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In Diffusive Molecular Communication (DMC), information is transmitted by diffusing molecules. Synaptic signaling, as a natural implementation of this paradigm, encompasses functional components that, once understood, can facilitate the development of synthetic DMC systems. To unleash this potential, however, a thorough understanding of the synaptic communication channel based on biophysical principles is needed. Since synaptic transmission critically depends also on non-neural cells, such understanding requires the consideration of the so-called tripartite synapse. In this paper, we develop a comprehensive channel model of the tripartite synapse encompassing a three-dimensional, finite-size spatial model of the synaptic cleft, molecule uptake at the presynaptic neuron and at glial cells, reversible binding to individual receptors at the postsynaptic neuron, and spillover to the extrasynaptic space. Based on this model, we derive analytical time domain expressions for the channel impulse response (CIR) of the synaptic DMC system and for the number of molecules taken up at the presynaptic neuron and at glial cells, respectively. These expressions provide insight into the impact of macroscopic physical channel parameters on the decay rate of the CIR and the reuptake rate, and reveal fundamental limits for synaptic signal transmission induced by chemical reaction kinetics and the channel geometry. Adapted to realistic parameters, our model produces plausible results when compared to previous experimental and simulation studies and we provide results from particle-based computer simulations to further validate the analytical model. The proposed comprehensive channel model admits a wide range of synaptic configurations making it suitable for the investigation of many practically relevant questions, such as the impact of glial cell uptake and spillover on signal transmission in the tripartite synapse.

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... Synaptic DMC has been studied in the MC community with emphasis on different aspects, such as information theoretic limits [11], the design of artificial synapses [12], and the long-term average signal decay [13], see also literature overviews in [3], [14]. Mean-field models, i.e., deterministic models for the average activation of postsynaptic receptors valid in the large system limit, have been developed for synapses employing enzymatic degradation [13], [15] and other channel clearance mechanisms [12], [14], [16]. ...

... Synaptic DMC has been studied in the MC community with emphasis on different aspects, such as information theoretic limits [11], the design of artificial synapses [12], and the long-term average signal decay [13], see also literature overviews in [3], [14]. Mean-field models, i.e., deterministic models for the average activation of postsynaptic receptors valid in the large system limit, have been developed for synapses employing enzymatic degradation [13], [15] and other channel clearance mechanisms [12], [14], [16]. However, stochastic fluctuations in the activation of postsynaptic receptors have been considered only recently [15]. ...

... In the deterministic model (1)-(4), the binding rate of the NTs to postsynaptic receptors is given by constant κ a . In fact, κ a results from a technique termed boundary homogenization [24] applied when mapping the actual three-dimensional reaction-diffusion process to the one-dimensional 2 process in (1)-(4) [14]. According to [15, Sec. ...

In synaptic molecular communication (MC), the activation of postsynaptic receptors by neurotransmitters (NTs) is governed by a stochastic reaction-diffusion process. This randomness of synaptic MC contributes to the randomness of the electrochemical downstream signal in the postsynaptic cell, called postsynaptic membrane potential (PSP). Since the randomness of the PSP is relevant for neural computation and learning, characterizing the statistics of the PSP is critical. However, the statistical characterization of the synaptic reaction-diffusion process is difficult because the reversible bi-molecular reaction of NTs with receptors renders the system nonlinear. Consequently, there is currently no model available which characterizes the impact of the statistics of postsynaptic receptor activation on the PSP. In this work, we propose a novel statistical model for the synaptic reaction-diffusion process in terms of the chemical master equation (CME). We further propose a novel numerical method which allows to compute the CME efficiently and we use this method to characterize the statistics of the PSP. Finally, we present results from stochastic particle-based computer simulations which validate the proposed models. We show that the biophysical parameters governing synaptic transmission shape the autocovariance of the receptor activation and, ultimately, the statistics of the PSP. Our results suggest that the processing of the synaptic signal by the postsynaptic cell effectively mitigates synaptic noise while the statistical characteristics of the synaptic signal are preserved. The results presented in this paper contribute to a better understanding of the impact of the randomness of synaptic signal transmission on neuronal information processing.

... This work was supported in part by the German Research Foundation (DFG) under grant SCHO 831/9-1. Synaptic DMC has been studied in the MC community with emphasis on different aspects, such as information theoretic limits [5], the design of artificial synapses [6], and the long-term average signal decay [7], see also literature overviews in [2], [8]. Mean-field models, i.e., deterministic models for the average receptor activation valid in the large system limit, have been developed for synapses employing enzymatic degradation [7], [9] and other channel clearance mechanisms [6], [8], [10]. ...

... Synaptic DMC has been studied in the MC community with emphasis on different aspects, such as information theoretic limits [5], the design of artificial synapses [6], and the long-term average signal decay [7], see also literature overviews in [2], [8]. Mean-field models, i.e., deterministic models for the average receptor activation valid in the large system limit, have been developed for synapses employing enzymatic degradation [7], [9] and other channel clearance mechanisms [6], [8], [10]. However, stochastic fluctuations in the postsynaptic receptor activation have been considered only recently [9]. ...

... In lack of any existing reference model for N (t), we compare the predictions of our model for P N (n) with the binomial model obtained under the assumption that NTs are degraded independently of each other, i.e., N (n) = P B (n; N 0 , n(t)/N 0 ). For the implementation details of the PBS, we refer the reader to [8], [9]. To compare the PBS with the results obtained with Alg. 1, we compute the empirical distribution of N (t) and O(t) at some time t based on 6, 000 PBS realizations. ...

In synaptic molecular communication, the activation of postsynaptic receptors by neurotransmitters (NTs) is governed by a stochastic reaction-diffusion process and, hence, inherently random. It is currently not fully understood how this randomness impacts downstream signaling in the target cell and, ultimately, neural computation and learning. The statistical characterization of the reaction-diffusion process is difficult because the reversible bi-molecular reaction of NTs and receptors renders the system nonlinear. Consequently, existing models for the receptor occupancy in the synaptic cleft rely on simplifying assumptions and approximations which limit their practical applicability. In this work, we propose a novel statistical model for the reaction-diffusion process governing synaptic signal transmission in terms of the chemical master equation (CME). We show how to compute the CME efficiently and verify the accuracy of the obtained results with stochastic particle-based computer simulations (PBSs). Furthermore, we compare the proposed model to two benchmark models proposed in the literature and show that it provides more accurate results when compared to PBSs. Finally, the proposed model is used to study the impact of the system parameters on the statistical dependence between binding events of NTs and receptors. In summary, the proposed model provides a step forward towards a complete statistical characterization of synaptic signal transmission.

... in [11]. One of these open problems is the analytical derivation of CIR of synaptic communication, which has been examined recently by omitting neurotransmitter degradation by enzymes and for a simplified geometry [6], [12]. ...

... In a recent work, [6] provided a loose upper bound on the long-time decay rate of the CIR for a synaptic channel surrounded by glial cells and without neurotransmitter degradation inside the synaptic cleft. The channel considered in [6] has the form of a square prism. ...

... In a recent work, [6] provided a loose upper bound on the long-time decay rate of the CIR for a synaptic channel surrounded by glial cells and without neurotransmitter degradation inside the synaptic cleft. The channel considered in [6] has the form of a square prism. While seemingly an arbitrary geometry choice, this is fully justified as the resulting upper bound is independent of channel geometry for all practical purposes. ...

