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

Mapping energy transport networks in proteins

The response of proteins to chemical reactions or impulsive excitation that occurs within the molecule has fascinated chemists for decades. In recent years ultrafast X-ray studies have provided ever more detailed information about the evolution of protein structural change following ligand photolysis, and time-resolved IR and Raman techniques, e.g., have provided detailed pictures of the nature and rate of energy transport in peptides and proteins, including recent advances in identifying transport through individual amino acids of several heme proteins. Computational tools to locate energy transport pathways in proteins have also been advancing. Energy transport pathways in proteins have since some time been identified by molecular dynamics (MD) simulations, and more recent efforts have focused on the development of coarse graining approaches, some of which have exploited analogies to thermal transport in other molecular materials. With the identification of pathways in proteins and protein complexes, network analysis has been applied to locate residues that control protein dynamics and possibly allostery, where chemical reactions at one binding site mediate reactions at distance sites of the protein. In this chapter we review approaches for locating computationally energy transport networks in proteins. We present background into energy and thermal transport in condensed phase and macromolecules that underlies the approaches we discuss before turning to a description of the approaches themselves. We also illustrate the application of the computational methods for locating energy transport networks and simulating energy dynamics in proteins with several examples

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

Formal executable descriptions of biological systems

The similarities between systems of living entities and systems of concurrent processes may support biological experiments in silico. Process calculi offer a formal framework to describe biological systems, as well as to analyse their behaviour, both from a qualitative and a quantitative point of view. A couple of little examples help us in showing how this can be done. We mainly focus our attention on the qualitative and quantitative aspects of the considered biological systems, and briefly illustrate which kinds of analysis are possible. We use a known stochastic calculus for the first example. We then present some statistics collected by repeatedly running the specification, that turn out to agree with those obtained by experiments in vivo. Our second example motivates a richer calculus. Its stochastic extension requires a non trivial machinery to faithfully reflect the real dynamic behaviour of biological systems

On the master equation approach to diffusive grain-surface chemistry: the H, O, CO system

We have used the master equation approach to study a moderately complex network of diffusive reactions occurring on the surfaces of interstellar dust particles. This network is meant to apply to dense clouds in which a large portion of the gas-phase carbon has already been converted to carbon monoxide. Hydrogen atoms, oxygen atoms, and CO molecules are allowed to accrete onto dust particles and their chemistry is followed. The stable molecules produced are oxygen, hydrogen, water, carbon dioxide (CO2), formaldehyde (H2CO), and methanol (CH3OH). The surface abundances calculated via the master equation approach are in good agreement with those obtained via a Monte Carlo method but can differ considerably from those obtained with standard rate equations.Comment: 13 pages, 5 figure