The Omicron BA.1 variant emerged in late 2021 and quickly spread across the world. Compared to the earlier SARS-CoV-2 variants, BA.1 has many mutations, some of which are known to enable antibody escape. Many of these antibody-escape mutations individually decrease the spike receptor-binding domain (RBD) affinity for ACE2, but BA.1 still binds ACE2 with high affinity. The fitness and evolution of the BA.1 lineage is therefore driven by the combined effects of numerous mutations. Here, we systematically map the epistatic interactions between the 15 mutations in the RBD of BA.1 relative to the Wuhan Hu-1 strain. Specifically, we measure the ACE2 affinity of all possible combinations of these 15 mutations (215 = 32,768 genotypes), spanning all possible evolutionary intermediates from the ancestral Wuhan Hu-1 strain to BA.1. We find that immune escape mutations in BA.1 individually reduce ACE2 affinity but are compensated by epistatic interactions with other affinity-enhancing mutations, including Q498R and N501Y. Thus, the ability of BA.1 to evade immunity while maintaining ACE2 affinity is contingent on acquiring multiple interacting mutations. Our results implicate compensatory epistasis as a key factor driving substantial evolutionary change for SARS-CoV-2 and are consistent with Omicron BA.1 arising from a chronic infection.

Tumor-infiltrating lymphocytes (TILs), in general, and especially CD8+ TILs, represent a favorable prognostic factor in non–small cell lung cancer (NSCLC). The tissue origin, regenerative capacities, and differentiation pathways of TIL subpopulations remain poorly understood. Using a combination of single-cell RNA and T cell receptor (TCR) sequencing, we investigate the functional organization of TIL populations in primary NSCLC. We identify two CD8+ TIL subpopulations expressing memory-like gene modules: one is also present in blood (circulating precursors) and the other one in juxtatumor tissue (tissue-resident precursors). In tumors, these two precursor populations converge through a unique transitional state into terminally differentiated cells, often referred to as dysfunctional or exhausted. Differentiation is associated with TCR expansion, and transition from precursor to late-differentiated states correlates with intratumor T cell cycling. These results provide a coherent working model for TIL origin, ontogeny, and functional organization in primary NSCLC.

The diversity of T-cell receptor (TCR) repertoires is achieved by a combination of two intrinsically stochastic steps: random receptor generation by VDJ recombination, and selection based on the recognition of random self-peptides presented on the major histocompatibility complex. These processes lead to a large receptor variability within and between individuals. However, the characterization of the variability is hampered by the limited size of the sampled repertoires. We introduce a new software tool SONIA to facilitate inference of individual-specific computational models for the generation and selection of the TCR beta chain (TRB) from sequenced repertoires of 651 individuals, separating and quantifying the variability of the two processes of generation and selection in the population. We find not only that most of the variability is driven by the VDJ generation process, but there is a large degree of consistency between individuals with the inter-individual variance of repertoires being about ∼2% of the intra-individual variance. Known viral-specific TCRs follow the same generation and selection statistics as all TCRs.

Over the past two decades, several broadly neutralizing antibodies (bnAbs) that confer protection against diverse influenza strains have been isolated. Structural and biochemical characterization of these bnAbs has provided molecular insight into how they bind distinct antigens. However, our understanding of the evolutionary pathways leading to bnAbs, and thus how best to elicit them, remains limited. Here, we measure equilibrium dissociation constants of combinatorially complete mutational libraries for two naturally isolated influenza bnAbs (CR9114, 16 heavy-chain mutations; CR6261, 11 heavy-chain mutations), reconstructing all possible evolutionary intermediates back to the unmutated germline sequences. We find that these two libraries exhibit strikingly different patterns of breadth: while many variants of CR6261 display moderate affinity to diverse antigens, those of CR9114 display appreciable affinity only in specific, nested combinations. By examining the extensive pairwise and higher-order epistasis between mutations, we find key sites with strong synergistic interactions that are highly similar across antigens for CR6261 and different for CR9114. Together, these features of the binding affinity landscapes strongly favor sequential acquisition of affinity to diverse antigens for CR9114, while the acquisition of breadth to more similar antigens for CR6261 is less constrained. These results, if generalizable to other bnAbs, may explain the molecular basis for the widespread observation that sequential exposure favors greater breadth, and such mechanistic insight will be essential for predicting and eliciting broadly protective immune responses.

The T-cell (TCR) repertoire relies on the diversity of receptors composed of two chains, called α and β, to recognize pathogens. Using results of high throughput sequencing and computational chain-pairing experiments of human TCR repertoires, we quantitively characterize the αβ generation process. We estimate the probabilities of a rescue recombination of the β chain on the second chromosome upon failure or success on the first chromosome. Unlike β chains, α chains recombine simultaneously on both chromosomes, resulting in correlated statistics of the two genes which we predict using a mechanistic model. We find that ∼35% of cells express both α chains. Altogether, our statistical analysis gives a complete quantitative mechanistic picture that results in the observed correlations in the generative process. We learn that the probability to generate any TCRαβ is lower than 10−12 and estimate the generation diversity and sharing properties of the αβ TCR repertoire.

We present a new method to compute Rényi entropies in one-dimensional critical systems. The null-vector conditions on the twist fields in the cyclic orbifold allow us to derive a differential equation for their correlation functions. The latter are then determined by standard bootstrap techniques. We apply this method to the calculation of various Rényi entropies. Contents arXiv:1709.09270v5 [math-ph] A Properties of hypergeometric functions 35 B Four-point function satisfying a second-order differential equation 36 B.1 Differential equation 36 B.2 Determination of the four-point function 37 C Direct computation of OPE coefficients of twist operators 38 D Direct computation of the function of Sec. 4 40 E Quantum Ising chain in an imaginary magnetic field 41 References 43

The diversity of T-cell receptor (TCR) repertoires is achieved by a combination of two intrinsically stochastic steps: random receptor generation by VDJ recombination, and selection based on the recognition of random self-peptides presented on the major histocompatibility complex. These processes lead to a large receptor variability within and between individuals. However, the characterization of the variability is hampered by the limited size of the sampled repertoires. We introduce a new software tool SONIA to facilitate inference of individual-specific computational models for the generation and selection of the TCR beta chain (TRB) from sequenced repertoires of 651 individuals, separating and quantifying the variability of the two processes of generation and selection in the population. We find not only that most of the variability is driven by the VDJ generation process, but there is a large degree of consistency between individuals with the inter-individual variance of repertoires being about ∼2% of the intra-individual variance. Known viral-specific TCRs follow the same generation and selection statistics as all TCRs.

The T-cell (TCR) repertoire relies on the diversity of receptors composed of two chains, called α and β, to recognize pathogens. Using results of high throughput sequencing and computational chain-pairing experiments of human TCR repertoires, we quantitively characterize the αβ generation process. We estimate the probabilities of a rescue recombination of the β chain on the second chromosome upon failure or success on the first chromosome. Unlike β chains, α chains recombine simultaneously on both chromosomes, resulting in correlated statistics of the two genes which we predict using a mechanistic model. We find that ∼ 28% of cells express both α chains. We report that clones sharing the same β chain but different α chains are overrepresented, suggesting that they respond to common immune challenges. Altogether, our statistical analysis gives a complete quantitative mechanistic picture that results in the observed correlations in the generative process. We learn that the probability to generate any TCRαβ is lower than 10 −12 making it very unlikely for two people to share a full receptor by chance. We also estimate the generation diversity of the full TCR repertoire.