In this letter, we first derive the analytical channel impulse response for a cylindrical synaptic channel surrounded by glial cells and validate it with particle-based simulations. Afterwards, we provide an accurate analytical approximation for the long-time decay rate of the channel impulse response by employing Taylor expansion to the characteristic equations that determine the decay rates of the system. We validate our approximation by comparing it with the numerical decay rate obtained from the characteristic equation. Overall, we provide a fully analytical description for the long-time behavior of synaptic diffusion, e.g., the clean-up processes inside the channel after communication has long concluded.

... Synaptic communication has been studied in the MC literature before and we refer the reader to [10], [11] for recent literature overviews. In most models for the synaptic communication channel, e.g. in [12]- [15], postsynaptic receptor saturation is neglected. ...

... In this way, ISI between subsequent releases of NTs is mitigated. While presynaptic and glial cell uptake has been considered previously by the authors (without receptor saturation) [11], [15], in this work, we focus on enzymatic degradation as clearance mechanism. ...

... The basic design of the particle simulator was adopted from [11] and we refer the interested reader to [11] for further details. Receptor saturation was incorporated into the simulator presented in [11] by setting the binding probability for a receptor to zero when a molecule was bound to this receptor, and back to its original value when the molecule unbound. ...

Synaptic communication is based on a biological Molecular Communication (MC) system which may serve as a blueprint for the design of synthetic MC systems. However, the physical modeling of synaptic MC is complicated by the possible saturation of the molecular receiver caused by the competition of neurotransmitters (NTs) for postsynaptic receptors. Receiver saturation renders the system behavior nonlinear in the number of released NTs and is commonly neglected in existing analytical models. Furthermore, due to the ligands' competition for receptors (and vice versa), the individual binding events at the molecular receiver are in general statistically dependent and the binomial model for the statistics of the received signal does not apply. In this work, we propose a novel deterministic model for receptor saturation in terms of a state-space description based on an eigenfunction expansion of Fick's diffusion equation. The presented solution is numerically stable and computationally efficient. Employing the proposed deterministic model, we show that saturation at the molecular receiver reduces the peak-value of the expected received signal and accelerates the clearance of NTs as compared to the case when receptor occupancy is neglected. We further derive a statistical model for the received signal in terms of the hypergeometric distribution which accounts for the competition of NTs for receptors and the competition of receptors for NTs. The proposed statistical model reveals how the signal statistics are shaped by the number of released NTs, the number of receptors, and the binding kinetics of the receptors, respectively, in the presence of competition. We show that the impact of these parameters on the signal variance depends on the relative numbers of NTs and receptors. The accuracy of the proposed deterministic and statistical models is verified by particle-based computer simulations.

... Synaptic communication has been studied in the MC literature before and we refer the reader to [5], [6] for recent literature overviews. In most models, e.g. in [7]- [10], postsynaptic receptor saturation is neglected. ...

... After NTs are released from presynaptic vesicles [23], they are in nature either uptaken by the presynaptic neuron or surrounding glial cells or degraded by enzymes to terminate synaptic signaling [2]. While presynaptic and glial cell uptake has been considered previously by the authors (without receptor saturation) [6], [10], in this work, we focus on enzymatic degradation as clearance mechanism. ...

... This modified state equation accounts for saturation and desorption at x = a according to (6) and enzymatic degradation, while the output equation (18) to calculate the NT concentration and flux remains unchanged. We note that (29) collapses to (17) if κ a = κ d = κ e C E = 0. ...

Synaptic communication is a natural Molecular Communication (MC) system which may serve as a blueprint for the design of synthetic MC systems. In particular, it features highly specialized mechanisms to enable inter-symbol interference (ISI)-free and energy efficient communication. The understanding of synaptic MC is furthermore critical for disruptive innovations in the context of brain-machine interfaces. However, the physical modeling of synaptic MC is complicated by the possible saturation of the molecular receiver arising from the competition of postsynaptic receptors for neurotransmitters. Saturation renders the system behavior nonlinear and is commonly neglected in existing analytical models. In this work, we propose a novel model for receptor saturation in terms of a nonlinear, state-dependent boundary condition for Fick's diffusion equation. We solve the resulting boundary-value problem using an eigenfunction expansion of the Laplace operator and the incorporation of the receiver memory as feedback system into the corresponding state-space description. The presented solution is numerically stable and computationally efficient. Furthermore, the proposed model is validated with particle-based stochastic computer simulations.

... Due to the diversity of neuron and synapse structures, the relative timing of Levels 1 and 2 can vary considerably. The authors of [339] showed that, depending on the size of a chemical synapse and its associated reaction rates, communication via the synapse could be either diffusion-limited or rate-limited. ...

... Levels 1 and 2 also impose constraints on the overall communication speed. The approach to analyze the communication speed of chemical synapses in [339] might be generalized to other communication systems to discern bottlenecks and their impact on higher levels, e.g., device sensitivity and responsiveness to environmental changes. ...

Molecular communication (MC) engineering is inspired by the use of chemical signals as information carriers in cell biology. The biological nature of chemical signaling makes MC a promising methodology for interdisciplinary applications requiring communication between cells and other microscale devices. However, since the life sciences and communications engineering fields have distinct approaches to formulating and solving research problems, the mismatch between them can hinder the translation of research results and impede the development and implementation of interdisciplinary solutions. To bridge this gap, this survey proposes a novel communication hierarchy for MC signaling in cell biology and maps phenomena, contributions, and problems to the hierarchy. The hierarchy includes: 1) the physical propagation of cell signaling at the Physical Signal Propagation level; 2) the generation, reception, and biochemical pathways of molecular signals at the Physical and Chemical Signal Interaction level; 3) the quantification of physical signals, including macroscale observation and control methods, and conversion of signals to information at the Signal-Data Interface level; 4) the interpretation of information in cell signals and the realization of synthetic systems to store, process, and communicate molecular signals at the Local Data Abstraction level; and 5) applications relying on communication with MC signals at the Application level. To further demonstrate the proposed hierarchy, it is applied to case studies on quorum sensing, neuronal signaling, and communication via DNA. Finally, several open problems are identified for each level and the integration of multiple levels. The proposed hierarchy provides language for communication engineers to study and interface with biological systems, and also helps biologists to understand how communications engineering concepts can be exploited to interpret, control, and manipulate signaling in cell biology.

... Due to the diversity of neuron and synapse structures, the relative timing of Levels 1 and 2 can vary considerably. The authors of [329] showed that, depending on the size of a chemical synapse and its associated reaction rates, communication via the synapse could be either diffusion-limited or rate-limited. ...

... Levels 1 and 2 also impose constraints on the overall communication speed. The approach to analyze the communication speed of chemical synapses in [329] might be generalized to other communication systems to discern bottlenecks and their impact on higher levels, e.g., device sensitivity and responsiveness to environmental changes. ...

