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Random Walks in Biology
Abstract
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... Introduction -For more than a century, simple stochastic processes like the random walk have been successfully used to model a variety of phenomena across disciplines [1][2][3]. For instance, the motion of bacteria in space [1,2] and the evolution of the price of a stock in finance [3] can be approximated as a sequence of jumps between states, which take place according to some probabilistic rule. ...
... Introduction -For more than a century, simple stochastic processes like the random walk have been successfully used to model a variety of phenomena across disciplines [1][2][3]. For instance, the motion of bacteria in space [1,2] and the evolution of the price of a stock in finance [3] can be approximated as a sequence of jumps between states, which take place according to some probabilistic rule. ...
... In many different contexts, it is natural to associate a (possibly non-linear) cost -or a reward -to the "change of state" of a stochastic process -often with unexpected or paradoxical consequences. For instance, the energy consumption of bacteria changes depending on the environment they move in [1]. Wireless devices absorb different amounts of energy when they switch between activity states ('off', 'idle', 'transmit' or 'receive') [4,5]. ...
We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while for fast jumps the cost is proportional to the velocity of the jump. The model -- inspired by the way taxi meters work -- exhibits a very rich behavior. The cost for trajectories of equal length and equal duration exhibits giant fluctuations at a critical value of the scaled distance travelled. Furthermore, the full distribution of the cost until the target is reached exhibits an interesting ``freezing'' transition in the large-deviation regime. All the analytical results are corroborated by numerical simulations, and wider applications of this general model are discussed.
... The size of such suspended particles and cell aggregates can vary over several orders of magnitude, affecting their sedimentation [14,15] and overall transport [16,17]. In particular, enhanced suspended particle velocity in confined environments has been observed and associated to their finite-size, also known as size exclusion effect [18,19]. ...
... Particle positions x j are updated through eq. (15). The new position results by averaging the velocity field u k+1 over the high viscosity region associated to the particle. ...
... To avoid this we impose a constraint on eq. (15). As soon as the distance between ∂Ω i and x j is less or equal to a, we adjust the velocity u k j by taking only the tangential component with respect to the boundary ∂Ω i . ...
Understanding the coupling between flow, hydrodynamic transport and dispersion of colloids with finite-size in porous media is a long-standing challenge. This problem is relevant for a broad range of natural and engineered subsurface processes, including contaminant and colloidal transport, mixing of bio-chemical compounds, kinetics of reactions and groundwater bio-remediation, but also transport phenomena related to different systems like membranes, or blood flow. While classical models for colloidal transport rely on macro-dispersion theory and do not take into consideration the complex and heterogeneous structure of the porous host medium, recent studies take into consideration the detailed structure of the porous system and its impact on the fluid velocity. However, the impact of confinement condition, represented by the ratio of particles radius $a$ and pore throat size $\lambda$, has been overlooked. Here, we use numerical simulations of fluid particle dynamics in resolved porous media to demonstrate that particles confinement affects the fluid macroscopic velocity field u which in turn affects the particles transport itself. Our results show that even for small confinement conditions ($a/\lambda \sim 2$~\%), fluid and transported particles are dynamically re-routed towards more permeable paths. This leads to the emergence of ephemeral laminar vortexes at pore throat entrances and affects the variance and mean fluid velocity.
... The diffusional flux of nutrients to the surface of a phytoplankton cell is dependent on a variety of factors, including cell size and shape, movement (e.g., sinking, swimming) relative to the surrounding medium, and the efficiency with which transporter proteins translocate nutrients across the cell membrane relative to the diffusive rate at which they arrive at the membrane [this relative rate determines the concentration gradient between the cell surface (S 0 ) and S 1 ]. Here, we will forgo a detailed description of molecular diffusion and, instead, refer interested readers to the rich literature that already exists describing solute flux across cell boundary layers [e.g., [38][39][40][41][42]. For simplicity, we will assume that phytoplankton are spherical cells, such that the diffusional flux (F D ) to the cell surface in the absence of relative motion is described by: ...
... which predicts that, if growth rate is limited purely by diffusion, the size-distribution of division rates will not scale in proportion to the surface:volume ratio (i.e., 1/d; upper heavy black lines in Fig 3A, 3D) but rather with the inverse square of cell diameter (i.e., 1/d 2 ; lower heavy black lines in Fig 3A, 3D) [41]. To place this initial prediction in context, it implies that a nutrient-limited 1 μm cell will be dividing 10,000 times faster than a nutrient-limited 100 μm cell. ...
... One of our initial concerns with constraining phytoplankton growth strictly through diffusion limitation was that resultant division rates would unrealistically vary inversely with cell diameter squared [41]. It was therefore satisfying when size distributions in division rate emerged from our semi-empirical model that varied by even less than the surface:volume ratio for nutrient concentrations representative of nearly all natural waters (Fig 3). ...
