In animals, miRNAs bind with their seed (positions 2 to 7 or 8) in a usually perfectly reverse-complementary fashion. Apart from that, there don't seem to be strict rules (although concepts such as "complementary 3' binding" are known). Some nucleotides bind, others don't. As a result, there are secondary structure motifs, bulges and loops in this case. As a side note: stacked pairs are also secondary structure motifs, but it seems that you didn't mean those. Also note: I am talking about secondary structure between miRNA and mRNA, not on the side of the miRNA or the mRNA alone.

Any article about miRNA targeting would probably do (I recommend a PubMed search).

I think it just binds to complementary RNA, but work in multiple species by Brian Gregory's lab suggests that target mRNAs have either less or more secondary structure at the target sites or just the seed sequence themselves, which may affect accessibility to miRNAs. See citations that follow if interested.

Fan Li, Qi Zheng, Paul Ryvkin, Isabelle Dragomir, Yaanik Desai, Subhadra Aiyer, Otto Valladares, Jamie Yang, Shelly Bambina, Leah R. Sabin, John I. Murray, Todd Lamitina, Arjun Raj, Sara Cherry, Li-San Wang, Brian D. Gregory, Global Analysis of RNA Secondary Structure in Two Metazoans, Cell Reports, Volume 1, Issue 1, 26 January 2012, Pages 69-82, ISSN 2211-1247, http://dx.doi.org/10.1016/j.celrep.2011.10.002.

(http://www.sciencedirect.com/science/article/pii/S2211124711000039)

Abstract: Summary

The secondary structure of RNA is necessary for its maturation, regulation, processing, and function. However, the global influence of RNA folding in eukaryotes is still unclear. Here, we use a high-throughput, sequencing-based, structure-mapping approach to identify the paired (double-stranded RNA [dsRNA]) and unpaired (single-stranded RNA [ssRNA]) components of the Drosophila melanogaster and Caenorhabditis elegans transcriptomes, which allows us to identify conserved features of RNA secondary structure in metazoans. From this analysis, we find that ssRNAs and dsRNAs are significantly correlated with specific epigenetic modifications. Additionally, we find key structural patterns across protein-coding transcripts that indicate that RNA folding demarcates regions of protein translation and likely affects microRNA-mediated regulation of mRNAs in animals. Finally, we identify and characterize 546 mRNAs whose folding pattern is significantly correlated between these metazoans, suggesting that their structure has some function. Overall, our findings provide a global assessment of RNA folding in animals.

Regulatory impact of RNA secondary structure across the Arabidopsis transcriptome.

Li F, Zheng Q, Vandivier LE, Willmann MR, Chen Y, Gregory BD. Plant Cell. 2012 Nov;24(11):4346-59. doi: 10.1105/tpc.112.104232. Epub 2012 Nov 13.

Abstract

The secondary structure of an RNA molecule plays an integral role in its maturation, regulation, and function. However, the global influence of this feature on plant gene expression is still largely unclear. Here, we use a high-throughput, sequencing-based, structure-mapping approach in conjunction with transcriptome-wide sequencing of rRNA-depleted (RNA sequencing), small RNA, and ribosome-bound RNA populations to investigate the impact of RNA secondary structure on gene expression regulation in Arabidopsis thaliana. From this analysis, we find that highly unpaired and paired RNAs are strongly correlated with euchromatic and heterochromatic epigenetic histone modifications, respectively, providing evidence that secondary structure is necessary for these RNA-mediated posttranscriptional regulatory pathways. Additionally, we uncover key structural patterns across protein-coding transcripts that indicate RNA folding demarcates regions of protein translation and likely affects microRNA-mediated regulation of mRNAs in this model plant. We further reveal that RNA folding is significantly anticorrelated with overall transcript abundance, which is often due to the increased propensity of highly structured mRNAs to be degraded and/or processed into small RNAs. Finally, we find that secondary structure affects mRNA translation, suggesting that this feature regulates plant gene expression at multiple levels. These findings provide a global assessment of RNA folding and its significant regulatory effects in a plant transcriptome.

As far as I know, the miRNA-mRNA binding depends on complementarity between the seed sequence in the 3'UTR and the nucleotides 2-8 of the miRNA. But additional complementarity with the 3'-end of the miRNA affects effectivity of the targeting. Appart from that the secondary structure of the 3'UTR close to the binding site also affect the binding.

Hi

Secondary structure elements in RNA are dependent on the size of the RNA molecule. Binding of a miRNA to its cognate target involve just a few nucleotides pairing with the target. So, the only secondary structure expected in the binding could be an helical-like in the section of dsRNA. This is also prevented by the RNA binding pocket existing in Ago2 proteins. See this paper:

http://www.cell.com/abstract/S0092-8674%2812%2900618-6?switch=standard

However, a very important issue is to consider, as already was pointed out by Matthew, is the secondary structure of the 3'-UTR that could prevent the efficient binding of a miRNA. There are some applications for target prediction, like PITA, that take into account this fact:

http://genie.weizmann.ac.il/pubs/mir07/index.html

Good luck. Hope it helps.

Cheers

Paco

I suggest you to read this review :

Bartel, D. P. (2004). MicroRNAs: genomics, biogenesis, mechanism, and function. Cell, 116(2), 281–97. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/14744438

Not only the 3'-UTR, a mature miR can interact with 5'-UTR of a mRNA. The reports are coming recently. You may search in PubMed or Google. For example: miR-1291 inhibits expression of IRE1α by targeting its mRNA 5' UTR (PMID: 23598528).

You can also read:

"A biophysical miRNA-mRNA interaction model infers canonical and noncanonical targets"

Khorshid, M. et al. Nature Methods, 2013

http://www.ncbi.nlm.nih.gov/pubmed/23334102