Cellular heterogeneity plays a pivotal role in a variety of functional processes in vivo including carcinogenesis. However, our knowledge about cell-to-cell diversity and how differences in individual cells manifest in alterations at the population level remains very limited mainly due to the lack of appropriate tools enabling studies at the single-cell level. We present a study on changes in cellular heterogeneity in the context of pre-malignant progression in response to hypoxic stress. Utilizing pre-malignant progression of Barrett’s esophagus (BE) as a disease model system we studied molecular mechanisms underlying the progression from metaplastic to dysplastic (pre-cancerous) stage. We used newly developed methods enabling measurements of cell-to-cell differences in copy numbers of mitochondrial DNA, expression levels of a set of mitochondrial and nuclear genes involved in hypoxia response pathways, and mitochondrial membrane potential. In contrast to bulk cell studies reported earlier, our study shows significant differences between metaplastic and dysplastic BE cells in both average values and single-cell parameter distributions of mtDNA copy numbers, mitochondrial function, and mRNA expression levels of studied genes. Based on single-cell data analysis, we propose that mitochondria may be one of the key factors in pre-malignant progression in BE.

Intercellular interactions play a central role at the tissue and whole organism level modulating key cellular functions in normal and disease states. Studies of cell-cell communications are challenging due to ensemble averaging effects brought about by intrinsic heterogeneity in cellular function which requires such studies to be conducted with small populations of cells. Most of the current methods for producing and studying such small cell populations are complex to implement and require skilled personnel limiting their widespread utility in biomedical research labs. We present a simple and rapid method to produce small populations with varying size of epithelial cells (10–50 cells/population) with high-throughput (~1 population/second) on flat surfaces via patterning of extracellular matrix (ECM) proteins and random seeding of cells. We demonstrate that despite inherent limitations of non-contact, drop-on-demand piezoelectric inkjet printing for protein patterning, varying mixtures of ECM proteins can be deposited with high reproducibility and level of control on glass substrates using a set of dynamically adjustable optimized deposition parameters. We demonstrate high consistency for the number of cells per population (~1 cell standard error of mean), the population’s size (~0.2 coefficient of variation) and shape, as well as accurate spatial placement of and distance between colonies of a panel of metaplastic and dysplastic esophageal epithelial cells with differing adhesion and motility characteristics. The number of cells per colony, colony size and shape can be varied by dynamically varying the amount of ECM proteins deposited per spatial location and the number of spatial locations on the substrate. The method is applicable to a broad range of biological and biomedical studies including cell-cell communications, cellular microenvironment, migration, and stimulus response.

We study the so-called Descent, or [bar over Q], Equation for the null polygonal supersymmetric Wilson loop in the framework of the pentagon operator product expansion. To properly address this problem, one requires to restore the cyclicity of the loop broken by the choice of OPE channels. In the course of the study, we unravel a phenomenon of twist enhancement when passing to a cyclically shifted channel. Currently, we focus on the consistency of the all-order Descent Equation for the particular case relating the NMHV heptagon to MHV hexagon. We find that the equation establishes a relation between contributions of different twists and successfully verify it in perturbation theory making use of available bootstrap predictions for elementary pentagons.

Precise spatial positioning and isolation of mammalian cells is a critical component of many single cell experimental methods and biological engineering applications. Although a variety of cell patterning methods have been demonstrated, many of these methods subject cells to high stress environments, discriminate against certain phenotypes, or are a challenge to implement. Here, we demonstrate a rapid, simple, indiscriminate, and minimally perturbing cell patterning method using a laser fabricated polymer stencil. The stencil fabrication process requires no stencil-substrate alignment, and is readily adaptable to various substrate geometries and experiments.

