Computational modeling of RNA-protein binding interactions under an external force

Abstract

RNA binding proteins play a crucial role in post-transcriptional gene regulation by controlling the transport, processing, and translation of their target RNAs. Post-transcriptional gene regulation leads to the differential expression of genetic material and loss of regulation or over-regulation relates to a large range of cancers and diseases - many of which have directly been associated with RNA binding proteins and their target RNAs. To understand RNA, RNA binding proteins, and how they function in gene expression, it is essential to characterize how RNA binding proteins interact with their target RNAs. Here, we aim to assess the potential for single molecule force spectroscopy experiments to be used in the characterization of RNA-protein binding by investigating to what extent a change of extension due to RNA-protein binding is experimentally measurable and what aspects of the interaction can be deduced from such measurements. We predict the effect of protein binding on RNA force extension measurements via the open-source ViennaRNA package, which we have modified to simultaneously consider an external force, protein binding, and RNA secondary structure. From this work, we see protein concentration-dependent responses to external forces with discernable differences in predicted extensions around biologically relevant concentrations and a connection to protein binding domain geometry for several RNA binding proteins.

Figures (18)

• Figure 1: Example representation of RNA secondary structure. The four RNA bases A (green), U (red), C (blue), and G (yellow) are either base-paired (depicted with a filled center) or non-paired (unfilled center). The RNA backbone is depicted by a solid grey line while the hydrogen bonds that form the base pairs are shown with dashed, black lines. In the inset, an example of a pseudoknot is shown. A pseudoknot is defined by the formation of base pairs between bases in a loop structure with bases outside of that helix-loop structure. Pseudoknot structures are explicitly excluded from this work.
• Figure 2: Simplified representation of the recursive algorithm used to calculate the partition function of a given RNA molecule. The partition function for any given strand spanning from some base $i$ to base $j$, labeled $Q_{i,j}$, is the sum of the partition function over the structures where $i$ is unpaired, given by $Q_{i+1,j}$, and the constrained partition function over the structures where base $i$ is bound to some sufficiently separated base $k$, given by $Q^c_{i,j}$. RNA segments over which unconstrained partition functions are calculated are depicted with dashed, green lines, RNA segments over which constrained partition functions are calculated are depicted with solid, orange lines, unpaired bases are represented by a black dot, and base pairs are indicated by an arched black line.
• Figure 3: Overview of the development of this work's model, involving combining (a) RNA secondary structure modeling modified with (b) external force and with (c) interacting protein to get a (d) final model simulating applying an external force on an RNA molecule with interacting binding protein. (a) Three example RNA secondary structures $s$ and their corresponding free energies $\Delta G_s$. (b) The same three example RNA secondary structures $s$ under an external pulling force $F$. Each structure is superimposed with a depiction of the freely jointed chain model and their corresponding end-to-end extensions $R_s$ and modified free energies are included. (c) An example RNA secondary structure with a protein binding site (highlighted in orange) is used to illustrate the competition between RNA secondary structure formation and RNA interactions with single-stranded RNA-binding proteins (yellow ovals). (d) A force spectroscopy experiment that would be simulated by this final RNA-interaction model where competition between RNA secondary structure formation and interactions with single-stranded RNA-binding proteins occurs while an external force $F$ is applied on an RNA molecule trapped between two beads (grey circles) separated by extension $R$ (or $R'$). The binding footprint of the proteins (yellow ovals) depicted in (c) and (d) is 10 nucleotides in length.
• Figure 4: (a) Definitions of relevant quantities for modeling an external pulling force on an RNA molecule. The external, non-paired bases are underlined by the solid lines and the external stem indicated by the underlining jagged line. The number of external, unpaired bases $N_{exB}$ and the number of external stems $N_{exST}$ are represented in this example as well as the distance between two subsequent single-stranded RNA bases $x_b$ and the extension of an external stem $x_{ST}$. (b) In the freely jointed chain model, a polymer is represented by a chain of rods which are able to rotate completely independently of one another. The end-to-end extension of the RNA molecule $R$ is the same as the end-to-end extension of the representative chain and the length of an individual rod $\ell_0$ is the Kuhn length for single-stranded RNA.
• Figure 5: (a) The p5ab RNA hairpin sequence and expected secondary structure P5abExp. (b) Simulated force-extension curve obtained from our RNA structure model with external force modifications (black curve) compared to the rupture force $F_{rip}$ and change in extension $\Delta x_{rip}$ measurements made by Liphardt et al. for p5ab in the absence of Mg$^{2+}$P5abExp. The $F_{rip}$$=$$13.3$$\pm$$1$ pN rupture force measured experimentally is indicated by the horizontal solid green line (and the experimental error indicated by the horizontal dashed green lines). The rip extension $\Delta x_{rip}$$=$$18$ nm measured from constant force measurements is indicated by the vertical solid darker green lines and corresponding enclosed shading and the rip extension $\Delta x_{rip}$$=$$23$$\pm$$4$ nm extracted from $\ln$(k) vs. F plots is indicated by the vertical solid lighter green lines (and lighter shading). The experimental error on the rip extension (as extracted from the $\ln$(k) vs. F plots) is shown with the vertical dashed green lines. The experimental measurements for the rip extensions $\Delta x_{rip}$ shown on the force extension plot have been centered on the simulated rip to highlight the agreement between the simulation with experiment P5abExp.