Molecular communication (MC) engineering is inspired by the use of chemical signals as information carriers in cell biology. The biological nature of chemical signaling makes MC a promising methodology for interdisciplinary applications requiring communication between cells and other microscale devices. However, since the life sciences and communications engineering fields have distinct approaches to formulating and solving research problems, the mismatch between them can hinder the translation of research results and impede the development and implementation of interdisciplinary solutions. To bridge this gap, this survey proposes a novel communication hierarchy for MC signaling in cell biology and maps phenomena, contributions, and problems to the hierarchy. The hierarchy includes: 1) the physical propagation of cell signaling at the Physical Signal Propagation level; 2) the generation, reception, and biochemical pathways of molecular signals at the Physical and Chemical Signal Interaction level; 3) the quantification of physical signals, including macroscale observation and control methods, and conversion of signals to information at the Signal-Data Interface level; 4) the interpretation of information in cell signals and the realization of synthetic systems to store, process, and communicate molecular signals at the Local Data Abstraction level; and 5) applications relying on communication with MC signals at the Application level. To further demonstrate the proposed hierarchy, it is applied to case studies on quorum sensing, neuronal signaling, and communication via DNA. Finally, several open problems are identified for each level and the integration of multiple levels. The proposed hierarchy provides language for communication engineers to study and interface with biological systems, and also helps biologists to understand how communications engineering concepts can be exploited to interpret, control, and manipulate signaling in cell biology.

... The transport equations for the 60 concentration distribution in the bulk and that on the surface are thus coupled. This form of 61 wall condition is simple and later widely used in applications of other fields such as biology 62 (Lotter et al. 2021) and hydraulics (Nordin & Troutman 1980). In practice, a first-order linear 63 reaction model is most popular for the adsorption-desorption process ( Roy et al. 2020). ...

Surface reactions such as the adsorption and desorption at boundaries are very common for solute dispersion in many applications of chemistry, biology, hydraulics, etc. To study how reversible adsorption affects the transient dispersion, Zhang et al. (J. Fluid Mech., vol. 828, 2017, pp. 733-752) have investigated the temporal evolution of moments using Laplace transform method. Due to difficulties introduced by the adsorption-desorption boundary condition, great challenges arise from the inverse Laplace transform: dealing with the singularities by the residue theorem can tremendously increase complexities. This work provides a much simpler analytical method to derive solutions in a more compact form while valid for the entire range of the reactive transport process. Such a progress demonstrates that the classic framework of separation of variables can be extended and applied to this more general adsorption-desorption condition, based on which higher-order statistics including skewness and kurtosis are possible to be explicitly explored in practice. Also extended is Gill's generalized dispersion model for solute concentration distributions, which can now address the entire transient dispersion characteristics, instead of just applied for the long-time asymptotic process as done previously. Regarding the most classic Taylor dispersion problem, we investigate the influence of the reversible adsorption-desorption on the solute cloud in a tube flow. Not only the transient dispersion characteristics of transverse-average concentration distribution but also those of the bulk, surface, and total-average distributions are discussed. We further investigate the influence of initial conditions on the non-uniformity of the transient dispersion over the cross-section.

... Synaptic communication was also studied from a communication theoretic perspective in [9] and in terms of its fundamental information theoretic limits in [10], [11]. The SMC models that explicitly consider the binding of individual NTs to postsynaptic receptors either assume a two-state (closed/open) kinetic scheme 1 for the receptors [5], [7], [8], [10], [11] or adopt intricate multistate models with many degrees of freedom [6]. However, the commonly employed two-state models neglect the desensitization of receptors, which is an important property of the main postsynaptic receptor types, see Fig. 2, and experimental data suggests that kinetic schemes with at least three states are required to reproduce the variety of receptor responses to NT releases observed in nature [12]. ...

Synaptic communication is studied by communication engineers for two main reasons. One is to enable novel neuroengineering applications that require interfacing with neurons. The other reason is to draw inspiration for the design of synthetic molecular communication systems. Both of these goals require understanding of how the chemical synaptic signal is sensed and transduced at the synaptic receiver (Rx). While signal reception in synaptic molecular communication (SMC) depends heavily on the kinetics of the receptors employed by the synaptic Rxs, existing channel models for SMC either oversimplify the receptor kinetics or employ complex, high-dimensional kinetic schemes limited to specific types of receptors. Both approaches do not facilitate a comparative analysis of different types of natural synapses. In this paper, we propose a novel deterministic channel model for SMC which employs a generic three-state receptor model that captures the characteristics of the most important receptor types in SMC. The model is based on a transfer function expansion of Fick's diffusion equation and accounts for release, diffusion, and degradation of neurotransmitters as well as their reversible binding to finitely many generic postsynaptic receptors. The proposed SMC model is the first that allows studying the impact of the characteristic dynamics of the main postsynaptic receptor types on synaptic signal transmission. Numerical results indicate that the proposed model indeed exhibits a wide range of biologically plausible dynamics when specialized to specific natural receptor types.

A more accurate synaptic modeling based on oxygen vacancy conductive mechanism has been presented in this paper. Two internal state variables, i.e. the length and area of conductive region, are used to describe the vertical and lateral growth/dissolution dynamics of the region, based on the physical mechanisms of ion drift and two different diffusion effects. Since the effect of length on the electric field is not negligible, it is introduced into the modeling. Besides, Fick and Soret diffusions are considered here, because they cause the model to produce a “forgetting” property and a “memory” retention. By the comparisons, this modeling captures the actual device better than others. In addition, the previous models can be derived from this one. Some rough analysis suggests that the modeling possibly captures different memristors by adjusting the parameters, and the effects of oxygen concentration and temperature on synapse can also be considered. Therefore, this modeling is more comprehensive and generalized. Several important synaptic functions are simulated, including excitatory postsynaptic current, paired‐pulse facilitation, spike‐rate dependent plasticity, and spike‐timing dependent plasticity, which may provide a theoretical basis for some potential applications such as artificial neural networks and artificial intelligence. This article is protected by copyright. All rights reserved.

Synaptic communication is based on a biological Molecular Communication (MC) system which may serve as a blueprint for the design of synthetic MC systems. However, the physical modeling of synaptic MC is complicated by the possible saturation of the molecular receiver caused by the competition of neurotransmitters (NTs) for postsynaptic receptors. Receiver saturation renders the system behavior nonlinear in the number of released NTs and is commonly neglected in existing analytical models. Furthermore, due to the ligands’ competition for receptors (and vice versa), the individual binding events at the molecular receiver are in general not statistically independent and the commonly used binomial model for the statistics of the received signal does not apply. Hence, in this work, we propose a novel deterministic model for receptor saturation in terms of a state-space description based on an eigenfunction expansion of Fick’s diffusion equation. The presented solution is numerically stable and computationally efficient. Employing the proposed deterministic model, we show that saturation at the molecular receiver effectively reduces the peak-value of the expected received signal and accelerates the clearance of NTs as compared to the case when receptor occupancy is neglected. We further derive a statistical model for the received signal in terms of the hypergeometric distribution which accounts for the competition of NTs for receptors and the competition of receptors for NTs. The proposed statistical model reveals how the signal statistics are shaped by the number of released NTs, the number of receptors, and the binding kinetics of the receptors, respectively, in the presence of competition. In particular, we show that the impact of these parameters on the signal variance is qualitatively different depending on the relative numbers of NTs and receptors. Finally, the accuracy of the proposed deterministic and statistical models is verified by particle-based computer simulations.

