. Author manuscript; available in PMC: 2020 May 1.

Published in final edited form as: FEBS Lett. 2019 Apr 24;593(10):1009–1019. doi: 10.1002/1873-3468.13383

Table 1.

Boltzmann factors for the proximal and distal segments of mRNA in the Gibbs ensemble

Segment and state	Boltzmann factor ^a
Proximal-open	exp(m[FX_F – ΔG_stretch] / k_BT)
Proximal-closed	exp(mΔG_bp / k_BT)
Proximal-bound	exp(mΔG_binding / k_BT)
Distal-open	exp(s[FX_F – ΔG_stretch] / k_BT)
Distal-closed	exp(sΔG_bp / k_BT)

exp denotes the exponential function. m=3 is the length of the proximal segment of mRNA [9], and s = 3 is the translocation step size for the ribosome dictated by codon size. F is the magnitude of applied external pulling force on the mRNA ends (e.g. by optical tweezers), and X_F is the extension of single-stranded RNA at each applied force F according to the worm-like chain (WLC) model [33–35] (Supp. Note 3). The free energies are chosen to be positive: ΔG_stretch is the stretching work for single-stranded mRNA per opened base pair in the WLC model [33], ΔG_bp is the average base pair stability at zero force according to nearest neighbor rules [36], and ΔG_binding (the only free parameter in this table) is the average mRNA-S3 binding stability per nucleotide at zero force. k_B is the Boltzmann constant, and T is temperature.