A microfluidic platform for combinatorial experiments

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Biological Engineering, 2018.Page 165 blank. Cataloged from PDF version of thesis.Includes bibliographical references (pages 151-164).Experiments in biology are often combinatorial in nature and require analysis of large multi-dimensional spaces, but the scales of these experiments are limited by logistical complexity, cost, and reagent consumption. By miniaturizing experiments across nanoliter-scale emulsions that can be processed at large scales, droplet microfluidic platforms are poised to attack these challenges. Here we describe a droplet microfluidic platform for combinatorial experiments that automates the assembly of reagent combinations, with order-of-magnitude improvements over conventional liquid handling. Moreover, our design is accessible, requiring only standard lab equipment such as micropipettes, and improves the chemical compatibility of droplet microfluidic platforms for small molecules. We applied our platform to two experimental problems: combinatorial drug screening and microbial ecology. First, we used our platform to enable screening of pairwise combinations of a panel of antibiotics and 4,000+ investigational and approved drugs to overcome intrinsic antibiotic resistance in the model Gram-negative bacterial pathogen E. coli. This screen processed 4+ million droplet-level assays by hand in just 10 days to discover more than 10 combinations of antibiotics and non-antibiotic drugs for further study. We then applied our platform to microbial ecology, where the interactions between microbes in communities can dictate functions important for both basic science and biotechnology. As a proof of concept, we used our platform to survey 960 pairwise interactions of microbes isolated from soil, and deconstruct higher-order interactions in a 4-strain community. Altogether, we expect that our platform can be used to efficiently attack combinatorial problems across molecular and cellular biology.by Anthony Benjamin Kulesa.Ph. D

Newton-Like Methods for Solving Underdetermined Nonlinear Equations with Nondifferentiable Terms

In this paper we consider Newton-like methods for solving underdetermined systems of nonlinear equations with nondifferentiable terms. After presenting local convergence analysis for the methods, we prove a semilocal convergence theorem as well as uniqueness of solution in a generalized sense. Another semilocal convergence theorem for the Newton-chord method is also established. Finally a numerical example is given. 1. Introduction Let H be an operator of R m into R n . We consider the system of nonlinear equations H(x) = 0; x 2 D ae R m : (1) If H is Fr'echet differentiable, then the standard technique for finding a solution of (1) is the generalized Newton's method due to Ben-Israel [5]: x k+1 = x k \Gamma H 0 (x k ) + H(x k ); k = 0; 1; 2; ::: (2) where x 0 2 D and H 0 (x k ) + denote the Moore-Penrose pseudoinverses of H 0 (x k ). There is much literature concerning convergence of the method (2) for the well-determined case m = n and H 0 (x k ..