When I use some web servers to predict a mRNA secondary structure, I find they always required in a small size sequence. If I use a long sequence and cut it into small parts, do these small parts change the energy or thermodynamic data from the origin sequence when predicting? Is there any effective way to find the right sites when cutting the long sequence?
Yes, the structure predicted by splitting up the sequence may not represent the actual structure of the full-length RNA. A simple hypothetical case would be that of an RNA whose 3' and 5' UTR interact to cause circularization.
I am afraid there is not clear rule for choosing the subsequences such that the assembly of the individual secondary structures is closest the the actual structure.
We may expect that, with better computational power, the limitation on the size of the sequence for secondary structure prediction, can be overcome.
However, there are experimental techniques using RNA-sequencing that can determine the actual secondary structure — SHAPE-seq (ver 2.0; Loughrey et al. 2014) and structure-seq (Ding et al. 2014). Structure-seq in-fact, tries to determine the RNA secondary structures in-vivo and hence may be a more powerful tool.
However, you said you are working with mRNAs. I guess for mRNAs you can predict the structures of UTRs and the CDS separately. Actually depends on what you are interested in. CDS usually does not harbour any structural motif and any secondary structure in the CDS is usually resolved by the helicase activity of eIF4A. However, secondary structures can slow down the translation elongation rate (Mao et al. 2010, Gorochowski et al. 2015).
Loughrey, D., Watters, K. E., Settle, A. H., & Lucks, J. B. (2014). SHAPE-Seq 2.0: systematic optimization and extension of high-throughput chemical probing of RNA secondary structure with next generation sequencing. Nucleic acids research, 42(21) e165.
Ding, Y., Tang, Y., Kwok, C. K., Zhang, Y., Bevilacqua, P. C., & Assmann, S. M. (2014). In vivo genome-wide profiling of RNA secondary structure reveals novel regulatory features. Nature, 505(7485), 696-700.
Mao, Y., Liu, H., Liu, Y., & Tao, S. (2014). Deciphering the rules by which dynamics of mRNA secondary structure affect translation efficiency in Saccharomyces cerevisiae. Nucleic acids research, 42(8), 4813-4822.
Gorochowski, T. E., Ignatova, Z., Bovenberg, R. A., & Roubos, J. A. (2015). Trade-offs between tRNA abundance and mRNA secondary structure support smoothing of translation elongation rate. Nucleic acids research, gkv199.