Under most natural marine conditions, phytoplankton cells suspended in the water column are too distantly spaced for direct competition for resources (i.e., overlapping cell boundary layers) to be a routine occurrence. Accordingly, resource-based competitive exclusion should be rare. In contrast, contemporary ecosystem models typically predict an exclusion of larger phytoplankton size classes under low-nutrient conditions, an outcome interpreted as reflecting the competitive advantage of small cells having much higher nutrient ‘affinities’ than larger cells. Here, we develop mechanistically-focused expressions for steady-state, nutrient-limited phytoplankton growth that are consistent with the discrete, distantly-spaced cells of natural populations. These expressions, when encompassed in a phytoplankton-zooplankton model, yield sustained diversity across all size classes over the full range in nutrient concentrations observed in the ocean. In other words, our model does not exhibit resource-based competitive exclusion between size classes previously associated with size-dependent differences in nutrient ‘affinities’.
... The deterministic orientational dynamics are disturbed by two types of stochastic reorientations of the swimming direction, which we now address with the help of the Smoluchowski equation. First, a bacterium tumbles, which is triggered when the rotation of one of its flagella reverses so that it leaves the flagellar bundle [45][46][47] . For a wild-type E.coli, tumbling occurs roughly every 1s, where it attains a new random orientation. ...
... Thus, its magnitude compares the persistence length to the body length l. A wild-type E. coli typically has Pe a ≲ 5 45,53 . We numerically solve Eq. (2) for arbitrary Pe f by expanding ψ in spherical harmonics and taking into account the first 100 harmonics. ...
Microswimmer suspensions in Newtonian fluids exhibit unusual macroscale properties, such as a superfluidic behavior, which can be harnessed to perform work at microscopic scales. Since most biological fluids are non-Newtonian, here we study the rheology of a microswimmer suspension in a weakly viscoelastic shear flow. At the individual level, we find that the viscoelastic stresses generated by activity substantially modify the Jeffery orbits well-known from Newtonian fluids. The orientational dynamics depends on the swimmer type; especially pushers can resist flow-induced rotation and align at an angle with the flow. To analyze its impact on bulk rheology, we study a dilute microswimmer suspension in the presence of random tumbling and rotational diffusion. Strikingly, swimmer activity and its elastic response in polymeric fluids alter the orientational distribution and substantially amplify the swimmer-induced viscosity.
CC licence: http://creativecommons.org/ licenses/by/4.0/.
... The random walk (RW) technique represents a common method used for the investigation of mass transport dynamics, and also in biological systems [33][34][35]. The RW method describes the diffusion phenomenon in a simple manner, without the need for more complex operations [36,37], and reveals features that could be difficult to discern with other approaches. It represents, therefore, an appropriate method to investigate bone nanostructure, since experimental investigations at nanoscale are still challenging. ...
... It represents, therefore, an appropriate method to investigate bone nanostructure, since experimental investigations at nanoscale are still challenging. Trajectories developed in RW models are defined as unbiased, meaning that the particle is equally likely to move in each direction, and is uncorrelated in direction, i.e., the direction of motion at a given time is independent of the directions at all preceding times [36,38]. ...
Bone tissue is mainly composed at the nanoscale of apatite minerals, collagen molecules and water that form the mineralized collagen fibril (MCF). In this work, we developed a 3D random walk model to investigate the influence of bone nanostructure on water diffusion. We computed 1000 random walk trajectories of water molecules within the MCF geometric model. An important parameter to analyse transport behaviour in porous media is tortuosity, computed as the ratio between the effective path length and the straight-line distance between initial and final points. The diffusion coefficient is determined from the linear fit of the mean squared displacement of water molecules as a function of time. To achieve more insight into the diffusion phenomenon within MCF, we estimated the tortuosity and diffusivity at different quotes in the longitudinal direction of the model. Tortuosity is characterized by increasing values in the longitudinal direction. As expected, the diffusion coefficient decreases as tortuosity increases. Diffusivity outcomes confirm the findings achieved by experimental investigations. The computational model provides insights into the relation between the MCF structure and mass transport behaviour that may contribute to the improvement of bone-mimicking scaffolds.
... We reasoned that if the biological mechanisms at work in individual PFs that dictate the probabilities of arrest or growth over time can be clarified, we might be able to simulate PFGA over time in a way that recapitulates the natural pattern. Our ISR data and proposed model (Llerena Cari et al., 2021) suggested that individual PFs experiencing regionally fluctuating stress and damage (and thus ISR activity) over time might reflect a situation analogous to a random walk (RW; Berg, 1993;Billingsley, 1995;Codling, Plank & Benhamou, 2008) relative to a threshold of growth activation (Fig. 1B). If so, threshold crossing would occur randomly for individual PFs over (simulated) time. ...
