Analytical Expressions of the Markov Chain of K-Ras4B Protein within the Catalytic Environment and a New Markov-State Model

Orchidea Maria Lecian

doi:10.61927/igmin133

21 of 152

Methodology of the Professional-Business Game for the Development of a Cadet Leader in Professional Training Courses (L-1B) of the Tactical Level of Military Education

Igor Kozubtsov

23 of 152

Properties of Indium Antimonide Nanocrystals as Nanoelectronic Elements

Nikolai Dmitrievich Zhukov

Biology Group Research Article 記事ID: igmin133

Analytical Expressions of the Markov Chain of K-Ras4B Protein within the Catalytic Environment and a New Markov-State Model

Computational Biology Molecular Biology Biophysics

Orchidea Maria Lecian ^*

Affiliation

Sapienza University of Rome, Rome, Italy

DOI10.61927/igmin133 全文HTML 全文PDF この記事を引用する

要約

The finite Markov chain to which there correspond the qualities of the conformational dynamics of the K-Ras4B proteins in the catalytic reaction is written. The corresponding Markov-Sates models are studied.

The properties of the K-Ras4B processes Markov chain allow one to define a new two-state MSM for the analytical description of the final-state transition. The time evolution of the eigenvalue corresponding to the final-state transition in the Galerkin description is written.

The tools for the analytical calculations of the relative error are therefore prepared.

New analytical formulations of the time evolution of the eigenvalue corresponding to the final-state transition are newly written from the experimental data and form the properties of the lag time in shaping the discretization error. The features of the discretization error are newly studied. A comparison with the experimental data is proposed.

