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A comparative insight into peptide folding with quantum CVaR-VQE algorithm, MD simulations and structural alphabet analysis

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Abstract

Quantum computing in biology is one of the most rapidly evolving fields of technology. Protein folding is one of the key challenges which requires accurate and efficient algorithms with a quick computational time. Structural conformations of proteins with disordered regions need colossal amount of computational resource to map its least energy conformation state. In this regard, quantum algorithms like variational quantum eigensolver (VQE) are applied in the current research work to predict the lowest energy value of 50 peptides of seven amino acids each. VQE is initially used to calculate the energy values over which variational quantum optimization is applied via conditional value at risk (CVaR) over 100 iterations of 500,000 shots each to obtain least ground-state energy value. This is compared to the molecular dynamics-based simulations of 50 ns each to calculate the energy values along with the folding pattern. The results suggest efficient folding outcomes from CVaR-VQE compared to MD-based simulations and HMM-SA. With the ever-expanding quantum hardware and improving algorithms, the problem of protein folding can be resolved to obtain in-depth insights on the biological process and drug design.

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References

  1. Shea, J.-E., Brooks Iii, C.L.: FROM folding theories to folding proteins: a review and assessment of simulation studies of protein folding and unfolding. Annu. Rev. Phys. Chem. 52(1), 499–535 (2001)

    Article  ADS  CAS  PubMed  Google Scholar 

  2. Scheraga, H.A., Khalili, M., Liwo, A.: Protein-folding dynamics: overview of molecular simulation techniques. Annu. Rev. Phys. Chem. 58(1), 57–83 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  3. Freddolino, P.L., Liu, F., Gruebele, M., Schulten, K.: Ten-microsecond molecular dynamics simulation of a fast-folding WW domain. Biophys. J. 94(10), L75–L77 (2008)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. Daidone, I., Amadei, A., Roccatano, D., Nola, A.D.: Molecular dynamics simulation of protein folding by essential dynamics sampling: folding landscape of horse heart cytochrome c. Biophys. J. 85(5), 2865–2871 (2003)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  5. Beck, D.: Methods for molecular dynamics simulations of protein folding/unfolding in solution. Methods 34(1), 112–120 (2004)

    Article  CAS  PubMed  Google Scholar 

  6. Sonavane, U.B., Ramadugu, S.K., Joshi, R.R.: Study of early events in the protein folding of Villin headpiece using molecular dynamics simulation. J. Biomol. Struct. Dyn. 26(2), 203–214 (2008)

    Article  CAS  PubMed  Google Scholar 

  7. Pal, S., Bhattacharya, M., Lee, S.-S., Chakraborty, C.: Quantum computing in the next-generation computational biology landscape: from protein folding to molecular dynamics. Mol. Biotechnol. (2023). https://doi.org/10.1007/s12033-023-00765-4

    Article  PubMed  PubMed Central  Google Scholar 

  8. GhÉLis, C., Yon, J.: Introduction to considerations of protein folding deduced from characteristics of folded proteins. In: Ghélis, C. (ed.) Protein folding, pp. 35–6. Elsevier, Amsterdam (1982)

    Chapter  Google Scholar 

  9. Robert, A., Barkoutsos, P.K., Woerner, S., Tavernelli, I.: Resource-efficient quantum algorithm for protein folding. npj Quantum Inform. 7(1), 38 (2021)

    Article  ADS  Google Scholar 

  10. Vogt, N., Zanker, S., Reiner, J.-M., Marthaler, M., Eckl, T., Marusczyk, A.: Preparing ground states with a broken symmetry with variational quantum algorithms. Quantum Sci. Technol. 6(3), 035003 (2021)

    Article  ADS  Google Scholar 

  11. Choquette, A., Di Paolo, A., Barkoutsos, P.K., Sénéchal, D., Tavernelli, I., Blais, A.: Quantum-optimal-control-inspired ansatz for variational quantum algorithms. Phys. Rev. Res. 3(2), 023092 (2021)

    Article  CAS  Google Scholar 

  12. Cerezo, M., Verdon, G., Huang, H.-Y., Cincio, L., Coles, P.J.: Challenges and opportunities in quantum machine learning. Nat. Comput. Sci. 2(9), 567–576 (2022)

    Article  CAS  PubMed  Google Scholar 

  13. Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., et al.: The variational quantum Eigensolver: a review of methods and best practices. Phys. Rep. 986, 1–128 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  14. Cerezo, M., Sone, A., Volkoff, T., Cincio, L., Coles, P.J.: Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat. Commun. 12(1), 1791 (2021)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  15. Uvarov, A.V., Biamonte, J.D.: On barren plateaus and cost function locality in variational quantum algorithms. J. Phys. A Math. Theor. 54(24), 245301 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  16. Lee, J., Huggins, W.J., Head-Gordon, M., Whaley, K.B.: Generalized unitary coupled cluster wave functions for quantum computation. J. Chem. Theory Comput. 15(1), 311–324 (2018)