Information theory provides maximum possible information transfer over communication channels, including neural channels recently emerged as remarkable for disruptive nanonetworking applications. Information theory was successfully applied to quantify the ability of biological sensory neurons to transfer the information from dynamic stimuli. However, a little of information theory has been subjected to quantify the reliability of neuro-transmission between synaptically coupled neurons. Neuro-transmission, regarded as molecular synaptic communication, relays information between neurons and significantly affects the overall brain processing performance. In this study, we use concepts from information theory to provide the framework based on closed-form expressions that quantify the information rate allowing assessment of neuro-transmission when the parameters are provided for any type of neurons. Considering Poissonian statistics and the rate coding model of neural communication, we show how the information transferred between cortical neurons depend on the molecular, physiological and morphological diversity of cells, the firing rate, and the synaptic wiring. With synaptic redundancy, we infer the ability of an isolated post-synaptic neuron to reliably convey information encoded in the spike train from a pre-synaptic neuron. Estimating information rate between neurons primarily serves in the evaluation of the overall performance of biological neural nanonetworks and the development of artificial nano-networks.

Disease-affected nervous systems exhibit anatomical or physiological impairments that degrade processing, transfer, storage, and retrieval of neural information, leading to physical or intellectual disabilities. Brain implants may potentially promote clinical means for detecting and treating neurological symptoms by establishing direct communication between the nervous and artificial systems. Current technology can modify the neural function at the supracellular level as in Parkinson's disease, epilepsy, and depression. However, recent advances in nanotechnology, nanomaterials, and molecular communications have the potential to enable brain implants to preserve the neural function at the subcellular level, which could increase effectiveness, decrease energy consumption, and make the leadless devices chargeable from outside the body or by utilizing the body's own energy sources. In this paper, we focus on understanding the principles of elemental processes in synapses to enable diagnosis and treatment of brain diseases with pathological conditions using biomimetic synaptically interactive brain-machine interfaces (BMIs). First, we provide an overview of the synaptic communication system, followed by an outline of brain diseases that promote dysfunction in the synaptic communication system. Then, we discuss the technologies for brain implants and propose future directions for the design and fabrication of cognitive BMIs. The overarching goal of this paper is to summarize the status of engineering research at the interface between the technology and the nervous system and direct the ongoing research toward the point where synaptically interactive BMIs can be embedded in the nervous system.

Designing novel artificial intra-body networks and/or synthetic neurons, which interact with operating cells and compensate for malfunctioning cells, requires understanding and quantifying the information transfer in neural networks. However, the latter is not studied enough in the existing literature. Here we quantify the information rate transmitted between two neurons by analyzing Poisson Multiple-Input Multiple-Output (MIMO) synaptic channels. The results provided are intuitive and prove that multiple synapses working in cooperation improve the reliability of the neuron-to-neuron communication channel. The results serve as a progressive step in the evaluation of the performance of biological neural networks and the development of artificial cells and networks.

Computational methods have been extensively used to understand underlying dynamics of molecular communication methods employed by nature. One very effective and popular approach is to utilize a Monte Carlo simulation. Although it is very reliable, this method can have a very high computational cost, which in some cases renders the simulation impractical. Therefore, in this paper, for the special case of an excitatory synaptic molecular communication channel, we present a novel mathematical model for the diffusion and binding of neurotransmitters that takes into account the effects of synaptic geometry in three-dimensional space and re-absorption of neurotransmitters by the transmitting neuron. Based on this model we develop a fast deterministic algorithm, which calculates expected value of the output of this channel, namely the amplitude of EPSP (Excitatory Postsynaptic Potential), for given synaptic parameters. We validate our algorithm by a Monte Carlo simulation, which shows total agreement between the results of two methods. Finally, we utilize our model to quantify effects of variation in synaptic parameters such as position of release site, receptor density, size of postsynaptic density (PSD), diffusion coefficient, uptake probability and number of neurotransmitters in a vesicle, on maximum number of bound receptors that directly affect peak amplitude of EPSP.

The G-protein coupled, protease-activated receptor 1 (PAR1) is a membrane protein expressed in astrocytes. Fine astrocytic processes are in tight contact with neurons and blood vessels and shape excitatory synaptic transmission due to their abundant expression of glutamate transporters. PAR1 is proteolytically-activated by bloodstream serine proteases also involved in the formation of blood clots. PAR1 activation has been suggested to play a key role in pathological states like thrombosis, hemostasis and inflammation. What remains unclear is whether PAR1 activation also regulates glutamate uptake in astrocytes and how this shapes excitatory synaptic transmission among neurons. Here we show that, in the mouse hippocampus, PAR1 activation induces a rapid structural re-organization of the neuropil surrounding glutamatergic synapses, which is associated with faster clearance of synaptically-released glutamate from the extracellular space. This effect can be recapitulated using realistic 3D Monte Carlo reaction-diffusion simulations, based on axial scanning transmission electron microscopy (STEM) tomography reconstructions of excitatory synapses. The faster glutamate clearance induced by PAR1 activation leads to short- and long-term changes in excitatory synaptic transmission. Together, these findings identify PAR1 as an important regulator of glutamatergic signaling in the hippocampus and a possible target molecule to limit brain damage during hemorrhagic stroke.

A molecular diffusion channel is a channel with memory, as molecules released into the medium hit the receptors after a random delay. Modulating over the diffusion channel is performed by choosing the type, intensity, or the released time of molecules diffused in the environment over time. Motivated by the desire to keep the encoder and decoder simple and the fact that channel state information (CSI) is difficult to obtain in diffusion channels, we consider modulation schemes that avoid intersymbol interference (ISI), wherein molecules of the same type are released at time instances that are sufficiently far apart. This ensures that molecules of a previous transmission are faded in the environment, before molecules of the same type are reused for signaling. Avoiding ISI puts a constraint on the input sequence to the channel. In this paper, we study the fundamental limits on reliable communication rate, due to this constraint on input sequences. The maximum reliable transmission rate of ISI-avoiding modulations is given by the constrained coding capacity of the graph that represents the permissible transmission sequences. However, achieving the constrained coding capacity requires long blocklengths and delays at the decoder, making it impractical for simple nano-machines. The main contribution of this paper is to consider modulations with small delay (short blocklength) and show that they get very close to constrained coding capacity.

Molecular communication via diffusion (MCvD) is inherently an energy efficient transportation paradigm, which requires no external energy during molecule propagation. Inspired by the fact that the emitted molecules have a finite probability to reach the receiver, this paper introduces an energy efficient scheme for the information molecule synthesis process of MCvD via a simultaneous molecular information and energy transfer (SMIET) relay. With this SMIET capability, the relay can decode the received information as well as generate its emission molecules using its absorbed molecules via chemical reactions. To reveal the advantages of SMIET, approximate closed-form expressions for the bit error probability and the synthesis cost of this two-hop molecular communication system are derived and then validated by particle-based simulation. Interestingly, by comparing with a conventional relay system, the SMIET relay system can be shown to achieve a lower minimum bit error probability via molecule division, and a lower synthesis cost via molecule type conversion or molecule division.

Neuronal communication is a biological phenomenon of the central nervous system that influences the activity of all intra-body nano-networks. The implicit biocompatibility and dimensional similarity of neurons with miniature devices make their interaction a promising communication paradigm for nano-networks. To understand the information transfer in neuronal networks, there is a need to characterize the noise sources and unreliability associated with different components of the functional apposition between two cells – the synapse. In this paper, we introduce analogies between the optical communication system and neuronal communication system to apply results from optical Poisson channels in deriving theoretical upper bounds on the information capacity of both bipartite- and tripartite synapses. The latter refer to the anatomical and functional integration of two communicating neurons and surrounding glia cells. The efficacy of information transfer is analyzed under different synaptic set-ups with progressive complexity, and is shown to depend on the peak rate of the communicated spiking sequence and neurotransmitter (spontaneous) release, neurotransmitter propagation, and neurotransmitter binding. The results provided serve as a progressive step in the evaluation of the performance of neuronal nano-networks and the development of new artificial nano-networks.