... The lefthand side of Eq. (1) is the ISR activity after n + 1 time steps, which is given by the ISR activity after n time steps (i.e., X(nDt)) plus or minus the amount Dx. This type of model is called a random walk because the value of X "walks" by taking steps of size Dx, and the direction of each step (either up or down) is random (Berg, 1993). ...
Mechanism(s) that control whether individual human primordial ovarian follicles (PFs) remain dormant, or begin to grow, are all but unknown. One of our groups has recently shown that activation of the Integrated Stress Response (ISR) pathway can slow follicular granulosa cell proliferation by activating cell cycle checkpoints. Those data suggest that the ISR is active and fluctuates according to local conditions in dormant PFs. Because cell cycle entry of (pre)granulosa cells is required for PF growth activation (PFGA), we propose that rare ISR checkpoint resolution allows individual PFs to begin to grow. Fluctuating ISR activity within individual PFs can be described by a random process. In this article, we model ISR activity of individual PFs by one-dimensional random walks (RWs) and monitor the rate at which simulated checkpoint resolution and thus PFGA threshold crossing occurs. We show that the simultaneous recapitulation of (i) the loss of PFs over time within simulated subjects, and (ii) the timing of PF depletion in populations of simulated subjects equivalent to the distribution of the human age of natural menopause can be produced using this approach. In the RW model, the probability that individual PFs grow is influenced by regionally fluctuating conditions, that over time manifests in the known pattern of PFGA. Considered at the level of the ovary, randomness appears to be a key, purposeful feature of human ovarian aging.
... Для дифузiйного процесу, що описується параболiчним рiвнянням, вiдомо, що математичне сподiвання часу виходу як функцiї початкового положення задовольняє елiптичне рiвняння [6]. В [7] ця задача розглядається в багатовимiрному просторi з областю, у якої лише частина межi є поглинаючою (крiзь яку частинки можуть вийти). ...
... Для нормальної дифузiї в [6] виведено рiвняння для математичного сподiвання часу очiкування виходу частинки з областi. Проте для ВБНЧ з часом очiкування стрибка з товстим хвостом (1) кiлькiсть стрибкiв має степеневу асимптотику з показником α [10]. ...
In the work considered process of continuous-time random walk, that has fat-tailed jump waiting time, on an equispaced grid of one-dimensional domain with absorbing boundary. Deduced fractional equation w.r.t. cumulative distribution function of first passage time. Obtained asymptotic of density of this variable and shown that it has fat tail.
... In one dimension and in the presence of a drift velocity, v, along the x-direction, a diffusion is governed by Fick's second equation for the concentration, ( ) C x , see Equation (4.5) in [6], 2 2 , ...
... In 1D and in the presence of a drift velocity, v, along the radial direction the diffusion is governed by Fick's second equation, see Equation (4.5) in [6], ...
... Individual lipid molecules are still limited to the two-dimensional plane of the membrane, but they can move freely and quickly (millions of exchanges per second) within it. 97 As a result, the membrane becomes fully fluidized and permeable throughout. 97 Taking advantage of this liposome property, temperature-sensitive (thermo-sensitive) liposomes have recently emerged as an appealing option for treating cancer and infectious disease in a controlled and predictable manner using external energy sources. ...
... 97 As a result, the membrane becomes fully fluidized and permeable throughout. 97 Taking advantage of this liposome property, temperature-sensitive (thermo-sensitive) liposomes have recently emerged as an appealing option for treating cancer and infectious disease in a controlled and predictable manner using external energy sources. 98 When thermosensitive liposomes are exposed to heating, the lipid bilayer undergoes a melting phase transition from a gel to a liquid-crystalline phase, allowing a rapid increase in bilayer permeability and thus the rapid release of small molecules or drugs. ...
