Figures
- Expanding protein universe and its origin from the biological Big Bang

Fig 1. An example of a large cluster of TIM barrel-fold protein domains. Protein domains whose DALI similarity Z score is greater than Z_min = 9 are connected by lines.

Fig 2. The dependence of the number of proteins in the maximal cluster on the threshold value of Z score Z_min for PDUG (a) and random graphs (b). (c) The probability density of the cluster sizes for PDUG and random graphs at their respective Z_c. Z_c indicates the critical value of the Z score threshold at which transition in the size of maximal cluster occurs. For PDUG Z_c ${approx}$ 9; for random graphs Z_c ${approx}$ 11. We generated 10 different realizations of random graphs, so each point of b represents an average over these 10 realizations. Interestingly, at minimal Z_min = 2, all of the nodes in random graphs are connected; thus, the largest cluster spans all of the protein domains. In contrast, just a small fraction of all nodes ( ${approx}$ 250) constitutes the largest cluster in PDUG (at Z_min = 2), pointing to a dramatic difference between PDUG and random graphs. This difference is further revealed in Fig. 3.

Fig 3. The distribution of node connectivity (k) for PDUG (a) and for random graph (b) at their corresponding Z_c. For PDUG Z_c ${approx}$ 9; for random graphs Z_c ${approx}$ 11. Node connectivity denotes how many proteins a given protein is connected to by structural similarity connections.

Fig 4. Proposed model of domain evolution. (a) Gene duplication (A $->$ A + B): the structural similarity between A and B is defined by some function w = (A,B) (e.g., RMSD or DRMSD). (b) If structural similarity w = (A,B) is greater than some critical value w_max, then we add a link connecting A and B. If structural similarity is above w_max, a new fold family is born. (c) The second generation progeny C (A $->$ B $->$ C) can connect to its grandparent A, if there is structural similarity between A and C: w_AC $<=$ w_max. (d) With each time step, mutations diverge protein structures from each other; i.e., structural similarity changes by some value D: w $->$ w' = w + D(D = 10^–4). If w' > w_max, we remove the edge between corresponding proteins. (e) The dependence of the size of the largest cluster in the graphs generated by our model on w_max, averaged over 20 realizations. (f) The probability of the node connectivity in our model, averaged over 10² realizations. Apart from the finite-size effects at large k, it exhibits power law distribution with exponent ${alpha}$ ${approx}$ 1.6.