Using three-dimensional microfluidic networks for solving computationally hard problems

Abstract

This paper describes the design of a parallel algorithm that uses moving fluids in a three-dimensional microfluidic system to solve a nondeterministically polynomial complete problem (the maximal clique problem) in polynomial time. This algorithm relies on (i) parallel fabrication of the microfluidic system, (ii) parallel searching of all potential solutions by using fluid flow, and (iii) parallel optical readout of all solutions. This algorithm was implemented to solve the maximal clique problem for a simple graph with six vertices. The successful implementation of this algorithm to compute solutions for small-size graphs with fluids in microchannels is not useful, per se, but does suggest broader application for microfluidics in computation and control. M icrofluidic systems are providing the basis for new types of rapid chemical and biological analyses (refs. 1-3). With the increasing complexity of microfluidic systems, there is also a growing need to carry out relatively complex processes-logic operations, fluidic control, and detection-on the chip. Although these processes can be (and usually are) controlled by electronic systems, it would be more natural and compatible to use the same medium (that is, a fluid) to carry out some or all elements of the required computation and control͞decision making. Here, we explore the potential of microfluidic systems in computation by using a representative ''hard'' problem-a parallel solution of a nondeterministically polynomial (NP) complete problem [the maximal clique problem (MCP)] for a graph with six vertices. This method we describe uses moving fluids to search the parallel branches of a three-dimensional (3D) microfluidic system simultaneously, exploits parallel fabrication of relief patterns by photolithography, and detects solutions in parallel with fluorescence imaging.Intuitively, a problem is in the class NP (i) if it can be solved only by an algorithm that searches through exponentially many candidate solutions, and (ii) when the correct solution has been identified, verification of the solution can be performed easily (ref. 4). No feasible sequential algorithm is known to solve NP problems. If one can, however, search all candidate solutions simultaneously in parallel, solution of NP problems becomes feasible. The potential for parallel searches is the foundation for interest in DNA-based computation (refs. 5-8) and in part for interest in quantum computation (refs. 9-12). In addition to sequence-specific recognition (the basis of DNA computation) and manipulation and resolution of entangled quantum states (the basis for quantum computation), other physical phenomena or systems might also be suited for solving computational problems. In this paper, we demonstrate the use of moving fluids in a microfluidic system to solve an NP complete problem.

A tissue P system and a DNA microfluidic device for solving the shortest common superstring problem

“…There are several previous works on DNA computing using microfluidic systems [6,12,4,8,9]. One [8] describes the design of a linear time DNA algorithm for the Hamiltonian Path Problem (HPP) suited for parallel implementation using a microfluidic system (this bioalgorithm shares some features with the algorithm for the Shortest Common Superstring Problem presented in this paper).…”

“…In another paper, Gehani and Reif [6] study the potential of biomolecular microflow computation, describe methods to efficiently route strands between chambers, and determine theoretical lower bounds on the quantities of DNA and the time needed to solve a problem in the microflow biomolecular model. Two other works [12,4] solve the Maximum Clique Problem with microfluidic devices. This is an NP-complete problem.…”

“…The second step of McCaskill's algorithm is a sorting procedure to determine the maximum clique. By contrast, Chiu et al [4] describes a novel approach that uses neither DNA strands nor selection procedures. Subgraphs and edges of the graph are hard codified with wells and reservoirs, respectively, connected by channels and containing fluorescent beads.…”

Protein Linear Molecular Motor-Powered Nanodevices

“…One prospect would be to use the possible, unusual ferroelectric properties of microtubules and/or the formation of travelling kink solitons, [155,156] for example, for new quantum electronic devices. A more immediate application would arise from DNA-based computation [157] and from maze-solving with microfluidics devices, [158] or by amoeboid cells. [159] Essentially, it is entirely possible that the motility of actin filaments, or microtubules, can be used to explore mazes or other more elaborate micro-or nano-fabricated networks that code a mathematical problem, [160] as illustrated in Fig.…”

Behavior of fluids in nanoscopic space

“…Clearly, the solvent ''slip'' along the hydrophobic pore walls of the CNTs is controlled by fluid-wall interactions. Such slip-flow behavior can be vital for generating the high-throughput rates required in nanofluidic devices (27,30).…”