Mathematical Analysis of Cooperating Nano-devices for Target Molecules Detection

We consider a set of very simple nano-devices that move randomly in the system. Each nano device is composed only of a sensor, and a storage of molecules. Furthermore, each device has a binary operation, i.e., once the sensor is activated, the device releases all of its stored molecules. The released molecules are used to establish coordination between the devices. We show that despite the apparent simplicity, the network can establish different functionalities, depending on the combination of devices and network parameters.

Devices with the considered capabilities have already been presented using various technologies. These nano-devices are expected to reach practical implementation for a variety of applications in the coming years. Due to the size constraints, the capabilities of a single device are limited, and these devices are expected to operate in large numbers. Yet, the mathematical framework for the analysis of such networks has not been established, and such networks were so far analyzed only through simulations.

This work provides predictions of the network behavior, as a function of the behavior of each device, and explain the roles of each system parameter. The analysis reveals that the same network can implement a mass amplifier (that releases an amount of molecules that is proportional to the input mass) or a binary detector (that generates a macro level response to the presence of a small mass of target molecules). Moreover, the work considers a network that combines several types of nano-devices, and quantifies the network behavior as a function of the densities of each device type. The network behavior is quantified in terms of mean and variance of the response and miss-detection and false-alarm probabilities.