参考文献

Zhang H, Ni D, Fan J, Li M, Zhang J, Hua C, Nussinov R, Lu S. Markov State Models and Molecular Dynamics Simulations Reveal the Conformational Transition of the Intrinsically Disordered Hypervariable Region of K-Ras4B to the Ordered Conformation. J Chem Inf Model. 2022 Sep 12;62(17):4222-4231. doi: 10.1021/acs.jcim.2c00591. Epub 2022 Aug 22. PMID: 35994329.
López CA, Agarwal A, Van QN, Stephen AG, Gnanakaran S. Unveiling the Dynamics of KRAS4b on Lipid Model Membranes. J Membr Biol. 2021 Apr;254(2):201-216. doi: 10.1007/s00232-021-00176-z. Epub 2021 Apr 7. PMID: 33825026; PMCID: PMC8052243.
Baum LE, Petrie T, Soules G, Weiss N. A Maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann Math Stat. 1970; 41:164-171.
Shrestha R, Chen D, Frank P, Dwight VN, Thomas JT. Recapitulation of cell-like KRAS4b membrane dynamics on complex biomimetic membranes, iScience. 2022; 25: 1; 103608.
Nussinov R, Zhang M, Maloney R, Jang H. Ras isoform-specific expression, chromatin accessibility, and signaling. Biophys Rev. 2021 Jul 31;13(4):489-505. doi: 10.1007/s12551-021-00817-6. PMID: 34466166; PMCID: PMC8355297.
Chakrabarti M, Jang H, Nussinov R. Comparison of the Conformations of KRAS Isoforms, K-Ras4A and K-Ras4B, Points to Similarities and Significant Differences. J Phys Chem B. 2016 Feb 4;120(4):667-79. doi: 10.1021/acs.jpcb.5b11110. Epub 2016 Jan 27. PMID: 26761128; PMCID: PMC7815164.
Fan J, Liu Y, Kong R, Ni D, Yu Z, Lu S, Zhang J. Harnessing Reversed Allosteric Communication: A Novel Strategy for Allosteric Drug Discovery. J Med Chem. 2021 Dec 23;64(24):17728-17743. doi: 10.1021/acs.jmedchem.1c01695. Epub 2021 Dec 8. PMID: 34878270.
Lu S, Ni D, Wang C, He X, Lin H, Wang Z, Zhang J. Deactivation Pathway of Ras GTPase Underlies Conformational Substates as Targets for Drug Design. ACS Catal. 2019; 9: 7188-7196.
Wang CX, Wang TT, Zhang KD, Li MY, Shen QC, Lu SY, Zhang J. Pan-KRAS inhibitors suppress proliferation through feedback regulation in pancreatic ductal adenocarcinoma. Acta Pharmacol Sin. 2022 Oct;43(10):2696-2708. doi: 10.1038/s41401-022-00897-4. Epub 2022 Mar 29. PMID: 35352018; PMCID: PMC9525295.
Shi Y, Cao S, Ni D, Fan J, Lu S, Xue M. The Role of Conformational Dynamics and Allostery in the Control of Distinct Efficacies of Agonists to the Glucocorticoid Receptor. Front Mol Biosci. 2022 Jul 7;9:933676. doi: 10.3389/fmolb.2022.933676. PMID: 35874618; PMCID: PMC9300934.
Lu S, Banerjee A, Jang H, Zhang J, Gaponenko V, Nussinov R. GTP Binding and Oncogenic Mutations May Attenuate Hypervariable Region (HVR)-Catalytic Domain Interactions in Small GTPase K-Ras4B, Exposing the Effector Binding Site. J Biol Chem. 2015 Nov 27;290(48):28887-900. doi: 10.1074/jbc.M115.664755. Epub 2015 Oct 9. PMID: 26453300; PMCID: PMC4661403.
Ioannis Papastathopoulos, Kirstin Strokorb, Jonathan A. Tawn, Adam Butler, Extreme Events of Markov Chains, Advances in Applied Probability Vol. 49, No. 1 ( 2017), 134-161.
Pantsar T. The current understanding of KRAS protein structure and dynamics. Comput Struct Biotechnol J. 2020; 18: 189-198.
Husic BE, Pande VS. Markov State Models: From an Art to a Science. J Am Chem Soc. 2018 Feb 21;140(7):2386-2396. doi: 10.1021/jacs.7b12191. Epub 2018 Feb 2. PMID: 29323881.
