Hong-Li Zeng

Genome-wide epistasis analysis is a powerful tool to infer gene interactions, which can guide drug and vaccine development and lead to deeper understanding of microbial pathogenesis. We have considered all complete severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) genomes deposited in the Global Initiative on Sharing All Influenza Data (GISAID) repository until four different cutoff dates, and used direct coupling analysis together with an assumption of quasi-linkage equilibrium to infer epistatic contributions to fitness from polymorphic loci. We find eight interactions, of which three are between pairs where one locus lies in gene ORF3a, both loci holding nonsynonymous mutations. We also find interactions between two loci in gene nsp13, both holding nonsynonymous mutations, and four interactions involving one locus holding a synonymous mutation. Altogether, we infer interactions between loci in viral genes ORF3a and nsp2, nsp12, and nsp6, between ORF8 and nsp4, and between loci in genes nsp2, nsp13, and nsp14. The paper opens the prospect to use prominent epistatically linked pairs as a starting point to search for combinatorial weaknesses of recombinant viral pathogens.

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We describe how the couplings in an asynchronous kinetic Ising model can be inferred. We consider two cases: one in which we know both the spin history and the update times and one in which we know only the spin history. For the first case, we show that one can average over all possible choices of update times to obtain a learning rule that depends only on spin correlations and can also be derived from the equations of motion for the correlations. For the second case, the same rule can be derived within a further decoupling approximation. We study all methods numerically for fully asymmetric Sherrington-Kirkpatrick models, varying the data length, system size, temperature, and external field. Good convergence is observed in accordance with the theoretical expectations.

Network structures are reconstructed from dynamical data by respectively naive mean field (nMF) and Thouless-Anderson-Palmer (TAP) approximations. TAP approximation adds simple corrections to the nMF approximation, taking into account the effect of the focused spin on itself via its influence on other neighboring spins. For TAP approximation, we use two methods to reconstruct the network: (a) iterative method; (b) casting the inference formula to a set of cubic equations and solving it directly. We investigate inference of the asymmetric Sherrington-Kirkpatrick (aS-K) model using asynchronous update. The solutions of the set of cubic equations depend on temperature T in the aS-K model, and a critical temperature T(c)≈2.1 is found. The two methods for TAP approximation produce the same results when the iterative method is convergent. Compared to nMF, TAP is somewhat better at low temperatures, but approaches the same performance as temperature increases. Both nMF and TAP approximation reconstruct better for longer data length L, but for the degree of improvement, TAP performs better than nMF.