{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T12:33:09Z","timestamp":1786365189571,"version":"build-2736575974"},"reference-count":88,"publisher":"American Chemical Society (ACS)","issue":"15","license":[{"start":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:00:00Z","timestamp":1783900800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:00:00Z","timestamp":1783900800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:00:00Z","timestamp":1783900800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,8,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Deep learning models have transformed several fields lately. In the past, capturing thermodynamic trends from free energies has relied on computationally expensive and time-consuming umbrella sampling simulations for dynamic proteins. Here, we investigate whether modern deep learning protein design methods (ProteinMPNN and ThermoMPNN) can obtain comparable energetic readouts more expeditiously. As a case study we use Troponin C (TnC) as a model system. TnC plays a central role in regulating muscle contraction through calcium-induced hydrophobic patch opening, transitioning between closed and open conformations. Disease associated mutations and isoform specific differences in TnC modulate this process by altering the free energies of hydrophobic patch opening. From ThermoMPNN, we quantified the free-energy differences associated with disease-linked variants in both open and closed states of cardiac TnC and compared with umbrella sampling results for the free energy of hydrophobic patch opening. We found a strong correlation with an R2 value of 0.82 between ThermoMPNN and umbrella sampling values for hydrophobic patch opening. The model accurately captured the lowered free energy of hydrophobic patch opening caused by hypertrophic cardiomyopathy (HCM) and designed calcium sensitizing mutations. In these cases, the average of difference in ThermoMPNN \u0394\u0394G values between the ensemble of closed and open structures was positive for 6\/7 mutations (\u0394\u0394Gclosed \u2013 \u0394\u0394Gopen &amp;gt; 0), indicating that the open structure is relatively more favorable than the closed state. Conversely, the model captured the increased free energy of hydrophobic patch opening caused by dilated cardiomyopathy (DCM) and designed calcium desensitizing mutations. Here the difference in the ThermoMPNN \u0394\u0394G values between the closed and open structures was negative for 5\/5 mutations (\u0394\u0394Gclosed \u2013 \u0394\u0394Gopen &amp;lt; 0), indicating the closed structure is relatively more favorable than the open state. We also showed that ProteinMPNN sequence probabilities distinguished isoform specific conformational preferences, correctly identifying skeletal TnC to favor a more open conformation compared to cardiac TnC. These observations were also consistent with previous umbrella sampling study. Together, these results demonstrate that deep learning frameworks have the potential to serve as viable alternative to traditional free energy methods like umbrella sampling to accurately determine trends in isoform-specific and mutational effects in TnC. More broadly, our findings highlight the potential of deep learning-based metrics to guide the design of calcium sensitizing and desensitizing mutations in TnC.<\/jats:p>","DOI":"10.1021\/acs.jcim.6c01925","type":"journal-article","created":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T11:22:12Z","timestamp":1783941732000},"page":"9448-9457","source":"Crossref","is-referenced-by-count":0,"title":["Deep Learning Models\nCapture Umbrella Sampling-Derived\nEnergetic Trends: A Troponin C Case Study"],"prefix":"10.1021","volume":"66","author":[{"given":"Akshaya","family":"Narayanasamy","sequence":"first","affiliation":[{"name":"University of California , , , ,","place":["Los Angeles, California, United States, 90095"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rocco","family":"Moretti","sequence":"additional","affiliation":[{"name":"Vanderbilt University , , , ,","place":["Nashville, Tennessee, United States, 37240"]},{"name":"Vanderbilt University , , , ,","place":["Nashville, Tennessee, United States, 37240"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jens","family":"Meiler","sequence":"additional","affiliation":[{"name":"Vanderbilt University , , , ,","place":["Nashville, Tennessee, United States, 37240"]},{"name":"Vanderbilt University , , , ,","place":["Nashville, Tennessee, United States, 37240"]},{"name":"University of Leipzig , , , ,","place":["Leipzig, Germany, 