Nanomaterials-based hybrid nano therapy is gaining attraction as a promising way to treat intracellular bacterial infections. Gold-based nanomaterials have been widely used for biomedical applications such as photothermal therapy (PTT). This thesis discusses the development of a combination therapeutic approach that kills intracellular bacteria in conjunction with photothermal and antibiotic therapy using gold nanorod (GNR) based nano-assembly. This NIR laser-activated nano-assembly delivers antibiotics to the site of infection and offers PTT. The synergistic application of both therapies increases the efficacy of treatment. The protected delivery of antibiotics and their release in the proximity of the bacterial surface decreases off-target toxicity and drug dosage. The core of the nano-assembly is composed of GNRs coated with a mesoporous silica shell (MS). The MS shell serves as a carrier for the anti-tuberculosis drug bedaquiline. The core-shell nanoparticle is encapsulated within a thermo-sensitive liposome (TSL). The TSL layer is further conjugated to the mycobacteria-targeting peptide NZX. NZX mediates the adhesion of the final nano-assembly onto the mycobacterial surface. Upon NIR laser irradiation GNRs convert the photon energy of the laser to localized heat, which melts the TSL, triggering the release of bedaquiline. The antibacterial activity of the final nano-assembly against Mycobacterium smegmatis (Msmeg) was 20 folds more efficacious than the free drug equivalent. Mtb can alter immune defense mechanisms exerted by the host macrophage. Hence, host-targeted nano-assemblies (HTNs) were fabricated by conjugating host targeting ligands (β-Glucan) onto the nano-assembly. The binding of β-Glucan conjugated HTNs to the dectin-1 receptor present on macrophages increases the free radical production and cellular uptake of HTNs. An NIR laser triggers the photothermally induced structural disruption of the nano-assembly, releasing the drug at the targeted sites. The released bedaquiline within the macrophage promotes phagosome acidification and phagolysosome formation, effectively killing 99% of intracellular bacteria. Similar nano-assemblies were developed for dual-targeted drug delivery against lung carcinoma and proved to be 20 fold more effective than the anticancer drug alone. Finally, a simple and rapid diagnostic test was developed for detecting mycobacteria within a minute using lectin conjugated multi-core silica-coated magnetic nanoparticles.
... Pólya's walk on Z k . Random walks have received extensive attention in various disciplines: in mathematics, in biology and even in chemistry [11,26]. In number theory, Lifshits and Weber [28] and Srichan [40] considered the Lindelöf hypothesis in Cauchy random walk; Jouve [25] connected the large sieve method with random walks on cosets of arithmetic group; McNew [34] studied random walks on the residues modulo n. ...
In this paper, for any integer $k\geq 2$, we study the distribution of the visible lattice points in certain generalized P\'{o}lya's walk on $\mathbb{Z}^k$: perturbed P\'{o}lya's walk and twisted P\'{o}lya's walk. For the first case, we prove that the density of visible lattice points in a perturbed P\'{o}lya's walk is almost surely $1/\zeta(k)$, where $\zeta(s)$ denotes the Riemann zeta function. A trivial case of our result covers the standard P\'{o}lya's walk. Moreover, we do numerical experiments for the second case, we conjecture that the density is also almost surely $1/\zeta(k)$.
... Two commonly studied random walks are differentiated by the distribution of step lengths: in Brownian motion, this is a negative exponential, while in Lévy motion, this is a power-law function that is more heavy-tailed than the negative exponential. In both models, most steps are short, but long steps are more common in Lévy than in Brownian motion (Codling et al. 2008;Berg 2018). ...
Of widespread interest in animal behavior and ecology is how animals search their environment for resources, and whether these search strategies are optimal. However, movement also affects predation risk through effects on encounter rates, the conspicuousness of prey, and the success of attacks. Here, we use predatory fish attacking a simulation of virtual prey to test whether predation risk is associated with movement behavior. Despite often being demonstrated to be a more efficient strategy for finding resources such as food, we find that prey displaying Lévy motion are twice as likely to be targeted by predators than prey utilizing Brownian motion. This can be explained by the predators, at the moment of the attack, preferentially targeting prey that were moving with straighter trajectories rather than prey that were turning more. Our results emphasize that costs of predation risk need to be considered alongside the foraging benefits when comparing different movement strategies.
... This distance (r) was tracked as a function of time (t) after the cathodic pulse and used to estimate diffusion coefficients (D) by assuming an Einstein's random walk (r 2 = 2Dt). 59,60 This procedure was repeated for 10 different videos for each RTIL type, with at least 10 different locations analyzed in each video. Fluorescence images were not background-subtracted, and no attempts were made to improve contrast and sharpness. ...
The study of electrochemical reactivity requires analytical techniques capable of probing the diffusion of reactants and products to and from electrified interfaces. Information on diffusion coefficients is often obtained indirectly by modeling current transients and cyclic voltammetry data, but such measurements lack spatial resolution and are accurate only if mass transport by convection is negligible. Detecting and accounting for adventitious convection in viscous and wet solvents, such as ionic liquids, is technically challenging. We have developed a direct, spatiotemporally resolved optical tracking of diffusion fronts which can detect and resolve convective disturbances to linear diffusion. By tracking the movement of an electrode-generated fluorophore, we demonstrate that parasitic gas evolving reactions lead to 10-fold overestimates of macroscopic diffusion coefficients. A hypothesis is put forward linking large barriers to inner-sphere redox reactions, such as hydrogen gas evolution, to the formation of cation-rich overscreening and crowding double layer structures in imidazolium-based ionic liquids.
