Burn JE, Perez PP, Metzger J, Edwards JA, Peacock WJ, Dennis ES (1999) The FLF MADS box gene: a repressor of flowering in Arabidopsis regulated by vernalization and methylation. Plant Cell 11: 445–458
Wood CC, Robertson M, Tanner G, Peacock WJ, Dennis ES, Helliwell CA (2006) The Arabidopsis thaliana vernalization response requires a polycomb-like protein complex that also includes VERNALIZATION INSENSITIVE 3. Proc Nat Acad Sci USA 103: 14631–14636
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Anderssen, R.S., Helliwell, C.A. Information recovery in molecular biology: causal modelling of regulated promoter switching experiments. J. Math. Biol. 67, 105–122 (2013). https://doi.org/10.1007/s00285-012-0536-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-012-0536-7
Keywords
- Vernalization
- Causal integral equations
- Kohlrausch
- Stress–strain experiments
- Step strain experiments
- FLOWERING LOCUS C
- HISTONE H3 LYSINE 27 TRIMETHYLATION
- Interconversion