With a positive monovalent ion placed at 3 (in the direction rOP1 + rOP2) away from each phosphate group. We removed the dangling phosphate groups at the 5 ends to avoid structural distortions upon minimization.pied by the solute or RNA molecule (Fennell et al. 2011). The electrostatic component is the excess energy of duplex formation when fixed, isolated conformations of strands 1 and 2 are brought to the final duplex configuration: DGelec = Gelec – Gelec – Gelec . duplex 1 2 This electrostatic contribution was computed using the Adaptive Poisson oltzmann Solver (APBS) (Baker et al. 2001) version 1.3. We used APBS’s standard parameter values (e.g., RNA and water dielectric constants of 2.0 and 78.54, respectively) and monovalent salt concentration of 150 mM to approximate physiological conditions (unless explicitly stated otherwise). We set the grid spacing to 0.4 in electrostatic calculations. Similarly, the interstrand van der Waals energy is defined as:vdw vdw vdw DEvdw = Eduplex – E1 – E2 .We computed this term using the TINKER routine “analyze” with the AMBER99 force field (Cornell et al. 1995). The nonpolar solvanonpolar tion energy DGsolv was computed using the HCT model (a generalized Born solvation approach) as implemented in TINKER. This term is usually small compared with other energy terms. The total binding energy (sum of electrostatics, van der Waals, and nonpolar solvation) was computed as a Boltzmann-weighted average of the structures in the ensemble at the given temperature. This binding energy reflects conformational fluctuations of duplexes in solution. When two molecules bind, there is a change in the translational, rotational, and vibrational degrees of freedom, which is entropic in origin. The free energy change associated with these degrees of freedom is given by Tidor and Karplus (1994): DGentropic = DGtrans + DGrot + DGvib , where these free energy components are written in the form Gtrans = Etrans – TStrans, etc.Nonyl β-D-glucopyranoside : 3 5 3 2pmkB T DGtrans = kB T – kB T + ln – ln(r) 2 2 2 h2 3 3 1 3 8p2 kB T – ln(s) DGrot = kB T – kB T + ln(pIA IB IC ) + ln 2 2 2 2 h3N-Binding free energy of double-stranded RNAsDouble-stranded RNAs are stabilized by van der Waals, electrostatic, and solvation energies.Cevostamab We use continuum or implicit solvent approaches to describe the effects of ions and water molecules. The electrostatic energy includes interactions between RNA strands and ions. The total duplex free binding energy is decomposed into electrostatic, non-electrostatic, and entropic components (Roux and Simonson 1999; Dong et al.PMID:24238415 2008): DGtotal = DGnonelec + DGelec + DGentropic , where Gentropic originates from the loss of translational, rotational, and vibrational motions upon duplex formation (Tidor and Karplus 1994) (elaborated below). The non-electrostatic component consists of the van der Waals and nonpolar solvation energies: DGnonelec = DEvdw + DGsolvnonpolarDGvib =i=1 hni hni + hn /k T 2 e i B -1 hni – kB T ln(1 – e-hni /kB T ) , ehni /kB T -3N–i=,which are assumed to be additive (Dill 1997). The nonpolar solvation term accounts for the energy needed to create the cavity occu-where IAIBIC is the product of the three principal moments of inertia; is the solute number density; is the symmetry factor (1 for nonsymmetric molecules); m is the mass; h is the Planck’s constant; i are the vibrational frequencies of the macromolecule computed using normal mode analysis; and N is the number of atoms. We computed the vibrational frequ.