... The first reason is that movement of molecules that disperse by passive diffusion is fast and efficient over small distances in closed compartments (such as the early Drosophila syncytium) but is too slow to reach faraway targets. This is because the timescale of diffusion increases with the square of the distance (t = L 2 /D, where t is time, D is the diffusion coefficient and L is the distance covered [35][36][37]). The second reason, which is directly related to the first, is that patterning of folded epithelia like the wing or leg discs in Drosophila (that are open compartments because they border fluid-filled spaces) is impossible if the morphogen diffuses away from the plane of epithelial cell layers, as this would prevent most Hh to find its receptor Ptc at distant sites on the same epithelium [38]. ...
Patterns of gene expression, cell growth and cell-type specification during development are often regulated by morphogens. Morphogens are signalling molecules produced by groups of source cells located tens to hundreds of micrometers distant from the responding tissue and are thought to regulate the fate of receiving cells in a direct, concentration-dependent manner. The mechanisms that underlie scalable yet robust morphogen spread to form the activity gradient, however, are not well understood and are currently intensely debated. Here, based on two recent publications, we review two in vivo derived concepts of regulated gradient formation of the morphogen Hedgehog (Hh). In the first concept, Hh disperses on the apical side of developing epithelial surfaces using the same mechanistic adaptations of molecular transport that DNA-binding proteins in the nucleus use. In the second concept, Hh is actively conveyed to target cells via long filopodial extensions, called cytonemes. Both concepts require the expression of a family of sugar-modified proteins in the gradient field called heparan sulphate proteoglycans as a prerequisite for Hh dispersal, yet propose different - direct versus indirect - roles of these essential extracellular modulators.
... The discrete pattern generation approach known as diffusion-limited aggregation (DLA) is motivated by the successive aggregation of new particles that propagate in terms of respective random walks (e.g. [15,16,17]). ...
The diversity of patterns to be found in nature is virtually unending. After briefly introducing concepts about discrete spaces, connectedness, and shape, the present work describes two simple approaches for generating random discrete patterns, namely raindrops as well as the straight-line implementation of diffusion-limited aggregation (DLA). Respective codes (non-optimal) are suggested, and examples of generated patterns are also presented.
... This PDE is numerically calculated [82,83]. We also define λ as the effective interaction distance, where l ¼ ffi ffi ffi ffi ffi ffi ffi ffi b=a p . ...
The capacity of cells to process information is currently used to design cell-based tools for ecological, industrial, and biomedical applications such as detecting dangerous chemicals or for bioremediation. In most applications, individual cells are used as the information processing unit. However, single cell engineering is limited by the necessary molecular complexity and the accompanying metabolic burden of synthetic circuits. To overcome these limitations, synthetic biologists have begun engineering multicellular systems that combine cells with designed subfunctions. To further advance information processing in synthetic multicellular systems, we introduce the application of reservoir computing. Reservoir computers (RCs) approximate a temporal signal processing task via a fixed-rule dynamic network (the reservoir) with a regression-based readout. Importantly, RCs eliminate the need of network rewiring, as different tasks can be approximated with the same reservoir. Previous work has already demonstrated the capacity of single cells, as well as populations of neurons, to act as reservoirs. In this work, we extend reservoir computing in multicellular populations with the widespread mechanism of diffusion-based cell-to-cell signaling. As a proof-of-concept, we simulated a reservoir made of a 3D community of cells communicating via diffusible molecules and used it to approximate a range of binary signal processing tasks, focusing on two benchmark functions-computing median and parity functions from binary input signals. We demonstrate that a diffusion-based multicellular reservoir is a feasible synthetic framework for performing complex temporal computing tasks that provides a computational advantage over single cell reservoirs. We also identified a number of biological properties that can affect the computational performance of these processing systems.
... HMEs recruited at i, while unbinding and diffusing are more likely to rebind in the 3D vicinity, leading to a concentration gradient around i. To estimate P c (i, j) in the case where the effective spreading from position i to a distal nucleosome j occur by the unbinding and diffusing of the HME recruited in i, we follow a formalism consistent with Li et al. [143]. H. Berg [144] showed that the probability for a slowly-diffusing particle to hit an object of size a initially at a distance R from the particle is P d = a/R. Within our context, R is thus the typical distance between i and j. ...