    Article  PubMed  Google Scholar 

  17. Holmes, Z., Sharma, K., Cerezo, M., Coles, P.J.: Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum. 3(1), 010313 (2022)

    Article  ADS  Google Scholar 

  18. Chandarana, P., Hegade, N.N., Montalban, I., Solano, E., Chen, X.: Digitized counterdiabatic quantum algorithm for protein folding. Phys. Rev. Appl. 20(1), 014024 (2023)

    Article  ADS  CAS  Google Scholar 

  19. Bharti, K., Cervera-Lierta, A., Kyaw, T.H., Haug, T., Alperin-Lea, S., Anand, A., et al.: Noisy intermediate-scale quantum algorithms. Rev. Modern Phys. 94(1), 015004 (2022)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  20. Wecker, D., Hastings, M.B., Troyer, M.: Progress towards practical quantum variational algorithms. Phys. Rev. A. 92(4), 042303 (2015)

    Article  ADS  Google Scholar 

  21. Wiersema, R., Zhou, C., de Sereville, Y., Carrasquilla, J.F., Kim, Y.B., Yuen, H.: Exploring entanglement and optimization within the Hamiltonian variational ansatz. PRX Quantum. 1(2), 020319 (2020)

    Article  Google Scholar 

  22. Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., et al.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242–246 (2017)

    Article  ADS  CAS  PubMed  Google Scholar 

  23. Farhi, E., Goldstone, J., Gutmann, S., Zhou, L.: The quantum approximate optimization algorithm and the sherrington-kirkpatrick model at infinite size. Quantum 6, 759 (2022)

    Article  Google Scholar 

  24. Dunker, A.K., Lawson, J.D., Brown, C.J., Williams, R.M., Romero, P., Oh, J.S., et al.: Intrinsically disordered protein. J. Mol. Graph. Model. 19(1), 26–59 (2001)

    Article  CAS  PubMed  Google Scholar 

  25. Campen, A., Williams, R., Brown, C., Meng, J., Uversky, V., Dunker, A.: TOP-IDP-scale: a new amino acid scale measuring propensity for intrinsic disorder. Protein Pept. Lett. 15(9), 956–963 (2008)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Du, Y., Huang, T., You, S., Hsieh, M.-H., Tao, D.: Quantum circuit architecture search for variational quantum algorithms. npj Quantum Inform. 8(1), 62 (2022)

    Article  ADS  Google Scholar 

  27. Belzunce, F., Riquelme, C.M., Mulero, J.: An Introduction to Stochastic Orders. Academic Press, London (2015). https://doi.org/10.1016/B978-0-12-803768-3.00001-6

    Book  Google Scholar 

  28. López, C.P.: Optimization techniques via the optimization toolbox. In: Lopez, C. (ed.) MATLAB optimization techniques. Apress, Berkeley, CA (2014). https://doi.org/10.1007/978-1-4842-0292-0_6

    Chapter  Google Scholar 

  29. Gutmann, H.-M.: A radial basis function method for global optimization. J. Global Optim. 19, 201–227 (2001)

    Article  MathSciNet  Google Scholar 

  30. MadhaviSastry, G., Adzhigirey, M., Day, T., Annabhimoju, R., Sherman, W.: Protein and ligand preparation: parameters, protocols, and influence on virtual screening enrichments. J. Comput. Aided Mol. Des. 27(3), 221–234 (2013)

    Article  ADS  CAS  Google Scholar 

  31. Greenwood, J.R., Calkins, D., Sullivan, A.P., Shelley, J.C.: Towards the comprehensive, rapid, and accurate prediction of the favorable tautomeric states of drug-like molecules in aqueous solution. J. Comput. Aided Mol. Des. 24(6–7), 591–604 (2010)

    Article  ADS  CAS  PubMed  Google Scholar 

  32. Shelley, J.C., Cholleti, A., Frye, L.L., Greenwood, J.R., Timlin, M.R., Uchimaya, M.: Epik: a software program for pK a prediction and protonation state generation for drug-like molecules. J. Comput. Aided Mol. Des. 21(12), 681–691 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  33. Roos, K., Wu, C., Damm, W., Reboul, M., Stevenson, J.M., Lu, C., et al.: OPLS3e: Extending force field coverage for drug-like small molecules. J. Chem. Theory Comput. 15(3), 1863–1874 (2019)