04103"]},{"name":"Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI and School of Embedded Composite Artificial Intelligence SECAI , , ,","place":["Dresden\/Leipzig, Germany, 04103"]},{"name":"Vanderbilt University , , , ,","place":["Nashville, Tennessee, United States, 37240"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3976-3473","authenticated-orcid":true,"given":"Steffen","family":"Lindert","sequence":"additional","affiliation":[{"name":"University of California , , , ,","place":["Los Angeles, California, United States, 90095"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,7,13]]},"reference":[{"issue":"7873","key":"2026081008112398500_cit1","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1038\/s41586-021-03819-2","article-title":"Highly accurate protein structure prediction\nwith AlphaFold","volume":"596","author":"Jumper","year":"2021","journal-title":"Nature"},{"key":"2026081008112398500_cit2","doi-asserted-by":"publisher","first-page":"na","DOI":"10.1101\/2021.10.04.463034","article-title":"Protein\ncomplex prediction with AlphaFold-Multimer","author":"Evans","year":"2022","journal-title":"bioRxiv"},{"issue":"6557","key":"2026081008112398500_cit3","doi-asserted-by":"publisher","first-page":"871","DOI":"10.1126\/science.abj8754","article-title":"Accurate prediction of protein structures and\ninteractions using a three-track neural network","volume":"373","author":"Baek","year":"2021","journal-title":"Science"},{"key":"2026081008112398500_cit4","volume-title":"Boltz-2: Towards Accurate and Efficient Binding Affinity\nPrediction","author":"Passaro","year":"2025"},{"issue":"6615","key":"2026081008112398500_cit5","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1126\/science.add2187","article-title":"Robust deep learning\u2013based protein sequence\ndesign using ProteinMPNN","volume":"378","author":"Dauparas","year":"2022","journal-title":"Science"},{"issue":"6","key":"2026081008112398500_cit6","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2314853121","article-title":"Transfer learning to\nleverage larger datasets for improved prediction of protein stability\nchanges","volume":"121","author":"Dieckhaus","year":"2024","journal-title":"Proc. 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Chem."},{"key":"2026081008112398500_cit20","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/bs.pmbts.2020.01.006","article-title":"Enhanced sampling\nand free energy calculations for protein simulations","volume":"170","author":"Liao","year":"2020","journal-title":"Prog. Mol. Biol. Transl Sci."},{"issue":"1","key":"2026081008112398500_cit21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.bpj.2020.11.014","article-title":"Troponin\nRevealed: Uncovering the Structure of the Thin Filament On-Off Switch\nin Striated Muscle","volume":"120","author":"Tobacman","year":"2021","journal-title":"Biophys. J."},{"issue":"12","key":"2026081008112398500_cit22","doi-asserted-by":"publisher","first-page":"3257","DOI":"10.1073\/pnas.1519541113","article-title":"Atomic resolution\nprobe for allostery in the regulatory thin filament","volume":"113","author":"Williams","year":"2016","journal-title":"Proc. Natl. Acad. Sci. U. S. 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Heart J."},{"issue":"12","key":"2026081008112398500_cit28","doi-asserted-by":"publisher","first-page":"1251","DOI":"10.1016\/j.jacc.2006.10.073","article-title":"Reviews of translational\nmedicine and genomics in cardiovascular\ndisease: new disease taxonomy and therapeutic implications cardiomyopathies:\ntherapeutics based on molecular phenotype","volume":"49","author":"Ashrafian","year":"2007","journal-title":"J.\nAm. Coll Cardiol"},{"key":"2026081008112398500_cit29","doi-asserted-by":"publisher","DOI":"10.3390\/ijms242417577","article-title":"Altering Calcium\nSensitivity in Heart Failure: A Crossroads of Disease Etiology and\nTherapeutic Innovation","volume":"24","author":"Saad","year":"2023","journal-title":"In International Journal\nof Molecular Sciences"},{"issue":"36","key":"2026081008112398500_cit30","doi-asserted-by":"publisher","first-page":"27785","DOI":"10.1074\/jbc.M110.112326","article-title":"Predicting cardiomyopathic\nphenotypes by altering Ca2+ affinity of cardiac troponin C","volume":"285","author":"Parvatiyar","year":"2010","journal-title":"J. Biol. 