Fig 1.
Antibody targeting and mutability of the hemagglutinin protein for the seasonal flu.
(A-B) Coarse-grain model of the hemagglutinin trimer of A/New Caledonia/20/1999 (NC99) H1N1 influenza protein in its closed form (A). The virus model has 40 HA molecules at a spacing of 14.8 nm. [Measured spike spacing on influenza is 14 nm [78]] (B). For each immunogen geometry (trimer—A or full virus—B), a detailed atomistic structure of the immunogen is coarse-grained and presented in rainbow colors (panel i). Here every colored bead on the immunogen is a residue, representing a different HA epitope (228 different possible sites on trimeric HA). The antibody structure is presented as the Fc (blue bead), two arm (magenta beads) and antigen binding fragment (Fab) (yellow beads). Panels ii within A-B depict coarse-grained simulations for the on-rate of the Ab first arm binding (see Eq (S4)) to these residues [data from [24]]. The on-rates estimated from the simulation are superimposed on the HA structure. Top view (left), side view (right). The on-rate to cyan residues is high, intermediate to white residues, low for purple residues, and was the average of multiple simulations. (C) Panel i depicts the entropy (see Eq (1)) of HA epitopes computed for the seasonal flu (pre-pandemic influenza H1N1 (1918–1957 and 1977–2009) (sequences from [40]). Panel ii shows the entropy of the residues superimposed on HA structure, where highly mutable residues are in cyan, intermediate in white and conserved residues in purple.
Fig 2.
Antibody pressure guided the mutability of the hemagglutinin.
(A) Panel i. HA protein. Each circle corresponds to a surface residue (epitope) and was colored differently for illustration. Panel ii. Surface residues (epitopes) were clustered (see Materials and Methods). Each epitope cluster is was colored differently for illustration. (B) The correlation coefficient between epitope cluster entropy (Eq (2)) and the epitope cluster on-rate (Eq (3)), as a function of cluster number, computed for HA in the virus presentation depicted in Fig 1B (blue), and at the trimer presentation depicted in Fig 1A (red). (C) Scatter plot of the epitope clusters entropy computed for the seasonal influenza H1N1 vs. the epitope clusters on-rate (the number of clusters is 60). The correlation coefficient between them is 0.82. Marked are clusters containing residues belonging to the five known antigenic sites of flu (Cb—green, Sa—yellow, Sb—blue, Ca1—cyan, Ca2—red). Also marked is the group 1 conserved broadly neutralizing antibodies epitope (purple). (D) Schematic of the relationship between entropy and computed Ab on-rate for circulating viruses evolving under Ab pressure.
Fig 3.
Antibody targeting and mutability of the sarbecovirus subgenus spike.
(A-B) Coarse-grain model of the SARS-CoV-2 spike (S protein) in its closed form (A) [45]. (B) The virus model has 65 S molecules at a density of 0.27 spikes per 100nm2 [46]. A detailed atomistic structure of the spike is coarse-grained and presented in rainbow colors (panels i). Every colored bead on the spike is a residue, representing a different S epitope (255 different possible sites on trimeric S). Panels ii depict coarse-grained simulations for the Ab on-rate to these residues (see Fig 1A-ii for definition and color-coding). (C) Panel i depicts the entropy (see Eq (1)) of each spike residue computed for the sarbecovirus subgenus spike (see Table 1). Panel ii shows the entropy of the residues superimposed on the spike structure. Same color-coding as in Fig 1C-ii. (D) Panel i. The spike protein of the coronavirus. Each circle corresponds to a surface residue (epitope) and was colored differently for illustration. Panel ii. Surface residues (epitopes) were clustered (see Materials and Methods). Each epitope cluster is was colored differently for illustration. The number of clusters is 60. (E) The correlation coefficient between epitope cluster entropy (Eq (2)) and the epitope cluster on-rate (Eq (3)), as a function of cluster number, computed for the corona spike in the virus presentation (blue), and at the trimer presentation (red). (F) Scatter plot of the epitope clusters entropy, computed for the sarbecovirus spike vs. the epitope cluster on-rate estimated from the simulations. The correlation coefficient between them is 0.69. Clusters that contain residues belonging to the RBD are in green and those containing residues belonging to the RBM are in red. (The number of clusters is 60).
Table 1.
Species used for the analysis detailed in Fig 3C.
Fig 4.
Spike evolution of the 2009 influenza pandemic and SARS-CoV-2.
Comparison of the diversity of sequences (mutability map) and the on-rate maps. For A-B, panel i depicts the residue entropy as a function at different positions. For A-B, panel ii depicts the entropy of the residues is superimposed on the spike. Same color coding as in Fig 1C-ii. Panel iii. Scatter plot of the entropy of epitope clusters, against the epitope cluster on-rate computed for the spike. (A) Sequence entropy of HA for the pandemic flu H1N1 (2009–2017) (sequences taken from www.gisaid.org, and [40]). The correlation coefficient between the epitope cluster entropy and on-rate is R = 0.18. (B) Sequence entropy of the S spike protein of SARS-CoV-2 computed for all S protein sequences up to May 31st 2021 (sequences downloaded from www.gisaid.org). The correlation coefficient between the epitope cluster entropy and epitope cluster on-rate is R = 0.058. Same legend as Fig 3F. Time-dependence sequence entropy of SARS-CoV-2. The entropy of the S spike protein of SARS-CoV-2 computed for sequences collected at 5 time periods since the beginning of the pandemic (panel i) and correlation to the on-rate map, following epitope clustering (panel ii) (same clusters as those shown and used in Fig 3D-ii and 3F). (C) up to February 1st 2020, R = -0.16, (D) February-May 2020, R = -0.079 (E) June-November 2020, R = 0.3, (F) December 2020, R = 0.39, (G) January-May 2021, R = 0.061. (H) The correlation coefficient as a function of time. (Find an interactive, comparison of the time-dependent mutability map to the on-rate map here https://amitaiassaf.github.io/SpikeGeometry/SARSCoV2EvoT.html). Functional role of SARS-CoV-2 spike mutations. (I) Residues where key mutations were identified in SARS-CoV-2 variants are marked with colored beads. Residues were ranked based on their on-rate (targeting) by Abs according to the model prediction. The upper 66th on-rate percentile rank is the threshold between “high on-rate” (mutation due to escape) and “low on-rate” (mutation due to other factors) residues. Red residues have high on-rate and mutations in them were found to confer Ab escape (true positives) [Residue positions: 136, 140, 141, 143, 244, 345, 441, 444, 447, 449, 450, 452, 489, 490 493, 499, and 501]. Blue residues have a high on-rate and mutations in them have not been shown as of yet to not confer Ab escape (false positives) [Residues: 69, 80, and 138]. Green residues have a low on-rate and mutations in them do not confer Ab escape (true negatives) [Residues: 614, 655, and 701]. Orange residues have a low on-rate and mutations in them confer Ab escape (false negatives) [Residues: 346, 439, and 453]. Yellow residues have a high on-rate but it is unknown whether mutations in them confer Ab escape [Residues: 102, 367]. See S1 Data for a complete list.