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Figure 1. Model Hamiltonian for amide I vibrations in a protein.

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Figure 2. (a) Correlation between the DFT-computed (¦Ø_DFT) (black lines/dots) and NN-predicted (¦Ø_NN) (red lines/dots) amide I vibrational frequencies after cross-validation. (b-d) Comparison of the DFT-computed amide I vibrational transition dipole moment in the x, y, z direction (¦Ìx,y,z_DFT) (black lines/dots) and NN-predicted (¦Ìx,y,z_NN) (red lines/dots) after cross-validation. (e) Amide I vibrational normal modes (a, b) and local modes (c, d) of GLDP with DFT B3LYP/cc-pVDZ. (f) Comparison of DFT-computed (J_DFT) (black lines/dots) and NN-predicted (J_NN) (red lines/dots) coupling constants of nearest neighboring amide I modes after cross-validation.

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Figure 3. Machine learning protocol for predicting protein IR spectroscopy.

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Figure 4. Good agreement (the quantitative agreement between the predicted and experimental spectra were measured by Spearman rank correlation coefficients, see Table 1) is obtained between the experimental spectra of the proteins measured in D2O (black lines) and the ML predictions based on 1000 MD configurations (red lines). Intensity is scaled to have the same maximum intensity for each panel.

Table 1. ML predicts IR protein spectra with the root mean square error (RMSE) and high Spearman rank correlation (¦Ñ) indicates the quantitative agreement with experiment. Structures of 12 proteins with different sizes were taken from the Protein Data Bank, representing a diverse range of secondary structure contents, i.e., different fractions of ¦Á-helix and ¦Â-sheet. The IR spectrum of each protein was computed based on 1000 MD configurations. All reported calculation times refer to calculations on eight cores of an Intel(R) Xeon(R) CPU (E5-2683v4 @ 2.1GHz).


ÎÒÃÇ´ÓSpearman rank correlation(¦Ñ)À´ºâÁ¿ÀíÂÛÄ£Äâ¹âÆ×ÓëʵÑé²âÁ¿¹âÆ×Ö®¼äµÄÏàËÆ¶È¡£´Óͼ4ºÍ±í1ÖпÉÖª£¬ÀíÂÛÔ¤²âÓëʵÑé²âÁ¿ÎǺϽϺÃ(11¸öµ°°×µÄ¦Ñ> 0.80£¬½öÓÐ1DHRµÄ¦ÑΪ0.71)¡£µÃÒæÓÚ»úÆ÷ѧϰ¶Ô¹âÆ×Ä£Äâ¾Þ´óµÄËÙ¶ÈÌáÉý£¬ÎÒÃÇ¿ÉÒÔÄ£Äâ1000¸öµ°°×Öʶ¯Á¦Ñ§¿ìÕÕ(Õâ¶ÔÖ±½ÓµÄÁ¿×Ó»¯Ñ§¼ÆËã»á·Ç³£°º¹ó)À´Ô¤²âºìÍâ¹âÆ×£¬´Ó¶ø²¶»ñÿÖÖµ°°×ÖʵĶ¯Ì¬ÌØÕ÷¡£×ÜÌåÀ´Ëµ£¬»úÆ÷ѧϰģÐÍÔ¤²âµÄ¹âÆ×³É¹¦µØÔÙÏÖÁËʵÑé¹âÆ×µÄ»ù±¾ÌØÕ÷(Ö÷·åºÍÏßÐÎ)¡£


Figure 5. (a) From left to right : Simulated (red line) and Experimental (black line) IR spectra of Ubiquitin at four different temperatures (1.6 ¡ã C ~ 82.6 ¡ã C) and the temperature variation of the dominant peak position. (b) The ML-predicted IR spectra of the Trp-cage protein along its folding path (S1£ºthe original unfolded strand structure; S25: slightly folded but retaining the coil structure; S50: folding rapidly with the emergence of helix elements; S75-S100: stably folded protein with helix structures forming a cage.) All spectra are averaged over 100 (1000) MD snapshots for each state of Trp-cage (Ubiquitin).

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ÂÛÎıêÌ⣺A Machine Learning Protocol for Predicting Protein Infrared Spectra.

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