Hunter JC, Manandhar A, Carrasco MA, Gurbani D, Gondi S, Westover KD. Biochemical and Structural Analysis of Common Cancer-Associated KRAS Mutations. Mol Cancer Res. 2015 Sep;13(9):1325-35. doi: 10.1158/1541-7786.MCR-15-0203. Epub 2015 Jun 2. PMID: 26037647.
Winters IP, Chiou SH, Paulk NK, McFarland CD, Lalgudi PV, Ma RK, Lisowski L, Connolly AJ, Petrov DA, Kay MA, Winslow MM. Multiplexed in vivo homology-directed repair and tumor barcoding enables parallel quantification of Kras variant oncogenicity. Nat Commun. 2017 Dec 12;8(1):2053. doi: 10.1038/s41467-017-01519-y. PMID: 29233960; PMCID: PMC5727199.
Haigis KM. KRAS Alleles: The Devil Is in the Detail. Trends Cancer. 2017 Oct;3(10):686-697. doi: 10.1016/j.trecan.2017.08.006. Epub 2017 Sep 12. PMID: 28958387; PMCID: PMC5824632.
Smith MJ, Ikura M. Integrated RAS signaling defined by parallel NMR detection of effectors and regulators. Nat Chem Biol. 2014 Mar;10(3):223-30. doi: 10.1038/nchembio.1435. Epub 2014 Jan 19. PMID: 24441586.
Pantsar T, Rissanen S, Dauch D, Laitinen T, Vattulainen I, Poso A. Assessment of mutation probabilities of KRAS G12 missense mutants and their long-timescale dynamics by atomistic molecular simulations and Markov state modeling. PLoS Comput Biol. 2018 Sep 10;14(9):e1006458. doi: 10.1371/journal.pcbi.1006458. PMID: 30199525; PMCID: PMC6147662.
Prakash P, Gorfe AA. Probing the Conformational and Energy Landscapes of KRAS Membrane Orientation. J Phys Chem B. 2019 Oct 17;123(41):8644-8652. doi: 10.1021/acs.jpcb.9b05796. Epub 2019 Oct 9. PMID: 31554397; PMCID: PMC7045699.
Lu S, Jang H, Nussinov R, Zhang J. The Structural Basis of Oncogenic Mutations G12, G13 and Q61 in Small GTPase K-Ras4B. Sci Rep. 2016 Feb 23;6:21949. doi: 10.1038/srep21949. PMID: 26902995; PMCID: PMC4763299.
Lecian OM. Analytical results from the two-states Markovv-states model and applications to validation of molecular dynamics. International Journal of Mathematics and Computer Research. 2023; 11: 9.
Suárez E, Adelman JL, Zuckerman DM. Accurate Estimation of Protein Folding and Unfolding Times: Beyond Markov State Models. J Chem Theory Comput. 2016 Aug 9;12(8):3473-81. doi: 10.1021/acs.jctc.6b00339. Epub 2016 Jul 11. PMID: 27340835; PMCID: PMC5022777.
Zhang X, Liang W, Zheng G, Li B. Decoding the deactivation mechanism of R192W mutation of ZAP-70 using molecular dynamics simulations and binding free energy calculations. J Mol Model. 2023 Nov 13;29(12):371. doi: 10.1007/s00894-023-05771-6. PMID: 37953318.
Qi X, Li G, Liu J, Mou L, Zhang Y, Guo S, Chen X, Li W. Structural and energetic insights into the selective inhibition of PKMYT1 against WEE1. J Biomol Struct Dyn. 2023 Jun 22:1-9. doi: 10.1080/07391102.2023.2225106. Epub ahead of print. PMID: 37345529.
Liang F, Kang Z, Sun X, Chen J, Duan X, He H, Cheng J. Inhibition mechanism of MRTX1133 on KRAS^G12D: a molecular dynamics simulation and Markov state model study. J Comput Aided Mol Des. 2023 Mar;37(3):157-166. doi: 10.1007/s10822-023-00498-1. Epub 2023 Feb 28. PMID: 36849761.
Pantsar T, Rissanen S, Dauch D, Laitinen T, Vattulainen I, Poso A. Assessment of mutation probabilities of KRAS G12 missense mutants and their long-timescale dynamics by atomistic molecular simulations and Markov state modeling. PLoS Comput Biol. 2018 Sep 10;14(9):e1006458. doi: 10.1371/journal.pcbi.1006458. PMID: 30199525; PMCID: PMC6147662.

