Deep Learning Models Capture Umbrella Sampling-Derived Energetic Trends: A Troponin C Case Study

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 ΔΔG values between the ensemble of closed and open structures was positive for 6/7 mutations (ΔΔGclosed - ΔΔGopen > 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 ΔΔG values between the closed and open structures was negative for 5/5 mutations (ΔΔGclosed - ΔΔGopen < 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.