A multitude of stable and heritable phenotypes arise from the same DNA sequence, owing to epigenetic regulatory mechanisms relying on the molecular cooperativity of ``reader-writer'' histone modifying enzymes. We introduce a unified modeling framework, the ''Painter model'', describing the mechanistic interplay between sequence-specific recruitment of chromatin regulators, chromatin-state-specific reader-writer processes and long-range spreading mechanisms. A systematic analysis of the model highlights the crucial impact of tridimensional chromatin organization and state-specific recruitment of enzymes on the stability of epigenomic domains and on gene expression. In particular, we show that enhanced 3D compaction of the genome and enzyme limitation facilitate the formation of ultra-stable, confined chromatin domains. To go beyond the effective 3D description, we study explicit 3D polymer dynamics. Since the physics of long, topologically-constrained polymers may significantly deviate from those of shorter chains, we theoretically investigate the extent of the minimal genomic region that one should consider around a given locus in order to effectively capture the correct dynamical and structural properties of the domain of interest. We show that this minimal size depends on the overall epigenomic context and on the entanglement properties of the long polymer. Finally, we introduce a theoretical framework coupling 3D polymer dynamics and epigeneome regulation by diffusing HMEs, the ``Living painter'' model, that exhibits intriguing properties on the coupling between 3D genome folding and epigenetic spreading, reflecting the scope and extension of the thesis.
... To investigate biased random walks, we measured the animal's probability of turning (pirouette) depending on its bearing with respect to the local airborne butanone gradient Figure 6e. We find that the animal is least likely to turn when it navigates up the local gradient and most likely to turn when it navigates down the gradient, a key signature of the biased random walk strategy (Berg, 2018;Mattingly et al., 2021). ...
Olfactory navigation is observed across species and plays a crucial role in locating resources for survival. In the laboratory, understanding the behavioral strategies and neural circuits underlying odor-taxis requires a detailed understanding of the animal's sensory environment. For small model organisms like C. elegans and larval D. melanogaster, controlling and measuring the odor environment experienced by the animal can be challenging, especially for airborne odors, which are subject to subtle effects from airflow, temperature variation, and from the odor's adhesion, adsorption or reemission. Here we present a method to flexibly control and precisely measure airborne odor concentration in an arena with agar while imaging animal behavior. Crucially and unlike previous methods, our method allows continuous monitoring of the odor profile during behavior. We construct stationary chemical landscapes in an odor flow chamber through spatially patterned odorized air. The odor concentration is measured with a spatially distributed array of digital gas sensors. Careful placement of the sensors allows the odor concentration across the arena to be accurately inferred and continuously monitored at all points in time. We use this approach to measure the precise odor concentration that each animal experiences as it undergoes chemotaxis behavior and report chemotaxis strategies for C. elegans and D. melanogaster larvae populations under different spatial odor landscapes.
... Eqs. (4) can be easily solved using the standard machinery of Brownian motion (see for instance [42,43]). Integrating the equation yields: ...
Sperm cooperation has evolved in a variety of taxa and is often considered a response to sperm competition, yet the benefit of this form of collective movement remains unclear. Here we use fine-scale imaging and a minimal mathematical model to study sperm aggregation in the rodent genus Peromyscus . We demonstrate that as the number of sperm cells in an aggregate increase, the group moves with more persistent linearity but without increasing speed; this benefit, however, is offset in larger aggregates as the geometry of the group forces sperm to swim against one another. The result is a non-monotonic relationship between aggregate size and average velocity with both a theoretically predicted and empirically observed optimum of 6-7 sperm/aggregate. To understand the role of sexual selection in driving these sperm group dynamics, we compared two sister-species with divergent mating systems and find that sperm of P. maniculatus (highly promiscuous), which have evolved under intense competition, form optimal-sized aggregates more often than sperm of P. polionotus (strictly monogamous), which lack competition. Our combined mathematical and experimental study of coordinated sperm movement reveals the importance of geometry, motion and group size on sperm velocity and suggests how these physical variables interact with evolutionary selective pressures to regulate cooperation in competitive environments.
... Animal movement is a complex behavioural trait that affects the survival of populations and species across taxa (Berg, 1983;Dingle, 2014). Long-and short-distance movements can follow predictable environmental constraints, allowing populations to take advantage of seasonal food resources (e.g. ...
Agent‐based modelling (ABM) shows promise for animal movement studies. However, a robust, open‐source and spatially explicit ABM coding platform is currently lacking.
We present abmR, an R package for conducting continental‐scale ABM simulations across animal taxa. The package features two movement functions, each of which relies on the Ornstein–Uhlenbeck (OU) process.
The theoretical background for abmR is discussed and the main functionalities are illustrated using example populations.
Potential future additions to this open‐source package may include the ability to specify multiple environmental variables or to model interactions between agents. Additionally, updates may offer opportunities for disease ecology and integration with other R movement modelling packages.