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[1] Zhang H, Ni D, Fan J, Li M, Zhang J, Hua C, Nussinov R, Lu S. Markov State Models and Molecular Dynamics Simulations Reveal the Conformational Transition of the Intrinsically Disordered Hypervariable Region of K-Ras4B to the Ordered Conformation. J Chem Inf Model. 2022 Sep 12;62(17):4222-4231. doi: 10.1021/acs.jcim.2c00591. Epub 2022 Aug 22. PMID: 35994329.

[2] López CA, Agarwal A, Van QN, Stephen AG, Gnanakaran S. Unveiling the Dynamics of KRAS4b on Lipid Model Membranes. J Membr Biol. 2021 Apr;254(2):201-216. doi: 10.1007/s00232-021-00176-z. Epub 2021 Apr 7. PMID: 33825026; PMCID: PMC8052243.

[3] Baum LE, Petrie T, Soules G, Weiss N. A Maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann Math Stat. 1970; 41:164-171.

[4] Shrestha R, Chen D, Frank P, Dwight VN, Thomas JT. Recapitulation of cell-like KRAS4b membrane dynamics on complex biomimetic membranes, iScience. 2022; 25: 1; 103608.

[5] Nussinov R, Zhang M, Maloney R, Jang H. Ras isoform-specific expression, chromatin accessibility, and signaling. Biophys Rev. 2021 Jul 31;13(4):489-505. doi: 10.1007/s12551-021-00817-6. PMID: 34466166; PMCID: PMC8355297.

[6] Chakrabarti M, Jang H, Nussinov R. Comparison of the Conformations of KRAS Isoforms, K-Ras4A and K-Ras4B, Points to Similarities and Significant Differences. J Phys Chem B. 2016 Feb 4;120(4):667-79. doi: 10.1021/acs.jpcb.5b11110. Epub 2016 Jan 27. PMID: 26761128; PMCID: PMC7815164.

[7] Fan J, Liu Y, Kong R, Ni D, Yu Z, Lu S, Zhang J. Harnessing Reversed Allosteric Communication: A Novel Strategy for Allosteric Drug Discovery. J Med Chem. 2021 Dec 23;64(24):17728-17743. doi: 10.1021/acs.jmedchem.1c01695. Epub 2021 Dec 8. PMID: 34878270.

[8] Lu S, Ni D, Wang C, He X, Lin H, Wang Z, Zhang J. Deactivation Pathway of Ras GTPase Underlies Conformational Substates as Targets for Drug Design. ACS Catal. 2019; 9: 7188-7196.

[9] Wang CX, Wang TT, Zhang KD, Li MY, Shen QC, Lu SY, Zhang J. Pan-KRAS inhibitors suppress proliferation through feedback regulation in pancreatic ductal adenocarcinoma. Acta Pharmacol Sin. 2022 Oct;43(10):2696-2708. doi: 10.1038/s41401-022-00897-4. Epub 2022 Mar 29. PMID: 35352018; PMCID: PMC9525295.

[10] Shi Y, Cao S, Ni D, Fan J, Lu S, Xue M. The Role of Conformational Dynamics and Allostery in the Control of Distinct Efficacies of Agonists to the Glucocorticoid Receptor. Front Mol Biosci. 2022 Jul 7;9:933676. doi: 10.3389/fmolb.2022.933676. PMID: 35874618; PMCID: PMC9300934.

[11] Lu S, Banerjee A, Jang H, Zhang J, Gaponenko V, Nussinov R. GTP Binding and Oncogenic Mutations May Attenuate Hypervariable Region (HVR)-Catalytic Domain Interactions in Small GTPase K-Ras4B, Exposing the Effector Binding Site. J Biol Chem. 2015 Nov 27;290(48):28887-900. doi: 10.1074/jbc.M115.664755. Epub 2015 Oct 9. PMID: 26453300; PMCID: PMC4661403.

[12] Ioannis Papastathopoulos, Kirstin Strokorb, Jonathan A. Tawn, Adam Butler, Extreme Events of Markov Chains, Advances in Applied Probability Vol. 49, No. 1 ( 2017), 134-161.

[13] Pantsar T. The current understanding of KRAS protein structure and dynamics. Comput Struct Biotechnol J. 2020; 18: 189-198.

[14] Husic BE, Pande VS. Markov State Models: From an Art to a Science. J Am Chem Soc. 2018 Feb 21;140(7):2386-2396. doi: 10.1021/jacs.7b12191. Epub 2018 Feb 2. PMID: 29323881.

[15] Hunter JC, Manandhar A, Carrasco MA, Gurbani D, Gondi S, Westover KD. Biochemical and Structural Analysis of Common Cancer-Associated KRAS Mutations. Mol Cancer Res. 2015 Sep;13(9):1325-35. doi: 10.1158/1541-7786.MCR-15-0203. Epub 2015 Jun 2. PMID: 26037647.

[16] Winters IP, Chiou SH, Paulk NK, McFarland CD, Lalgudi PV, Ma RK, Lisowski L, Connolly AJ, Petrov DA, Kay MA, Winslow MM. Multiplexed in vivo homology-directed repair and tumor barcoding enables parallel quantification of Kras variant oncogenicity. Nat Commun. 2017 Dec 12;8(1):2053. doi: 10.1038/s41467-017-01519-y. PMID: 29233960; PMCID: PMC5727199.

