Theory and Analysis of Generalized Mixing and Dilution of Biochemical Fluids Using Digital Microfluidic Biochips

摘要

Digital microfluidic (DMF) biochips are recently being advocated for fast on-chip implementation of biochemical laboratory assays or protocols, and several algorithms for diluting and mixing of reagents have been reported. However, all methods for such automatic sample preparation suffer from a drawback that they assume the availability of input fluids in pure form, that is, each with an extreme concentration factor (CF) of 100%. In many real-life scenarios, the stock solutions consist of samples/reagents with multiple CFs. No algorithm is yet known for preparing a target mixture of fluids with a given ratio when its constituents are supplied with random concentrations. An intriguing question is whether or not a given target ratio is feasible to produce from such a general input condition. In this article, we first study the feasibility properties for the generalized mixing problem under the (1 : 1) mix-split model with an allowable error in the target CFs not exceeding 1/2(d), where the integer d is user specified and denotes the desired accuracy level of CF. Next, an algorithm is proposed which produces the desired target ratio of N reagents in O(Nd) mix-split steps, where N (>= 3) denotes the number of constituent fluids in the mixture. The feasibility analysis also leads to the characterization of the total space of input stock solutions from which a given target mixture can be derived, and conversely, the space of all target ratios, which are derivable from a given set of input reagents with arbitrary CFs. Finally, we present a generalized algorithm for diluting a sample S in minimum (1 : 1) mix-split steps when two or more arbitrary concentrations of S (diluted with the same buffer) are supplied as inputs. These results settle several open questions in droplet-based algorithmic microfluidics and offer efficient solutions for a wider class of on-chip sample preparation problems.