[
Proc Natl Acad Sci U S A.,
2005]
MicroRNAs (miRNAs) are a recently discovered set of regulatory genes that constitute up to an estimated 1% of the total number of genes in animal genomes, including Caenorhabditis elegans, Drosophila, mouse, and humans [Lagos-Quintana, M., Rauhut, R., Lendeckel, W. M Tuschl, T. (2001) Science 294, 853-858; Lai, E. C., Tomancak, P., Williams, R. W. M Rubin, G.M. (2003) Genome Biol. 4, R42; Lau, N. C., Lim, L. P., Weinstein, E. G. M Bartel, D. P. (2001) Science 294, 858-862; Lee, R. C. M Ambros, V. (2001) Science 294, 862-8644; and Lee, R. C., Feinbaum, R. L. M Ambros, V. (1993) Cell 115, 787-798]. In animals, miRNAs regulate genes by attenuating protein translation through imperfect base pair binding to 3' UTR sequences of target genes. A major challenge in understanding the regulatory role of miRNAs is to accurately predict regulated targets. We have developed an algorithm for predicting targets that does not rely on evolutionary conservation. As one of the features of this algorithm, we incorporate the folded structure of mRNA. By using Drosophila miRNAs as a test case, we have validated our predictions in 10 of 15 genes tested. One of these validated genes is mad as a target for bantam. Furthermore, our computational and experimental data suggest that miRNAs have fewer targets than previously reported.
[
Bull Math Biol,
2019]
We present mathematical techniques for exhaustive studies of long-term dynamics of asynchronous biological system models. Specifically, we extend the notion of [Formula: see text]-equivalence developed for graph dynamical systems to support systematic analysis of all possible attractor configurations that can be generated when varying the asynchronous update order (Macauley and Mortveit in Nonlinearity 22(2):421, 2009). We extend earlier work by Veliz-Cuba and Stigler (J Comput Biol 18(6):783-794, 2011), Goles et al. (Bull Math Biol 75(6):939-966, 2013), and others by comparing long-term dynamics up to topological conjugation: rather than comparing the exact states and their transitions on attractors, we only compare the attractor structures. In general, obtaining this information is computationally intractable. Here, we adapt and apply combinatorial theory for dynamical systems from Macauley and Mortveit (Proc Am Math Soc 136(12):4157-4165, 2008. https://doi.org/10.1090/S0002-9939-09-09884-0 ; 2009; Electron J Comb 18:197, 2011a; Discret Contin Dyn Syst 4(6):1533-1541, 2011b. https://doi.org/10.3934/dcdss.2011.4.1533 ; Theor Comput Sci 504:26-37, 2013. https://doi.org/10.1016/j.tcs.2012.09.015 ; in: Isokawa T, Imai K, Matsui N, Peper F, Umeo H (eds) Cellular automata and discrete complex systems, 2014. https://doi.org/10.1007/978-3-319-18812-6_6 ) to develop computational methods that greatly reduce this computational cost. We give a detailed algorithm and apply it to(i) thelac operon model forEscherichia coli proposed by Veliz-Cuba and Stigler (2011), and(ii) the regulatory network involved in the control of the cell cycle and cell differentiation in theCaenorhabditis elegans vulva precursor cells proposed by Weinstein et al.(BMC Bioinform 16(1):1, 2015). In both cases, we uncover all possible limit cycle structures for these networks under sequential updates. Specifically, for the lac operon model, rather than examining all[Formula: see text] sequential update orders, we demonstrate that it is sufficient to consider344 representative update orders, and, more notably, that these344 representatives give rise to 4 distinct attractor structures. A similar analysis performed for the C.elegans model demonstrates that it has precisely125 distinct attractor structures. We conclude with observations on the variety and distribution of the models' attractor structures and use the results to discuss their robustness.