The performance of communication systems is fundamentally limited by the loss of energy through propagation and circuit inefficiencies. In this article, we show that it is possible to achieve ultra low energy communications at the nano-scale, if diffusive molecules are used for carrying data. Whilst the energy of electromagnetic waves will inevitably decay as a function of transmission distance and time, the energy in individual molecules does not. Over time, the receiver has an opportunity to recover some, if not all of the molecular energy transmitted. The article demonstrates the potential of ultra-low energy simultaneous molecular information and energy transfer (SMIET) through the design of two different nano-relay systems, and the discusses how molecular communications can benefit more from crowd energy harvesting than traditional wave-based systems.

Serving as peers in the central nervous system, neurons make use of two communication paradigms, electrochemical, and molecular. Owing to their effective coordination of all the voluntary and involuntary actions of the body, an intriguing neuronal communication nominates as a potential paradigm for nano-networking. In this paper, we propose an alternative representation of the neuron-to-neuron communication process, which should offer a complementary insight into the electrochemical signals propagation. To this end, we apply communication-engineering tools and abstractions, represent information about chemical and ionic behavior with signals, and observe biological systems as input-output systems characterized by a frequency response. In particular, we inspect the neuron-to-neuron communication through the concepts of electrochemical communication, which we refer to as the intra-neuronal communication due to the pulse transmission within the cell, and molecular synaptic transmission, which we refer to as the inter-neuronal communication due to particle transmission between the cells. The inter-neuronal communication is explored by means of the transmitter, the channel, and the receiver, aiming to characterize the spiking propagation between neurons. Reported numerical results illustrate the contribution of each stage along the neuronal communication pathway, and should be useful for the design of a new communication technique for nano-networks and intrabody communications.

Diffusive molecular communication (MC) is a promising strategy for the transfer of information in synthetic networks at the nanoscale. If such devices could communicate, then it would expand their cumulative capacity and potentially enable applications such as cooperative diagnostics in medicine, bottom-up fabrication in manufacturing, and sensitive environmental monitoring. Diffusion-based MC relies on the random motion of information molecules due to collisions with other molecules. This dissertation presents a novel system model for three-dimensional diffusive MC where molecules can also be carried by steady uniform flow or participate in chemical reactions. The expected channel impulse response due to a point source of molecules is derived and its statistics are studied. The mutual information between consecutive observations at the receiver is also derived. A simulation framework that accommodates the details of the system model is introduced. A joint estimation problem is formulated for the underlying system model parameters. The Cramer-Rao lower bound on the variance of estimation error is derived. Maximum likelihood estimation is considered and shown to be better than the Cramer-Rao lower bound when it is biased. Peak-based estimators are proposed for the low-complexity estimation of any single channel parameter. Optimal and suboptimal receiver design is considered for detecting the transmission of ON/OFF keying impulses. Optimal joint detection provides a bound on detector performance. The weighted sum detector is proposed as a suboptimal alternative that is more physically realizable. The performance of a weighted sum detector can become comparable to that of the optimal detector when the environment has a mechanism to reduce intersymbol interference. A model for noise sources that continuously release molecules is studied. The time-varying and asymptotic impact of such sources is derived. The model for asymptotic noise is used to approximate the impact of multiuser interference and also the impact of older bits of intersymbol interference.

Synaptic transmission relies on spatially and temporally coordinated multistep processes that allow neuronal communication; activity-dependent changes in synaptic transmission underlie synaptic plasticity. These processes are coordinated by a large number of specific proteins whose dynamic interactions, expression, and regulation define the efficacy of transmission and the mode of synaptic plasticity. In this chapter, we discuss the molecular mechanisms of some of the basic processes associated with neurotransmission in the presynaptic terminal-vesicle docking, priming, and fusion-elaborate on the contribution of specific proteins to different modes of vesicle recycling, and discuss their nanoscale distribution in the synapses. We also describe the involvement of these proteins in synaptic plasticity and animal behavior, the expression ratios between specific proteins and the possible contribution of these ratios to various modes and kinetics of neurotransmitter release.

The propagation of the neural information in the cerebral cortex relies on the transfer of electrochemical impulses and diffusion of neurotransmitter molecules between neuron cells connected in a network through synaptic junctions. In this scenario, increasing interest is growing on the critical role of glia cells, in particular astrocytes, in supporting the neuronal communication. Neuroglias communicate to each other through calcium signaling and are able to sense the activity of adjacent neurons and release gliotransmitter molecules such as glutamate and D-serine, which bind on receptors located on the synaptic terminal of neurons. In other terms, astrocytes can potentially modulate the neuronal activity of adjacent neurons as well as distant neurons through calcium signaling. In this paper, we describe the neuron-astrocyte communication paradigm, first identifying the molecular processes constituting the communication and then representing each process with equivalent electronic circuits, characterized by frequency response. The aim of this work is to propose an alternative tool for the stimulus-response analysis of the astrocyte-neuron system, in particular to quantify the impact of astrocytic stimulation on the natural activity of spiking neurons. The frequency response of the equivalent circuits shows that certain stimulation patterns evoked through the astrocytes are more effective than others and have the potential of significantly alter the neuronal activity.

Molecular communication is a new field of communication where molecules are
used to transfer information. Among the proposed methods, molecular
communication via diffusion (MCvD) is particularly effective. One of the main
challenges in MCvD is the intersymbol interference (ISI), which inhibits
communication at high data rates. Furthermore, at the nano scale, energy
efficiency becomes an essential problem. Before addressing these problems, a
pre-determined threshold for the received signal must be calculated to make a
decision. In this paper, an analytical technique is proposed to determine the
optimum threshold, whereas in the literature, these thresholds are generally
calculated empirically. Since the main goal of this paper is to build an MCvD
system suitable for operating at high data rates without sacrificing quality,
new modulation and filtering techniques are proposed to decrease the effects of
ISI and enhance energy efficiency. As a transmitter-based solution, a
modulation technique for MCvD, molecular transition shift keying (MTSK), is
proposed in order to increase the data rate via suppressing the ISI.
Furthermore, for energy efficiency, a power adjustment technique that utilizes
the residual molecules is proposed. Finally, as a receiver-based solution, a
new energy efficient decision feedback filter (DFF) is proposed as a substitute
for the decoders such as minimum mean squared error (MMSE) and decision
feedback equalizer (DFE). The error performance of DFF and MMSE equalizers are
compared in terms of bit error rates, and it is concluded that DFF may be more
advantageous when energy efficiency is concerned, due to its lower
computational complexity.

In the nanonetworking literature, many solutions have been suggested to
enable the nanomachine-to-nanomachine communication. Among these solutions, we
focus on what constitutes the basis for molecular communication paradigms
--molecular communication via diffusion (MCvD). In this paper, we start with an
analytical modeling of a spherical absorbing receiver under messenger molecule
degradation and show that our formulations are in agreement with the simulation
results of a similar topology. Next, we identify how such signal
characteristics as pulse peak time and pulse amplitude are affected by
degradation. Indeed, we show analytically how in MCvD, signal shaping is
achieved through degradation. We also compare communication under messenger
molecule degradation with the case of no-degradation and electromagnetic
communication in terms of channel characteristics. Lastly, we evaluate the
communication performance of the scenarios having various degradation rates.
Here, we assess the system performance according to traditional network metrics
such as the level of inter-symbol interference, detection performance, bit
error rate, and channel capacity. Our results indicate that introducing
degradation significantly improves the system performance when the rate of
degradation is appropriately selected. We make a thorough analysis of the
communication scenario by taking into account different detection thresholds,
symbol durations, and communication distances.

