**5. Conclusions**

Our study leads to the following conclusions:



**Supplementary Materials:** The following are available online at https://www.mdpi.com/1422-006 7/22/10/5301/s1, Figure S1: Representative conformations from unrestrained simulations for three peptide variants and the distribution of root mean square deviation from tight hairpin structure (PDB. 2kxa, model 1) for wild type, E11 deprotonated hemagglutin fusion peptide (wt− HAfp) simulation in trans-membrane orientation. Figure S2: Insertion depths of N-terminal amino group nitrogen atom and C*α* atoms of wt HAfp in considered configurations. Figure S3: Potentials of mean force for translocation between bulk water and membrane center for restrained peptides. Figure S4: Relations between contributions to free energy considered for obtaining binding free energies of unrestrained peptides at surface and deep minima, relative to unrestrained peptides in water. Figure S5: Results for Charmm36 force field. Figure S6: Supervised insertion attempts based on N-terminus progression. Figure S7: Scheme for Trp quenching calculations. Figure S8: Experimental results for lipid mixing. Figure S9: Experimental results for peptide binding to POPC SUVs. Figure S10: Experimental results for calcein leakage. Table S1: Insertion depths of Br atoms. Table S2: List of tREMD temperatures and list of conducted simulations. Table S3: List of umbrella sampling runs.

**Author Contributions:** Conceptualization, P.S. and R.W.; investigation, P.S., A.D., P.B. and R.W.; writing—original draft preparation, P.S.; and writing—review and editing, R.W. and P.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by EMBO Installation Grant 3051/2015 and the Opus gran<sup>t</sup> (National Science Centre UMO-2018/29/B/NZ1/02434) to P.S. R.W. and P.B. were supported by the Sonata Bis 8 gran<sup>t</sup> (National Science Centre UMO-2018/30/E/NZ1/00257). Computer simulations were carried out with the support of the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM), University of Warsaw, under gran<sup>t</sup> No. GA76-7, and by PLGrid Infrastructure.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** MD configuration files, system topologies, system structures, trajectories, and source experimental data are available on figshare (DOI 10.6084/m9.figshare.14365508).

**Acknowledgments:** We acknowledge Anna Wegrzyn (Faculty of Biology, University of Warsaw) for her assistance in binding experiments.

**Conflicts of Interest:** The authors declare no conflict of interest.