... Eventually, the flagellum rotation switches back to ACW as well as to a normal configuration, leading to the reorganization of the bundle and to a new run phase. The frequency of tumbles is controlled by a chemotaxis signalling network, enabling navigation towards or away from certain regions in the medium [11,12]. ...
In many situations, bacteria move in complex environments, as soils, oceans or the human gut-track, where carrier fluids show complex structures associated with non-Newtonian rheology. Many fundamental questions concerning the ability to navigate in such environments remain unsolved. Recently, it has been shown that the kinetics of bacterial motion in structured fluids as liquid crystals (LCs) is constrained by the orientational molecular order (or director field) and that novel spatio-temporal patterns arise. A question unaddressed so far is how bacteria change swimming direction in such an environment. In this work, we study the swimming mechanism of a single bacterium, Esherichia coli , constrained to move along the director field of a lyotropic chromonic liquid crystal confined to a planar cell. Here, the spontaneous ‘run and tumble’ motion of the bacterium gets frustrated: the elasticity of the LC prevents flagella from unbundling. Interestingly, to change direction, bacteria execute a reversal motion along the director field, driven by the relocation of a single flagellum, a ‘frustrated tumble’. We characterize this phenomenon in detail experimentally, exploiting exceptional spatial and temporal resolution of bacterial and flagellar dynamics, using a two colour Lagrangian tracking technique. We suggest a possible mechanism accounting for these observations.
... where ϕ is the porosity, S i is the i state phase saturation, Fick's rule [18] is used to represent diffusive mass fluxes JD β x in the medium, and each flux term can be expressed as Eqs. 2 and 3. ...
... Examples of related modeling approaches include but are not limited to [9,10,11,12,13,14,15,16]. The models developed in the present work are also directly related to the concept of flow and diffusion in complex networks, a subject that has been addressed in several works including but by no means limited to [17,18,19,20,21]. In particular, the developed models incorporate drains (or sinks) to the flow of resources, therefore being related to works involving directed networks as those described in [22,23,24], among other interesting approaches. ...
This work develops as a study of the global and individual dynamics of resources networks involving a single source. Finite resources are distributed in equal parcels at each discrete time step. Each node of the resources networks corresponds to an agent that processes the respectively received portion of resources, so that a fraction s is kept into the node, a fraction f is forwarded to connected nodes, a fraction w is transformed into work/results, and a fraction d is wasted (system inefficiency). All agents are assumed to have the same resources distribution scheme (fractions). The considered framework is potentially related to several types of real-world resources networks involving flow of energy, matter or even information, and can also be understood as a type of random walk with sources and sinks. Two reference configurations, called parallel and sequential, are identified, and it is shown that though the overall resources dynamics is completely determined in terms only of the dynamical parameters s and f, the individual signatures can vary markedly with these distinct configurations of these same parameters, as well as with the network topology. An analytical characterization of the overall resources dynamics is then presented. This is followed by additional studies of the effect of the parameters s and f , as well as the network properties, on the respectively obtained individual resource signatures. Uniformly random and a scale free types of networks are respectively considered. Several interesting results are obtained and discussed, including the observation of strong correlations between the resource values and the node degree when s+f is close to 1, while an opposite relationship has been found regarding correlations between the resources values and the distance to the source node. In addition, the considered scale free network tended to promote, at least for the considered structure and assumptions, noticeable correlation between the resource values and the node degree for a more extensive range of the parameters s and f. "... the unending intricacies of the physical world could be the result of continuous transformation of resources among interconnected components." Excerpt from the present work.
... This means we use Poissonian statistics to account for the effective retention of motile bacteria in the vicinity of grain surfaces. This picture is classically based on the idea that the run to tumble process promoting surface detachment is itself a memory-less Poisson process (Berg 2018). However, there has been recent evidence that the run-time distribution for bacterial motion in a free fluid is a long-tail non-Poissonian process (Figueroa- Morales et al. 2020b), which is also at the origin of long-tailed distributions of bacteria sojourn times on flat surfaces (Junot et al. 2022). ...
Understanding flow and transport of bacteria in porous media is crucial to technologies such as bioremediation, biomineralization and enhanced oil recovery. While physicochemical bacteria filtration is well documented, recent studies showed that bacterial motility plays a key role in the transport process. Flow and transport experiments performed in microfluidic chips containing randomly placed obstacles confirmed that the distributions of non-motile bacteria stays compact, whereas for the motile strains, the distributions are characterized by both significant retention as well as fast downstream motion. For motile bacteria, the detailed microscopic study of individual bacteria trajectories reveals two salient features: (i) the emergence of an active retention process triggered by motility, (ii) enhancement of dispersion due to the exchange between fast flow channels and low flow regions in the vicinity of the solid grains. We propose a physical model based on a continuous time random walk approach. This approach accounts for bacteria dispersion via variable pore-scale flow velocities through a Markov model for equidistant particle speeds. Motility of bacteria is modelled by a two-rate trapping process that accounts for the motion towards and active trapping at the obstacles. This approach captures the forward tails observed for the distribution of bacteria displacements, and quantifies an enhanced hydrodynamic dispersion effect that originates in the combined effect of pore-scale flow variability and bacterial motility. The model reproduces the experimental observations, and predicts bacteria dispersion and transport at the macroscale.