This paper studies the mitigation of intersymbol interference in a diffusive molecular communication system using enzymes that freely diffuse in the propagation environment. The enzymes form reaction intermediates with information molecules and then degrade them so that they cannot interfere with future transmissions. A lower bound expression on the expected number of molecules measured at the receiver is derived. A simple binary receiver detection scheme is proposed where the number of observed molecules is sampled at the time when the maximum number of molecules is expected. Insight is also provided into the selection of an appropriate bit interval. The expected bit error probability is derived as a function of the current and all previously transmitted bits. Simulation results show the accuracy of the bit error probability expression and the improvement in communication performance by having active enzymes present.

Communication between nanoscale devices is an area of considerable importance as it is essential that future devices be able to form nanonetworks and realise their full potential. Molecular communication is a method based on diffusion, inspired by biological systems and useful over transmission distances in the nm to μmμm range. The propagation of messenger molecules via diffusion implies that there is thus a probability that they can either arrive outside of their required time slot or ultimately, not arrive at all. Therefore, in this paper, the use of a error correcting codes is considered as a method of enhancing the performance of future nanonetworks. Using a simple block code, it is shown that it is possible to deliver a coding gain of ∼1.7 dB at transmission distances of 1μm. Nevertheless, energy is required for the coding and decoding and as such this paper also considers the code in this context. It is shown that these simple error correction codes can deliver a benefit in terms of energy usage for transmission distances of upwards of 25μm for receivers of a 5μm radius.

The diffusion equation for a constant and a linear potential is solved with boundary conditions which account for back-reaction (desorption). The solution is given in terms of Green’s function, from which expressions for the survival probability are derived. Inclusion of back reaction generally results in an ultimate survival probability of unity.

Why synapses release a certain amount of neurotransmitter is poorly understood. We combined patch-clamp electrophysiology with computer simulations to estimate how much glutamate is discharged at two distinct central synapses of the rat. We found that, regardless of some uncertainty over synaptic microenvironment, synapses generate the maximal current per released glutamate molecule while maximizing signal information content. Our result suggests that synapses operate on a principle of resource optimization.

Past models of somatosensory cortex have successfully
demonstrated map formation and subsequent map reorganization
following localized repetitive stimuli or deafferentation. They
provide an impressive demonstration that fairly simple assumptions
about ...

Particle-based simulators represent molecules of interest with point-like particles that diffuse and react in continuous space. These simulators are often used to investigate spatial or stochastic aspects of biochemical systems. This paper presents new particle-based simulation algorithms for modeling interactions between molecules and surfaces; they address irreversible and reversible molecular adsorption to, desorption from and transmission through membranes. Their central elements are: (i) relationships between adsorption, desorption and transmission coefficients on the one hand, and simulator interaction probabilities on the other, and (ii) probability densities for initial placements of desorbed molecules. These algorithms, which were implemented and tested in the Smoldyn simulator, are accurate, easy to implement and computationally efficient. They allow longer time steps and better address reversible processes than an algorithm that Erban and Chapman recently presented (Physical Biology 4:16-28, 2007). This paper also presents a method for simulating unbounded diffusion in a limited spatial domain using a partially absorbing boundary, as well as new solutions to the diffusion differential equation with reversible Robin boundary conditions.

This letter focuses on a diffusion-based molecular communication system, fed by a nanoscale energy-harvesting mechanism, and conceives a power control mechanism based on feedback control theory. Specifically, the load current drained by the transmitter interface is set proportionally to the available energy harvested from the environment by using a closed-loop control scheme. The resulting system is analytically described through a nonlinear state equation, that jointly considers harvesting and discharging processes. Its asymptotic stability is evaluated around the equilibrium point, while considering some technological constraints. Finally, a numerical example is discussed to clearly show the behavior of the proposed approach in conceivable scenarios.

The information from outside world is encoded into spikes by the sensory neurons. These spikes are further propagated to different brain regions through various neural pathways. In the cortical region, each neuron receives inputs from multiple neurons that change its membrane potential. If the accumulated change in the membrane potential is more than a threshold value, a spike is generated. According to various studies in neuroscience, this spiking threshold adapts with time depending on the previous spike. This causes short-term changes in the neural responses giving rise to short-term plasticity. Therefore, in this paper, we analyze a multiple-input single-output (MISO) neuro-spike communication channel and study the effects of dynamic spiking threshold on mutual information and maximum achievable sum rate of the channel. Since spike generation consumes a generous portion of the metabolic energy provided to the brain, we further put metabolic constraint in calculating the mutual information and find a trade-off between maximum achievable sum rate and metabolic energy consumed. Moreover, we analyze three types of neurons present in the cortical region, i.e., Regular spiking, Intrinsic bursting and Fast spiking neurons. We aim to characterize these neurons in terms of encoding/transmission rates and energy expenditure. It will provide a guideline for the practical implementation of bio-inspired nanonetworks as well as for the development of ICT-based diagnosis and treatment techniques for neural diseases.

Communication among neurons, known as neurospike communication, is the most promising technique for realization of a bio-inspired nanoscale communication paradigm to achieve biocompatible nanonetworks. In neuro-spike communication, the information, encoded into spike trains, is communicated to various brain regions through neuronal network. An output neuron needs to receive signal from multiple input neurons to generate a spike. Hence, in this paper, we aim to quantify the information transmitted through the multiple-input single-output (MISO) neuro-spike communication channel by taking into account models for axonal propagation, synaptic transmission and spike generation. Moreover, the spike generation and propagation in each neuron requires opening and closing of numerous ionic channels on the cell membrane, which consumes considerable amount of ATP molecules called metabolic energy. Thus, we evaluate how applying a constraint on available metabolic energy affects the maximum achievable mutual information of this system. To this aim, we derive a closed form equation for the sum rate of the MISO neuro-spike communication channel and analyze it under the metabolic cost constraints. Finally, we discuss the impacts of changes in number of pre-synaptic neurons on the achievable rate and quantify the trade-off between maximum achievable sum rate and the consumed metabolic energy.

Understanding the communication theoretical capabilities of information transmission among neurons, known as neuro-spike communication, is a significant step in developing bio-inspired solutions for nanonetworking. In this study, we focus on a part of this communication known as synaptic transmission for pyramidal neurons in Cornu Ammonis (CA) area of hippocampus location in the brain and propose a communication-based model for it that includes effects of spike shape variation on neural calcium signaling and the vesicle release process downstream of it. For this aim, we find impacts of spike shape variation on opening of voltage-dependent calcium channels (VDCCs), which control the release of vesicles from pre-synaptic neuron by changing the influx of calcium ions. Moreover, we derive the structure of optimum receiver based on Neyman-Pearson detection method to find the effects of spike shape variations on the functionality of neuro-spike communication. Numerical results depict that changes in both spike width and amplitude affect the error detection probability. Moreover, these two factors do not control the performance of the system independently. Hence, a proper model for neuro-spike communication should contain effects of spike shape variations during axonal transmission on both synaptic propagation and spike generation mechanisms to enable us to accurately explain the performance of this communication paradigm.