We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and describe the angular distribution of global charges in outgoing radiation created from the vacuum by some source. The charge flow correlations can be expressed in terms of Wightman correlation functions in a certain limit. We explain how to compute these quantities starting from their Euclidean analogues by means of a nontrivial analytic continuation which, in the framework of CFT, can be performed elegantly in Mellin space. The relation between the charge flow correlations and Euclidean correlation functions can be reformulated directly in configuration space, bypassing the Mellin representation, as a certain Lorentzian double discontinuity of the correlation function integrated along the cuts. We illustrate the general formalism in N = 4 SYM, making use of the well-known results on the four-point correlation function of half-BPS scalar operators. We compute the double scalar flow correlation in N = 4 SYM, at weak and strong coupling and show that it agrees with known results obtained by different techniques. One of the remarkable features of the N = 4 theory is that the scalar and energy flow correlations are proportional to each other. Imposing natural physical conditions on the energy flow correlations (finiteness, positivity and regularity), we formulate additional constraints on the four-point correlation functions in N = 4SYM that should be valid at any coupling and away from the planar limit.

We analyze the near-collinear limit of the null polygonal hexagon super Wilson loop in the planar N = 4 super-Yang–Mills theory. We focus on its Grassmann components which are dual to next-to-maximal helicity-violating (NMHV) scattering amplitudes. The kinematics in question is studied within a framework of the operator product expansion that encodes propagation of excitations on the background of the color flux tube stretched between the sides of Wilson loop contour. While their dispersion relation is known to all orders in 't Hooft coupling from previous studies, we find their form factor couplings to the Wilson loop. This is done making use of a particular tessellation of the loop where pentagon transitions play a fundamental role. Being interested in NMHV amplitudes, the corresponding building blocks carry a nontrivial charge under the SU(4) R-symmetry group. Restricting the current consideration to twist-two accuracy, we analyze two-particle contributions with a fermion as one of the constituents in the pair. We demonstrate that these nonsinglet pentagons obey bootstrap equations that possess consistent solutions for any value of the coupling constant. To confirm the correctness of these predictions, we calculate their contribution to the super Wilson loop demonstrating agreement with recent results to four-loop order in 't Hooft coupling.

We study event shapes in N = 4SYM describing the angular distribution of energy and R-charge in the final states created by the simplest half-BPS scalar operator. Applying the approach developed in the companion paper arXiv:1309.0769, we compute these observables using the correlation functions of certain components of the N = 4 stress-tensor supermultiplet: the half-BPS operator itself, the R-symmetry current and the stress tensor. We present master formulas for the all-order event shapes as convolutions of the Mellin amplitude defining the correlation function of the half-BPS operators, with a coupling-independent kernel determined by the choice of the observable. We find remarkably simple relations between various event shapes following from N = 4 superconformal symmetry. We perform thorough checks at leading order in the weak coupling expansion and show perfect agreement with the conventional calculations based on amplitude techniques. We extend our results to strong coupling using the correlation function of half-BPS operators obtained from the AdS/CFT correspondence.

We compute one-loop renormalization group equations for non-singlet twist-four operators in QCD. The calculation heavily relies on the light-cone gauge formalism in the momentum fraction space that essentially rephrases the analysis of all two-to-two and two-to-three transition kernels to purely algebraic manipulations both for non- and quasipartonic operators. This is the first brute force calculation of this sector available in the literature. Fourier transforming our findings to the coordinate space, we checked them against available results obtained within a conformal symmetry-based formalism that bypasses explicit diagrammatic calculations and confirmed agreement with the latter.

Scattering amplitudes in maximally supersymmetric gauge theory are dual to super-Wilson loops on null polygonal contours. The operator product expansion for the latter revealed that their dynamics is governed by the evolution of multiparticle GKP excitations. They were shown to emerge from the spectral problem of an underlying open spin chain. In this work we solve this model with the help of the Baxter Q-operator and Sklyanin's Separation of Variables methods. We provide an explicit construction for eigenfunctions and eigenvalues of GKP excitations. We demonstrate how the former define the so-called multiparticle hexagon transitions in super-Wilson loops and prove their factorized form at leading order of 't Hooft coupling for particle number-preserving transitions that were suggested earlier in a generic case.