    Article  CAS  PubMed  Google Scholar 

  34. Mark, P., Nilsson, L.: Structure and dynamics of the TIP3P, SPC, and SPC/E water models at 298 K. J. Phys. Chem. A 105(43), 9954–9960 (2001)

    Article  CAS  Google Scholar 

  35. Bowers, K.J., Sacerdoti, F.D., Salmon, J.K., Shan, Y., Shaw, D.E., Chow, E., et al.: Molecular dynamics—Scalable algorithms for molecular dynamics simulations on commodity clusters. In: Proceedings of the 2006 ACM/IEEE conference on Supercomputing—SC '06, ACM Press (2006)

  36. Uttarkar, A., Niranjan, V.: Brefeldin A variant via combinatorial screening acts as an effective antagonist inducing structural modification in EPAC2. Mol. Simul. 48(17), 1592–1603 (2022)

    Article  CAS  Google Scholar 

  37. Niranjan, V., Uttarkar, A., Ramakrishnan, A., Muralidharan, A., Shashidhara, A., Acharya, A., et al.: De novo design of anti-COVID Drugs using machine learning-based equivariant diffusion model targeting the spike protein. Curr. Issues Mol. Biol. 45(5), 4261–4284 (2023)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Rey, J., Murail, S., de Vries, S., Derreumaux, P., Tuffery, P.: PEP-FOLD4: a pH-dependent force field for peptide structure prediction in aqueous solution. Nucleic Acids Res. 51(W1), W432–W437 (2023). https://doi.org/10.1093/nar/gkad376

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. Camproux, A.C., et al.: A hidden markov model derived structural alphabet for proteins. J. Mol. Biol. 339(3), 591–605 (2004). https://doi.org/10.1016/j.jmb.2004.04.005

    Article  CAS  PubMed  Google Scholar 

  40. Perdomo, A., Truncik, C., Tubert-Brohman, I., Rose, G., Aspuru-Guzik, A.: Construction of model Hamiltonians for adiabatic quantum computation and its application to finding low-energy conformations of lattice protein models. Phys. Rev. A. 78(1), 012320 (2008)

    Article  ADS  Google Scholar 

  41. Perdomo-Ortiz, A., Dickson, N., Drew-Brook, M., Rose, G., Aspuru-Guzik, A.: Finding low-energy conformations of lattice protein models by quantum annealing. Sci. Rep. 2(1), 1–7 (2012)

    Article  Google Scholar 

  42. Babbush, R., Perdomo-Ortiz, A., O’Gorman, B., Macready, W., Aspuru-Guzik, A.: Construction of Energy Functions for Lattice Heteropolymer Models: Efficient Encodings for Constraint Satisfaction Programming and Quantum Annealing. In: Prigogine, I., Rice, S.A. (eds.) Advances in chemical physics, pp. 201–44. Wiley, London (2014)

    Google Scholar 

  43. Fingerhuth, M., Babej, T., Wittek, P.: Adiabatic quantum computation. Definitions: Qeios, (2019)

  44. Fingerhuth, M., Babej, T., Wittek, P.: Open-source software in quantum computing. PLoS ONE 13(12), e0208561 (2018)

    Article  PubMed  PubMed Central  Google Scholar 

  45. Barkoutsos, P.K., Nannicini, G., Robert, A., Tavernelli, I., Woerner, S.: Improving variational quantum optimization using CVaR. Quantum 4, 256 (2020)

    Article  Google Scholar 

  46. Boulebnane, S., Lucas, X., Meyder, A., Adaszewski, S., Montanaro, A.: Peptide conformational sampling using the quantum approximate optimization algorithm. npj Quantum Inform. 9(1), 70 (2023)

    Article  ADS  Google Scholar 

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Acknowledgements

The authors thank Department of Computer Science and Engineering, the R V College of Engineering, Bangalore, for providing GPU (NVIDIA A100) computational support. The authors thank the support of Dr. Venugopal K, from the Department of Mathematics. A heartfelt thanks to Suman A for her unconditional support. A warm heartfelt thanks to the staff and administration at the R V College of Engineering for their support.

Funding

This research work was funded by Ministry of Electronics and Information Technology under the Meity QCaL Cohort-II which provides the access to Amazon Braket.

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VN was in for ideation and conceptualization. AU contributed to the computational analysis and drafting the manuscript. Both the authors have read and agreed to the published version of the manuscript.

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Correspondence to Vidya Niranjan.

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Uttarkar, A., Niranjan, V. A comparative insight into peptide folding with quantum CVaR-VQE algorithm, MD simulations and structural alphabet analysis. Quantum Inf Process 23, 48 (2024). https://doi.org/10.1007/s11128-024-04261-9

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