In this paper we analyse molecular communications (MC) in a proposed artificial synapse (AS), whose main difference from biological synapses (BSs) is that it is closed, i.e., transmitter molecules cannot diffuse out from AS. Such a setup has both advantages and disadvantages. Besides higher structural stability, being closed, AS never runs out of transmitters. Thus, MC in AS is disconnected from outer environment, which is very desirable for possible intra-body applications. On the other hand, clearance of transmitters from AS has to be achieved by transporter molecules on the presynaptic membrane of AS. Except from these differences, rest of AS content is taken to be similar to that of a glutamatergic BS. Furthermore, in place of commonly used Monte Carlo based random walk experiments, we derive a deterministic algorithm that attacks for expected values of desired parameters such as evolution of receptor states. To assess validity of our algorithm we compare its results with average results of an ensemble of Monte Carlo experiments, which shows near exact match. Moreover, our approach requires significantly less amount of computation compared to Monte Carlo approach, making it useful for parameter space exploration necessary for optimisation in design of possible MC devices, including but not limited to AS. Results of our algorithm are presented in case of single quantal release only, and they support that MC in closed AS with elevated uptake has similar properties to that in BS. In particular, similar to glutamatergic BSs, the quantal size and density of receptors are found to be main sources of synaptic plasticity. On the other hand, the proposed model of AS is found to have slower decaying transients of receptor states compared to BSs, especially desensitised ones, which is due prolonged clearance of transmitters from AS.

This paper studies the problem of receiver modeling in molecular communication systems. We consider the diffusive molecular communication channel between a transmitter nano-machine and a receiver nano-machine in a fluid environment. The information molecules released by the transmitter nano-machine into the environment can degrade in the channel via a first-order degradation reaction and those that reach the receiver nano-machine can participate in a reversible bimolecular reaction with receiver receptor proteins. Thereby, we distinguish between two scenarios. In the first scenario, we assume that the entire surface of the receiver is covered by receptor molecules. We derive a closed-form analytical expression for the expected received signal at the receiver, i.e., the expected number of activated receptors on the surface of the receiver. Then, in the second scenario, we consider the case where the number of receptor molecules is finite and the uniformly distributed receptor molecules cover the receiver surface only partially. We show that the expected received signal for this scenario can be accurately approximated by the expected received signal for the first scenario after appropriately modifying the forward reaction rate constant. The accuracy of the derived analytical results is verified by Brownian motion particle-based simulations of the considered environment, where we also show the impact of the effect of receptor occupancy on the derived analytical results.

This comprehensive guide, by pioneers in the field, brings together, for the first time, everything a new researcher, graduate student or industry practitioner needs to get started in molecular communication. Written with accessibility in mind, it requires little background knowledge, and provides a detailed introduction to the relevant aspects of biology and information theory, as well as coverage of practical systems. The authors start by describing biological nanomachines, the basics of biological molecular communication and the microorganisms that use it. They then proceed to engineered molecular communication and the molecular communication paradigm, with mathematical models of various types of molecular communication and a description of the information and communication theory of molecular communication. Finally, the practical aspects of designing molecular communication systems are presented, including a review of the key applications. Ideal for engineers and biologists looking to get up to speed on the current practice in this growing field.

Synapses exist in different structural forms exhibiting a variety of morphological complexities, which are complimented by a myriad of dendritic spine shapes. This chapter shows how electron microscopy can demonstrate the incredible variety of synapse and spine relationships. It uses both two-dimensional images and three-dimensional reconstructions of ultrathin sections of synapses and spines to illustrate this great variety of morphological forms. The diversity of synapses, spines, and dendritic structures is also reflected in the nature of their relationships to each other, which far from being on a simple one-to-one basis, may be very complex either as multisynaptic boutons, or multi-innervated spines. We also examine those structures which can be visualized within both the synaptic bouton and dendritic spine, and the dendrite itself. All the images and reconstructions are from tissue in the mammalian hippocampus, and the region from which the images are taken is shown in Figure 1(A) and (B).

Bioinspired communication techniques are emerging with increasing interest in parallel with recent advancements of nanotechnology. Particular interest is observed in the development of neuronal interfaces for human-machine communication and nanoscale neuronal devices. We propose a novel description of the communication pathways existing in the neuronal circuits, based on the abstract dynamics between different components of the neuronal communication. In the analysis, a critical role is played by glia cells, such as the astrocytes, which support and actively modulate the neuronal activity of adjacent neurons, as shown in experiments conducted the last decades. For this reason, the concept of tripartite synapse, where two neurons are interfaced with the astrocyte, is central in our abstraction. First, we define the layers of the bidirectional neuron-astrocyte communication and describe mathematically the relations connecting different quantities, i.e., intracellular molecular concentrations and currents produced on the cellular membrane. Second, the astrocytic Ca<sup>2+</sup> signaling is investigated for the design of a neuronal communication interface based on the propagation of calcium waves through the astrocytic network. The proposed analysis provides an organized framework for an alternative description of the synaptic communication as well as for aiding the development of artificial biomimetic devices and prostheses.

Molecular communication is an emerging communication technology for applications requiring nanoscale networks. Transferring vital information about external and internal conditions of the body through the nervous system is an important type of intra-body molecular nanonetworks. Thus, investigating the performance of such systems from the communication theoretic perspective gives us insight on the limitation of neuro-spike communication and ways to design artificial neural systems. In this letter, we study the performance of the neuro-spike communication under different stochastic impairments such as axonal shot noise, synaptic noise, and random vesicle release. The objective is to optimally detect the spikes at the receiving neuron. Since several uncertainties occur under each hypothesis, composite hypothesis is employed to find the optimum detection policy. Furthermore, we obtain closed-form solutions for the optimal detector and derive the binary decision error at the postsynaptic terminal.

Neuro-spike communication is an important branch of molecular communications and has attracted much attention recently. Seminal works on the analyses of signal processing and channel models for the synaptic communication have recently been carried out. However, these works do not consider interference. In this paper, we propose an interference model for synaptic channels with particular focus on InterSymbol Interference (ISI) and Single-Input Single-Output (SISO) channel. We have investigated the overlapping between the two consecutively signals which are sent from a presynaptic terminal to a postsynaptic terminal and their interferences. Furthermore, important parameters of synaptic communication channel that are related to the ISI are also analyzed. The relationship between channel rate region and ISI is also studied.

Neurons within human brain make use of two communication paradigms while pursuing an objective, namely, classical electromagnetic and molecular. Physiological studies revealed that communication performance between neurons, including memory formation and learning processes, highly depends on the concentration of calcium ions, whereas the intracellular calcium concentration hinges on regulation of neuron's membrane potential. Hence, the neuronal communication performance can be affected via controlled stimulation of targeted cell. In this paper we analyze the neuronal communication as potential paradigm to be applied for communication between nano-scale devices and define the stochastic spiking model, that is confined to randomness associated with neuron's firing, in order to acquire and quantify the neuron's response given specified stimulus. We also present synaptic transmission process and modifications related to memory formation and storage using existing simplified theoretical models on calcium dependent behavior and learning. Using modeling, theory, and findings presented in this paper, one can design the stimulus with adequate power spectral density in order to evoke desired synaptic modifications in terms of its strengthening and weakening. Similar approach provides a basement for future technologies and controlling method for nano-scale communication between peers.

