Extended master equation models for molecular communication networks

We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signalling molecules, which are diffused over the medium, to the receiver to realise the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time series of signalling molecule counts, while diffusion in the medium and chemical reactions at the receivers are modelled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show how RDMEX can be used to determine the mean and covariance of the receiver output signals, and derive closed-form expressions for the mean receiver output signal of the RDMEX model. These closed-form expressions reveal that the output signal of a receiver can be affected by the presence of other receivers. Numerical examples are provided to demonstrate the properties of the model.Comment: IEEE Transactions on Nanobioscience, 201

Impact of receiver reaction mechanisms on the performance of molecular communication networks

In a molecular communication network, transmitters and receivers communicate by using signalling molecules. At the receivers, the signalling molecules react, via a chain of chemical reactions, to produce output molecules. The counts of output molecules over time is considered to be the output signal of the receiver. This output signal is used to detect the presence of signalling molecules at the receiver. The output signal is noisy due to the stochastic nature of diffusion and chemical reactions. The aim of this paper is to characterise the properties of the output signals for two types of receivers, which are based on two different types of reaction mechanisms. We derive analytical expressions for the mean, variance and frequency properties of these two types of receivers. These expressions allow us to study the properties of these two types of receivers. In addition, our model allows us to study the effect of the diffusibility of the receiver membrane on the performance of the receivers

Molecular communication networks with general molecular circuit receivers

In a molecular communication network, transmitters may encode information in concentration or frequency of signalling molecules. When the signalling molecules reach the receivers, they react, via a set of chemical reactions or a molecular circuit, to produce output molecules. The counts of output molecules over time is the output signal of the receiver. The aim of this paper is to investigate the impact of different reaction types on the information transmission capacity of molecular communication networks. We realise this aim by using a general molecular circuit model. We derive general expressions of mean receiver output, and signal and noise spectra. We use these expressions to investigate the information transmission capacities of a number of molecular circuits

Using transcription-based detectors to emulate the behaviour of sequential probability ratio-based concentration detectors

The sequential probability ratio test (SPRT) from statistics is known to have the least mean decision time compared to other sequential or fixed-time tests for given error rates. In some circumstances, cells need to make decisions accurately and quickly, therefore it has been suggested the SPRT may be used to understand the speed-accuracy tradeoff in cellular decision making. It is generally thought that in order for cells to make use of the SPRT, it is necessary to find biochemical circuits that can compute the log-likelihood ratio needed for the SPRT. However, this paper takes a different approach. We recognise that the high-level behaviour of the SPRT is defined by its positive detection or hit rate, and the computation of the log-likelihood ratio is just one way to realise this behaviour. In this paper, we will present a method which uses a transcription-based detector to emulate the hit rate of the SPRT without computing the exact log-likelihood ratio. We consider the problem of using a promoter with multiple binding sites to accurately and quickly detect whether the concentration of a transcription factor is above a target level. We show that it is possible to find binding and unbinding rates of the transcription factor to the promoter's binding sites so that the probability that the amount of mRNA produced will be higher than a threshold is approximately equal to the hit rate of the SPRT detector. Moreover, we show that the average time that this transcription-based detector needs to make a positive detection is less than or equal to that of the SPRT for a wide range of concentrations. We remark that the last statement does not contradict Wald's optimality result because our transcription-based detector uses an open-ended test