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Gen Physiol"},{"issue":"11","key":"2026081008112398500_cit33","doi-asserted-by":"publisher","first-page":"1950","DOI":"10.1021\/bi4000172","article-title":"Effects of calcium\nbinding and the hypertrophic cardiomyopathy\nA8V mutation on the dynamic equilibrium between closed and open conformations\nof the regulatory N-domain of isolated cardiac troponin C","volume":"52","author":"Cordina","year":"2013","journal-title":"Biochemistry"},{"key":"2026081008112398500_cit34","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.abb.2016.03.011","article-title":"Enhanced troponin I binding explains\nthe functional\nchanges produced by the hypertrophic cardiomyopathy mutation A8V of\ncardiac troponin C","volume":"601","author":"Zot","year":"2016","journal-title":"Arch. Biochem. Biophys."},{"key":"2026081008112398500_cit35","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.yjmcc.2015.08.017","article-title":"The structural and\nfunctional effects of the familial\nhypertrophic cardiomyopathy-linked cardiac troponin C mutation, L29Q","volume":"87","author":"Robertson","year":"2015","journal-title":"J. Mol. Cell Cardiol"},{"issue":"38","key":"2026081008112398500_cit36","doi-asserted-by":"publisher","first-page":"31845","DOI":"10.1074\/jbc.M112.377713","article-title":"A mutation in TNNC1-encoded\ncardiac troponin C, TNNC1-A31S,\npredisposes to hypertrophic cardiomyopathy and ventricular fibrillation","volume":"287","author":"Parvatiyar","year":"2012","journal-title":"J. Biol. Chem."},{"key":"2026081008112398500_cit37","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms10794","article-title":"Rationally\nengineered Troponin C modulates in vivo cardiac function\nand performance in health and disease","volume":"7","author":"Shettigar","year":"2016","journal-title":"Nat.\nCommun."},{"issue":"9","key":"2026081008112398500_cit38","doi-asserted-by":"publisher","first-page":"1975","DOI":"10.1021\/bi901867s","article-title":"Effect\nof calcium-sensitizing mutations on calcium\nbinding and exchange with troponin C in increasingly complex biochemical\nsystems","volume":"49","author":"Tikunova","year":"2010","journal-title":"Biochemistry"},{"issue":"34","key":"2026081008112398500_cit39","doi-asserted-by":"publisher","first-page":"35341","DOI":"10.1074\/jbc.M405413200","article-title":"Designing calcium-sensitizing\nmutations in the regulatory\ndomain of cardiac troponin C","volume":"279","author":"Tikunova","year":"2004","journal-title":"J. Biol. Chem."},{"issue":"28","key":"2026081008112398500_cit40","doi-asserted-by":"publisher","first-page":"11915","DOI":"10.1074\/jbc.M116.770776","article-title":"Changes in the dynamics of the cardiac\ntroponin C molecule explain the effects of Ca(2+)-sensitizing mutations","volume":"292","author":"Stevens","year":"2017","journal-title":"J. Biol. Chem."},{"issue":"2","key":"2026081008112398500_cit41","doi-asserted-by":"publisher","first-page":"H306","DOI":"10.1152\/ajpheart.00272.2020","article-title":"Dilated cardiomyopathy mutations\nin thin-filament regulatory\nproteins reduce contractility, suppress systolic Ca(2+), and activate\nNFAT and Akt signaling","volume":"319","author":"Robinson","year":"2020","journal-title":"Am. J. Physiol Heart\nCirc Physiol"},{"issue":"2","key":"2026081008112398500_cit42","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1161\/CIRCGENETICS.113.000324","article-title":"Desensitization of myofilaments\nto Ca2+ as\na therapeutic target for hypertrophic cardiomyopathy with mutations\nin thin filament proteins","volume":"7","author":"Alves","year":"2014","journal-title":"Circ Cardiovasc Genet"},{"issue":"39","key":"2026081008112398500_cit43","doi-asserted-by":"publisher","first-page":"34404","DOI":"10.1074\/jbc.M111.267211","article-title":"Functional\ncharacterization of TNNC1 rare variants identified in dilated cardiomyopathy","volume":"286","author":"Pinto","year":"2011","journal-title":"J. Biol. Chem."},{"issue":"20","key":"2026081008112398500_cit44","doi-asserted-by":"publisher","first-page":"2169","DOI":"10.1161\/CIRCULATIONAHA.109.929646","article-title":"Peripartum cardiomyopathy as a part of familial dilated\ncardiomyopathy","volume":"121","author":"van Spaendonck-Zwarts","year":"2010","journal-title":"Circulation"},{"issue":"3","key":"2026081008112398500_cit45","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1016\/j.jmb.2007.10.062","article-title":"Modulation\nof Cardiac Troponin C\nFunction by the Cardiac-Specific N-Terminus of Troponin I: Influence\nof PKA Phosphorylation and Involvement in Cardiomyopathies","volume":"375","author":"Baryshnikova","year":"2008","journal-title":"J. Mol. Biol."