[17] Haigis KM. KRAS Alleles: The Devil Is in the Detail. Trends Cancer. 2017 Oct;3(10):686-697. doi: 10.1016/j.trecan.2017.08.006. Epub 2017 Sep 12. PMID: 28958387; PMCID: PMC5824632.

[18] Smith MJ, Ikura M. Integrated RAS signaling defined by parallel NMR detection of effectors and regulators. Nat Chem Biol. 2014 Mar;10(3):223-30. doi: 10.1038/nchembio.1435. Epub 2014 Jan 19. PMID: 24441586.

[19] Pantsar T, Rissanen S, Dauch D, Laitinen T, Vattulainen I, Poso A. Assessment of mutation probabilities of KRAS G12 missense mutants and their long-timescale dynamics by atomistic molecular simulations and Markov state modeling. PLoS Comput Biol. 2018 Sep 10;14(9):e1006458. doi: 10.1371/journal.pcbi.1006458. PMID: 30199525; PMCID: PMC6147662.

[20] Prakash P, Gorfe AA. Probing the Conformational and Energy Landscapes of KRAS Membrane Orientation. J Phys Chem B. 2019 Oct 17;123(41):8644-8652. doi: 10.1021/acs.jpcb.9b05796. Epub 2019 Oct 9. PMID: 31554397; PMCID: PMC7045699.

[21] Lu S, Jang H, Nussinov R, Zhang J. The Structural Basis of Oncogenic Mutations G12, G13 and Q61 in Small GTPase K-Ras4B. Sci Rep. 2016 Feb 23;6:21949. doi: 10.1038/srep21949. PMID: 26902995; PMCID: PMC4763299.

[22] Lecian OM. Analytical results from the two-states Markovv-states model and applications to validation of molecular dynamics. International Journal of Mathematics and Computer Research. 2023; 11: 9.

[23] Suárez E, Adelman JL, Zuckerman DM. Accurate Estimation of Protein Folding and Unfolding Times: Beyond Markov State Models. J Chem Theory Comput. 2016 Aug 9;12(8):3473-81. doi: 10.1021/acs.jctc.6b00339. Epub 2016 Jul 11. PMID: 27340835; PMCID: PMC5022777.

[24] Zhang X, Liang W, Zheng G, Li B. Decoding the deactivation mechanism of R192W mutation of ZAP-70 using molecular dynamics simulations and binding free energy calculations. J Mol Model. 2023 Nov 13;29(12):371. doi: 10.1007/s00894-023-05771-6. PMID: 37953318.

[25] Qi X, Li G, Liu J, Mou L, Zhang Y, Guo S, Chen X, Li W. Structural and energetic insights into the selective inhibition of PKMYT1 against WEE1. J Biomol Struct Dyn. 2023 Jun 22:1-9. doi: 10.1080/07391102.2023.2225106. Epub ahead of print. PMID: 37345529.

[26] Liang F, Kang Z, Sun X, Chen J, Duan X, He H, Cheng J. Inhibition mechanism of MRTX1133 on KRAS^G12D: a molecular dynamics simulation and Markov state model study. J Comput Aided Mol Des. 2023 Mar;37(3):157-166. doi: 10.1007/s10822-023-00498-1. Epub 2023 Feb 28. PMID: 36849761.

[27] Pantsar T, Rissanen S, Dauch D, Laitinen T, Vattulainen I, Poso A. Assessment of mutation probabilities of KRAS G12 missense mutants and their long-timescale dynamics by atomistic molecular simulations and Markov state modeling. PLoS Comput Biol. 2018 Sep 10;14(9):e1006458. doi: 10.1371/journal.pcbi.1006458. PMID: 30199525; PMCID: PMC6147662.

Analytical Expressions of the Markov Chain of K-Ras4B Protein within the Catalytic Environment and a New Markov-State Model

Affiliation

要約