Bistability in gene transcription: Interplay of messenger RNA, protein, and nonprotein coding RNA

Abstract

The author proposes a kinetic model describing the interplay of messenger ribonucleic acid (mRNA), protein, produced via translation of this RNA, and nonprotein coding RNA (ncRNA). The model includes association of mRNA and ncRNA and regulation of the ncRNA production by protein. In the case of positive feedback between the production of protein and ncRNA, the steady state of the system is found to be unique. For negative feedback, the model predicts in the mean-field case either unique steady state or bistable kinetics. With incorporation of fluctuations, the bistability is manifested in the form of kinetic bursts provided that the number of reactants is low. Basically, the model describes the simplest biological switch operating with participation of ncRNA. Although the results obtained are applicable to ncRNSs in general, the presentation is focused primarily on microRNAs (miRNAs) which form a large important subclass of ncRNAs and are thought to regulate up to one third of all human genes.

Introduction

The central dogma of molecular biology is that in cells the information flows from deoxyribonucleic acid (DNA) to protein through its intermediary ribonucleic acid (RNA) (Alberts et al., 2002). Specifically, the heritage encoded in DNA is expressed via a templated polymerization called transcription, in which the genes (segments of the DNA sequence) are used as templates to guide the synthesis of RNA by RNA polymerase (RNAP). In turn, RNA or, more specifically, mRNA serves to direct the synthesis of proteins by ribosomes. Gene transcription, performed by RNAP, is often controlled by master regulatory proteins. Due to the feedback between these processes, the kinetics of mRNA and protein formation may be complex even in the simplest genetic networks. In addition, the number of mRNA and regulatory proteins is often low Guptasarma, 1995, Ghaemmaghami et al., 2003 and accordingly the gene transcription frequently exhibits stochastic features. The corresponding mean-field (MF) and stochastic kinetic models focused on bistability and oscillations in simple genetic networks are numerous (see reviews by Mariani et al., 2004, Bornholdt, 2005, Kaern et al., 2005, Paulsson, 2005, Kaufmann and van Oudenaarden, 2007, recent articles by Bratsun et al., 2005, Raser and O’Shea, 2005, Zhou et al., 2005, Friedman et al., 2006, Guido et al., 2006, Isaacson and Peskin, 2006, Lipshtat et al., 2006, Rateitschak and Wolkenhauer, 2007, Yoda et al., 2007, Zhdanov, 2006, Zhdanov, 2007a, Zhdanov, 2007b, and references therein). There are also many studies of large genetic networks constructed by using the conventional schemes of the interplay of mRNAs and proteins (Bornholdt, 2005). (For a general analysis of multiple equilibria in complex chemical reaction networks, see recent articles by Craciun and Feinberg, 2006, Craciun et al., 2006.)

With appropriate specification including, e.g., operons, etc. (Alberts et al., 2002), the conventional view outlined above is fully applicable to prokaryotes whose genomes consist of tightly packed protein-coding sequences. For eukaryotic cells, there is however increasing evidence that the patterns of programming and functional regulation may be dramatically different (see reviews by Bartel, 2004, Costa, 2005, Costa, 2007, Goodrich and Kugel, 2006, Michalak, 2006). The genomes of the latter cells contain relatively rare protein-coding sequences (the corresponding fraction of the human genome is, e.g., about 1.5% Bertone et al., 2004). The rest of the genome is nevertheless transcribed as well. For mouse, for example, the transcribed genes constitute 62% of the genome and about half of the transcripts represents nonprotein coding RNA (ncRNA) (RIKEN, 2005). Now, it becomes obvious that such RNAs form the cornerstone of a regulatory network of signalling that operates in concert with the protein network Costa, 2005, Michalak, 2006.

Experimentally, the bulk of the data on ncRNAs has been obtained primarily by using the ncRNA microarray technique (see, e.g., recent studies by Baskerville and Bartel, 2005, Xi et al., 2007, Bak et al., 2008 and a review by Yin et al., 2008a). The advantage of this technique is that it makes it possible to identify hundreds of ncRNAs. The shortcoming is that the corresponding studies tend to explore tissues, not individual cell types, and do not provide any kinetic information, because the gene expression is characterized by using averaged data for cell populations. One of the consequences of these limitations is that the stochastic and oscillatory features might often be missed. Although at present the temporal features of gene expression kinetics can be observed directly (see e.g. experiments with RNAs by Golding and Cox, 2004 and proteins by Cai et al., 2006, Yu et al., 2006), the corresponding experiments with ncRNAs are still lacking.

