Stochastic reaction and diffusion systems in molecular communications: Recent results and open problems

Abstract

Chemical reactions and diffusion are two basic mechanisms governing the dynamics of molecules in a fluid.As such, they play a critical role in molecular communication for channel modeling, design of detection rules, implementation of molecular circuits for computation, and modeling interactions with external biochemical systems. For finite numbers of information-carrying molecules, stochastic models naturally arise with the simplest example given by the Wiener process, often known as Brownian motion. Nevertheless, the Wiener process fails to be accurate when external forces, friction, and chemical reactions are present. Recently, there have been several contributions that tailor molecular communication systems to these more challenging channel conditions. In this paper, we first overview a general family of stochastic models of reaction and diffusion systems, including both Langevin diffusion and the reaction-diffusion master equation. These models form a basis for the use of these models as molecular communication channels, from which modulation and detection schemes can be developed. We survey recent results on the design of these schemes, with a focus on a recently developed approach which is robust to a wide range of channel models, known as equilibrium signaling. We then turn to the implementation of these detection schemes and related parameter estimation problems via stochastic molecular circuits, based on stochastic chemical reaction networks. Finally, interactions between molecular communication systems and stochastic biological systems as well as open problems are discussed.Our overarching goal is to highlight how the consideration of general stochastic models of reaction and diffusion can be utilized in order to widen the application of molecular communications both within engineered systems, and also as motivation for advances in the mathematical characterization of these models.

Molecular Communication in Vacuum

“…Here T is calculated in the same way as in (17), except that v is replaced with v s . In the next section, we will analyze the results obtained from our proposed systems.…”

“…While such information rates are not an impediment in nature (e.g., in intercellular signalling transduction networks [16]), or in bio-inspired applications, where only simple control signals may be required, there is no reason in principle why information rates must be low in molecular communication. Although the uncertainty inherent in diffusion-based communication arises from the very low mean free path of any individual molecule (leading to the Wiener process as a propagation model [17]), this uncertainty can be counteracted by transmitting an enormous number of molecules, leading to an exceptionally high data rate [18]. tems, widely used in chemical analysis.…”

Non-Markovian Diffusion and Adsorption–Desorption Dynamics: Analytical and Numerical Results

“…Describing the physical world is complex and necessitates employing various methods, both experimental and theoretical, to grasp and interpret the behavior of systems. Diffusion is prevalent in various situations that can be usual or anomalous and may appear combined with different processes, such as adsorption-desorption [1] and reaction-diffusion [2]. In the case of normal diffusion, the system exhibits Markovian characteristics [3], particularly the mean square displacement with a linear dependence on time, i.e., ⟨(r − ⟨r⟩) 2 ⟩ ∼ t. In contrast, anomalous diffusion results in stochastic processes that govern the system exhibiting non-Markovian features [4], yielding a nonlinear relationship for the mean square displacement, e.g., ⟨(r − ⟨r⟩) 2 ⟩ ∼ t α , where α < 1 or α > 1 corresponds to subor superdiffusion, respectively [5,6].…”

Biocomputing Model Using Tripartite Synapses Provides Reliable Neuronal Logic Gating With Spike Pattern Diversity

“…Furthermore, communication in biological systems is characterised by an extraordinarily highefficiency [8]. Since molecules are available at the biological nano-scale, time constants, such as diffusion times, are reduced, reagents take less time to diffuse and mix in the reaction space, and so chemical reactions are facilitated [9], [10].…”