Immune checkpoint inhibitors, which unleash a patient’s own T cells to kill tumors, are revolutionizing cancer treatment. To unravel the genomic determinants of response to this therapy, we used whole-exome sequencing of non–small cell lung cancers treated with pembrolizumab, an antibody targeting programmed cell death-1 (PD-1). In two independent cohorts, higher nonsynonymous mutation burden in tumors was associated with improved objective response, durable clinical benefit, and progression-free survival. Efficacy also correlated with the molecular smoking signature, higher neoantigen burden, and DNA repair pathway mutations; each factor was also associated with mutation burden. In one responder, neoantigen-specific CD8+ T cell responses paralleled tumor regression, suggesting that anti–PD-1 therapy enhances neoantigen-specific T cell reactivity. Our results suggest that the genomic landscape of lung cancers shapes response to anti–PD-1 therapy.

BACKGROUND Immune checkpoint inhibitors are effective cancer treatments, but molecular determinants of clinical benefit are unknown. Ipilimumab and tremelimumab are antibodies against cytotoxic T-lymphocyte antigen 4 (CTLA-4). Anti–CTLA-4 treatment prolongs overall survival in patients with melanoma. CTLA-4 blockade activates T cells and enables them to destroy tumor cells. METHODS We obtained tumor tissue from patients with melanoma who were treated with ipilimumab or tremelimumab. Whole-exome sequencing was performed on tumors and matched blood samples. Somatic mutations and candidate neoantigens generated from these mutations were characterized. Neoantigen peptides were tested for the ability to activate lymphocytes from ipilimumab-treated patients. RESULTS Malignant melanoma exomes from 64 patients treated with CTLA-4 blockade were characterized with the use of massively parallel sequencing. A discovery set consisted of 11 patients who derived a long-term clinical benefit and 14 patients who derived a minimal benefit or no benefit. Mutational load was associated with the degree of clinical benefit (P = 0.01) but alone was not sufficient to predict benefit. Using genomewide somatic neoepitope analysis and patient-specific HLA typing, we identified candidate tumor neoantigens for each patient. We elucidated a neo-antigen landscape that is specifically present in tumors with a strong response to CTLA-4 blockade. We validated this signature in a second set of 39 patients with melanoma who were treated with anti–CTLA-4 antibodies. Predicted neoantigens activated T cells from the patients treated with ipilimumab. CONCLUSIONS These findings define a genetic basis for benefit from CTLA-4 blockade in melanoma and provide a rationale for examining exomes of patients for whom anti–CTLA-4 agents are being considered. (Funded by the Frederick Adler Fund and others.)

It is well known that the multifractal spectrum of a self-similar measure satisfying the open set condition is a closed interval. Recently, there has been interest in the overlapping case and it is known that in this case there can be isolated points. We prove that for an interesting class of self-similar measures with overlap the spectrum consists of a closed interval union together with at most two isolated points. In the case of convolutions of uniform Cantor measures we determine the end points of the interval and the isolated points. We also give an example of a related self-similar measure where the spectrum is a union of two disjoint intervals. In contrast, we prove that if one considers quotient measures of this class on the quotient group [0, 1], rather than the real line, the multifractal spectrum is a closed interval.

Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. We find a sufficient condition for a.s. absence of a total collision (when all particles collide) and of other types of collisions, say of the three lowest-ranked particles. This continues the work of Ichiba, Karatzas, Shkolnikov (2013) and .Date: May 23, 2016. Version 32. 2010 Mathematics Subject Classification. Primary 60K35, secondary 60J60, 60J65, 91B26.It was noted in [65, Corollary 1.3] that if there are a.s. no triple collisions, then there are a.s. no simultaneous collisions. As we see in this example, it is possible to find diffusion coefficients so that the system avoids simultaneous collisions of the type (4), but exhibits triple collisions with positive probability.Also, the collision as in (3) is stronger than a triple or a simultaneous collision. 1.3. Outline of the proofs. The main results of this paper are Theorems 2.3 and 2.4. Theorems 1.1 and 1.2, along with other examples in Section 2, are corollaries of these two results. Theorems 2.3 and 2.4 are proved in Sections 3 and 4. Let us give a brief outline of the proofs. Consider the gaps between the consecutive ranked particles:These form an (N − 1)-dimensional process in R N −1 + , which is called the gap process and is denoted by Z = (Z(t), t ≥ 0). It turns out that Z is a particular case of a well-known process, which is called a semimartingale reflected Brownian motion (SRBM) in a positive multidimensional orthant. We discuss this relationship in subsection 4.2.

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