},{"issue":"2","key":"2026081008112398500_cit46","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.gene.2015.07.074","article-title":"Structure and function\nof cardiac troponin C (TNNC1):\nImplications for heart failure, cardiomyopathies, and troponin modulating\ndrugs","volume":"571","author":"Li","year":"2015","journal-title":"Gene"},{"issue":"26","key":"2026081008112398500_cit47","doi-asserted-by":"publisher","first-page":"15970","DOI":"10.1016\/S0021-9258(18)55492-2","article-title":"The structure and\nregulation of expression of the murine fast skeletal troponin C gene.\nIdentification of a developmentally regulated, muscle-specific transcriptional\nenhancer","volume":"265","author":"Parmacek","year":"1990","journal-title":"J. Biol. Chem."},{"issue":"26","key":"2026081008112398500_cit48","doi-asserted-by":"publisher","first-page":"8289","DOI":"10.1021\/bi9901679","article-title":"Binding of Cardiac Troponin-I147\u2013163\nInduces a Structural Opening in Human Cardiac Troponin-C","volume":"38","author":"Li","year":"1999","journal-title":"Biochemistry"},{"issue":"29","key":"2026081008112398500_cit49","doi-asserted-by":"publisher","first-page":"18216","DOI":"10.1074\/jbc.272.29.18216","article-title":"Structure\nof cardiac muscle troponin\nC unexpectedly reveals a closed regulatory domain","volume":"272","author":"Sia","year":"1997","journal-title":"J. Biol. Chem."},{"issue":"52","key":"2026081008112398500_cit50","doi-asserted-by":"publisher","first-page":"15654","DOI":"10.1021\/bi026687c","article-title":"The solution\nstructure of a cardiac troponin C-troponin I-troponin T complex shows\na somewhat compact troponin C interacting with an extended troponin\nI-troponin T component","volume":"41","author":"Heller","year":"2002","journal-title":"Biochemistry"},{"key":"2026081008112398500_cit51","doi-asserted-by":"publisher","DOI":"10.1016\/j.gene.2024.148651","article-title":"Troponin C gene mutations on cardiac muscle\ncell and skeletal Regulation: A comprehensive review","volume":"927","author":"Aborode","year":"2024","journal-title":"Gene"},{"issue":"27","key":"2026081008112398500_cit52","doi-asserted-by":"publisher","first-page":"7388","DOI":"10.1021\/acs.jpcb.1c03844","article-title":"Computational Methods Elucidate Consequences of Mutations\nand Post-translational Modifications on Troponin I Effective Concentration\nto Troponin C","volume":"125","author":"Cool","year":"2021","journal-title":"J. Phys. Chem. B"},{"issue":"22","key":"2026081008112398500_cit53","doi-asserted-by":"publisher","first-page":"5666","DOI":"10.1021\/acs.jcim.2c00508","article-title":"Umbrella Sampling Simulations Measure Switch Peptide\nBinding and Hydrophobic Patch Opening Free Energies in Cardiac Troponin","volume":"62","author":"Cool","year":"2022","journal-title":"J. Chem. Inf. Model."},{"issue":"6","key":"2026081008112398500_cit54","doi-asserted-by":"publisher","first-page":"3052","DOI":"10.1021\/acs.jcim.1c00419","article-title":"Adaptative Steered\nMolecular Dynamics Study of Mutagenesis\nEffects on Calcium Affinity in the Regulatory Domain of Cardiac Troponin\nC","volume":"61","author":"Hantz","year":"2021","journal-title":"J. Chem. Inf. Model."},{"issue":"23","key":"2026081008112398500_cit55","doi-asserted-by":"publisher","first-page":"6201","DOI":"10.1021\/acs.jcim.2c01132","article-title":"Computational Exploration\nand Characterization of Potential\nCalcium Sensitizing Mutations in Cardiac Troponin C","volume":"62","author":"Hantz","year":"2022","journal-title":"J. Chem. Inf. Model."},{"issue":"11","key":"2026081008112398500_cit56","doi-asserted-by":"publisher","first-page":"3462","DOI":"10.1021\/acs.jcim.3c00196","article-title":"Targeting Troponin\nC with Small Molecules Containing\nDiphenyl Moieties: Calcium Sensitivity Effects on Striated Muscles\nand Structure\u2013Activity Relationship","volume":"63","author":"Hantz","year":"2023","journal-title":"J. Chem. Inf. Model."},{"issue":"6","key":"2026081008112398500_cit57","doi-asserted-by":"publisher","first-page":"2964","DOI":"10.1021\/acs.jcim.9b00256","article-title":"Mechanism\nof Cardiac Troponin C Calcium\nSensitivity Modulation by Small Molecules Illuminated by Umbrella\nSampling Simulations","volume":"59","author":"Bowman","year":"2019","journal-title":"J. Chem. Inf Model"},{"issue":"8","key":"2026081008112398500_cit58","doi-asserted-by":"publisher","first-page":"1784","DOI":"10.1016\/j.bpj.2012.08.058","article-title":"Long-Timescale Molecular Dynamics\nSimulations Elucidate the Dynamics and Kinetics of Exposure of the\nHydrophobic Patch in Troponin C","volume":"103","author":"Lindert","year":"2012","journal-title":"Biophys. 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