Molecular communications emerges as a promising scheme for communications between nanoscale devices. In diffusion-based molecular communications, molecules as information symbols diffusing in the fluid environments suffer from molecule crossovers, i.e., the arriving order of molecules is different from their transmission order, leading to intersymbol interference (ISI). In this paper, we introduce a new family of channel codes, called ISI-free codes, which improve the communication reliability while keeping the decoding complexity fairly low in the diffusion environment modeled by the Brownian motion. We propose general encoding/decoding schemes for the ISI-free codes, working upon the modulation schemes of transmitting a fixed number of identical molecules at a time. In addition, the bit error rate (BER) approximation function of the ISI-free codes is derived mathematically as an analytical tool to decide key factors in the BER performance. Compared with the uncoded systems, the proposed ISI-free codes offer good performance with reasonably low complexity for diffusion-based molecular communication systems.

Communication between neurons occurs via transmission of neural spike trains through junctional structures, either electrical or chemical synapses, providing connections among nerve terminals. Since neural communication is achieved at synapses, the process of neurotransmission is called synaptic communication. Learning and memory processes are based on the changes in strength and connectivity of neural networks which usually contain multiple synaptic connections. In this paper, we investigate multiple-access neuro-spike communication channel, in which the neural signal, i.e., the action potential, is transmitted through multiple synaptic paths directed to a common postsynaptic neuron terminal. Synaptic transmission is initiated with random vesicle release process from presynaptic neurons to synaptic paths. Each synaptic channel is characterized by its impulse response and the number of available postsynaptic receptors. Here, we model the multiple-access synaptic communication channel, and investigate the information rate per spike at the postsynaptic neuron, and how postsynaptic rate is enhanced compared to single terminal synaptic communication channel. Furthermore, we analyze the synaptic transmission performance by incorporating the role of correlation among presynaptic terminals, and point out the postsynaptic rate improvement.

Nanoscale communications is an appealing domain in nanotechnology. Novel nanoscale communications techniques are currently being devised inspired by some naturally existing phenomena such as the molecular communications governing cellular signaling mechanisms. Among these, neuro-spike communications, which governs the communications between neurons, is a vastly unexplored area. The ultimate goal of this paper is to accurately investigate nanoscale neuro-spike communications characteristics through the development of a realistic physical channel model between two neurons. The neuro-spike communications channel is analyzed based on the probability of error and delay in spike detection at the output. The derived communication theoretical channel model may help designing novel artificial nanoscale communications methods for the realization of future practical nanonetworks, which are the interconnections of nanomachines.

The role of diffusion in the kinetics of reversible ligand binding to receptors on a cell surface or to a macromolecule with multiple binding sites is considered. A formalism is developed that is based on a Markovian master equation for the distribution function of the number of occupied receptors containing rate constants that depend on the ligand diffusivity. The formalism is used to derive (1) a nonlinear rate equation for the mean number of occupied receptors and (2) an analytical expression for the relaxation time that characterizes the decay of equilibrium fluctuations of the occupancy of the receptors. The relaxation time is shown to depend on the ligand diffusivity and concentration, the number of receptors, the cell radius, and intrinsic association∕dissociation rate constants. This result is then used to estimate the accuracy of the ligand concentration measurements by the cell, which, according to the Berg-Purcell model, is related to fluctuations in the receptor occupancy, averaged over a finite interval of time. Specifically, a simple expression (which is exact in the framework of our formalism) is derived for the variance in the measured ligand concentration in the limit of long averaging times.

The simplest general theory of the kinetics of reversible diffusion-influenced reactions that is exact both at short and long times for A+B⇌C and A+B⇌C+D is presented. The formalism is based on an approximate set of reaction-diffusion equations for the pair distribution functions which incorporate the influence of the chemical reaction by using effective rate constants that are determined self-consistently. For small deviations from equilibrium and contact reactivity, the relaxation function is given explicitly in the Laplace domain in terms of the Smoluchowski rate coefficient that describes the corresponding diffusion controlled irreversible reaction. Consequently, the kinetics can be easily obtained for arbitrary diffusion coefficients and equilibrium concentrations. © 2002 American Institute of Physics.

Three formalisms that describe the influence of diffusion on the kinetics of the reversible reaction, A+B⇌AB, are discussed and compared. The simplest involves a modification of the irreversible rate equations of Smoluchowski theory; the second is based on a generalization of physically appealing convolution relations that hold rigorously for reversible reactions between isolated pairs, and the third can be obtained by using a superposition approximation to truncate the hierarchy of equations satisfied by the reactive reduced distribution functions. The various formalisms are developed to the point that their implementation requires knowledge only of the time‐dependent irreversible association rate coefficient and the microscopic dissociation rate constant. All these approaches give the correct equilibrium concentrations at infinite time, have the same short‐time behavior, reduce correctly when the dissociation rate is zero, and become equivalent in the reaction‐controlled limit. However, none of them provides an exact treatment of the underlying many‐particle diffusive model of the reaction. Some illustrative calculations are presented and the relative merits of these approaches are discussed. All three approaches predict that the relaxation of a small initial deviation of the concentrations from their equilibrium values is nonexponential, except, of course, in the reaction‐controlled limit. With a view towards treating monomer–excimer kinetics, the formalisms are generalized to incorporate unimolecular decay pathways.

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An artefact of simulating diffusion-controlled reactions with a discrete time-step, which arises from lack of knowledge of the trajectory within the time-step, is discussed. A method of interpolating the trajectory to arbitrary accuracy is derived and the interpolated ‘brownian bridge’ process is used to calculate the probability that reaction has occurred during the time-step given the initial and final positions of the particles.

Preface 1. Models for diffusion Part I. Fundamentals of Diffusion: 2. Diffusion in dilute solutions 3. Diffusion in concentrated solutions 4. Dispersion Part II. Diffusion Coefficients: 5. Values of diffusion coefficients 6. Diffusion of interacting species 7. Multicomponent diffusion Part III. Mass Transfer: 8. Fundamentals of mass transfer 9. Theories of mass transfer 10. Absorption 11. Absorption in biology and medicine 12. Differential distillation 13. Staged distillation 14. Extraction 15. Absorption Part IV. Diffusion Coupled with other Processes: 16. General questions and heterogeneous chemical reactions 17. Homogeneous chemical reactions 18. Membranes 19. Controlled release and related phenomena 20. Heat transfer 21. Simultaneous heat and mass transfer Problems Subject index Materials index.

The neuronal doctrine, developed a century ago regards neuronal networks as the sole substrate of higher brain function. Recent advances in glial physiology have promoted an alternative hypothesis, which places information processing in the brain into integrated neuronal-glial networks utilizing both binary (neuronal action potentials) and analogue (diffusional propagation of second messengers/metabolites through gap junctions or transmitters through the interstitial space) signal encoding. It has been proposed that the feed-forward and feed-back communication between these two types of neural cells, which underlies information transfer and processing, is accomplished by the release of neurotransmitters from neuronal terminals as well as from astroglial processes. Understanding of this subject, however, remains incomplete and important questions and controversies require resolution. Here we propose that the primary function of perisynaptic glial processes is to create an "astroglial cradle" that shields the synapse from a multitude of extrasynaptic signaling events and provides for multifaceted support and long-term plasticity of synaptic contacts through variety of mechanisms, which may not necessarily involve the release of "glio" transmitters.