Structurally, ncRNAs can be divided into two groups including: (i) large ncRNAs obtained directly after gene transcription and (ii) small ncRNAs (from 20 to 300 nucleotides) obtained by cleavage of large ncRNAs. In turn, small ncRNAs can be divided at least into five subgroups (Yazgan and Krebs, 2007). One of the most important and interesting subgroup of small ncRNAs includes microRNAs (miRNAs) which are 20–22 nucleotides long Bartel, 2004, Gammell, 2007, Kulshreshtha et al., 2007, Wilfred et al., 2007, Wurdinger and Costa, 2007. The latter RNAs are transcribed as long ncRNA and then generated via a two-step processing pathway including first the formation of a few different $\sim 65$-nt pre-miRNAs and then conversion of each of them into the corresponding miRNA Lee et al., 2003, Cai et al., 2004, Gammell, 2007.

The numerous biological functions of ncRNAs are based on their abilities to pair with target mRNAs or to bind to and modulate the activity of proteins (Goodrich and Kugel, 2006). In particular, the main action of miRNAs is to silence target genes Gammell, 2007, Kulshreshtha et al., 2007. Specifically, a miRNA pairs with a target mRNA and then either prevents translation or results in rapid degradation of the miRNA–mRNA complex. At present, miRNAs are thought to regulate up to one third of all human genes Rajewsky, 2006, Mattes et al., 2008. The biological functions of miRNAs have been tracked out in a wide variety of cellular processes, including differentiation, proliferation, death and metabolism, both in the normal state and during deceases, e.g., cancer Gammell, 2007, Kulshreshtha et al., 2007, Wilfred et al., 2007, Fabbri et al., 2008.

Although the general understanding of ncRNA functions is now fairly complete, one should bear in mind that the bulk of the data in this field was obtained by analysing the correlations in the ncRNA and mRNA expression and also by using computational target predictions (see a review by Rajewsky, 2006). The direct experimental identification and validation of ncRNA targets is still the most fundamental challenge in ncRNA (or miRNA) biology (see a recent review by Kuhn et al., 2008).

In analogy with mRNA, ncRNA formation can be controlled by transcription factors (proteins) involved in the regulation of “conventional” genes (Kulshreshtha et al., 2007). For example, the miR-1 genes are direct targets of muscle differentiation regulators including Serum Response Factor, MyoD and Mef2 genes (see a review by Kulshreshtha et al., 2007 and references therein). Recently, evidence surfaced that miRNA expression can also be regulated post-transcriptionally (Leuschner and Martinez, 2007). Like in studies of the ncRNA targets, the identification and validation of feedbacks in the interplay of ncRNAs, mRNAs and proteins is now based primarily on the analysis of the correlations in the ncRNA and mRNA expression and computational predictions Tsang et al., 2007, Zhou et al., 2007. Although such studies are not fully reliable for any given combination of species, they provide a basis for global vision of the situation. In particular, the expression of about one half of all miRNAs is now thought to be influenced by positive and negative feedbacks (Tsang et al., 2007).

Although the key processes occurring in the mRNA, ncRNA and protein pool have already been established, the understanding of the details of the kinetic interplay between them is now limited. To clarify what may happen in this case and to guide the experiments, one can use kinetic models describing various situations. The available models are focused on the interplay of ncRNA and mRNA Levine et al., 2007a, Levine et al., 2007b, Levine et al., 2007c, Mitrai et al., 2007, Shimoni et al., 2007. The models treating the feedbacks between the production of mRNAs, ncRNAs and proteins are still lacking. To show the likely specifics of the latter case, we analyse in this work the kinetics of the ncRNA-mediated suppression of the mRNA population in the situation when the ncRNA production is influenced by protein produced via mRNA translation. The analysis of this problem is of interest because as already noted the experiments and computational predictions indicate that the formation of ncRNA can be regulated by proteins Kulshreshtha et al., 2007, Tsang et al., 2007. The scenario we treat includes ncRNA association with mRNA and subsequent suppression of the translation or rapid degradation of the mRNA*ncRNA complex. This scenario is typical for ncRNA in general and for miRNA in particular. Another scenario including ncRNA-protein association is analysed elsewhere (Zhdanov, 2008b)