... At long time-and length-scales, run-and-tumble motion resembles Brownian motion [87], with a diffusion coefficient D�m −1 v 2 τ, where m is the dimension (we assume that d is close to the adapted level d 0 ). Brownian motion in the model is biased by longer runs when the agent is moving up the gradient. ...
Studying the brain circuits that control behavior is challenging, since in addition to their structural complexity there are continuous feedback interactions between actions and sensed inputs from the environment. It is therefore important to identify mathematical principles that can be used to develop testable hypotheses. In this study, we use ideas and concepts from systems biology to study the dopamine system, which controls learning, motivation, and movement. Using data from neuronal recordings in behavioral experiments, we developed a mathematical model for dopamine responses and the effect of dopamine on movement. We show that the dopamine system shares core functional analogies with bacterial chemotaxis. Just as chemotaxis robustly climbs chemical attractant gradients, the dopamine circuit performs ‘reward-taxis’ where the attractant is the expected value of reward. The reward-taxis mechanism provides a simple explanation for scale-invariant dopaminergic responses and for matching in free operant settings, and makes testable quantitative predictions. We propose that reward-taxis is a simple and robust navigation strategy that complements other, more goal-directed navigation mechanisms.
... In this article, the word refers either to directional displacement like e.g. water flow (Figure 2a) or non-directional migration whose examples include the random walk of particles [49] ( Figure 2b). Theoretically, ECM components that are carrying out different movements and/or those moving at different speeds can coexist in one place ( Figure 2c). ...
Extracellular matrices (ECMs) are essential for the architecture and function of animal tissues. ECMs have been thought to be highly stable structures; however, too much stability of ECMs would hamper tissue remodelling required for organ development and maintenance. Regarding this conundrum, this article reviews multiple lines of evidence that ECMs are in fact rapidly moving and replacing components in diverse organisms including hydra, worms, flies, and vertebrates. Also discussed are how cells behave on/in such dynamic ECMs, how ECM dynamics contributes to embryogenesis and adult tissue homoeostasis, and what molecular mechanisms exist behind the dynamics. In addition, it is highlighted how cutting-edge technologies such as genome engineering, live imaging, and mathematical modelling have contributed to reveal the previously invisible dynamics of ECMs. The idea that ECMs are unchanging is to be changed, and ECM dynamics is emerging as a hitherto unrecognized critical factor for tissue development and maintenance.
... We first consider nutrient limitation based on the diffusion models (Berg, 1993). Consider a cubic cell of unity dimensions with six equal-sized absorbing surfaces. ...
Some microalgal species can increase their collective size by forming colonies; notable examples are chained colonies in diatoms and Scenedesmus sp., and spherical colonies in Phaeocystis globosa. For a given cell-specific growth rate, chain formation increases collective length quickly to fend off ciliates, but not against tube- and pallium-feeding heterotrophic dinoflagellates or metazoan grazers with ability to manipulate chains to aid ingestion. Sphere increases in volume relatively slowly but would be difficult to manipulate even for metazoan grazers. Diffusive nutrient supply to a chained colony would be a fixed proportion of that to solitary cells, regardless of chain length, whereas cells within a spherical colony would experience increasing nutrient limitation with increasing colony size. One hemisphere of a spherical colony would inevitably receive less irradiance, creating an auto-light limitation. Experimental data showed that light decreased substantially as it passed through a P. globosa colony, and the optical density of the colony increased linearly with colony diameter. However, neither in situ nutrient nor light limitation alone can explain an order-of-magnitude difference in colony size between the European and the Asian P. globosa populations. Instead, some evidence of different expression of gene(s) involved in colony formation and enlargement suggests genomic variations among the different populations.
... This procedure is expected to modify only part of the pore walls since we created two boundary conditions with one pore entrance in contact with the bulk APTMS concentration and the other with zero APTMS concentration ( Figure S1a). Assuming a cylindrical shape of the pore, the profile of the silane concentration in the pore is linear, 27 suggesting that there might be a density gradient of the attached amines along the pore length. Limiting the amination to only a fraction of the walls was, however, assured by the choice of incubation time and APTMS concentration. ...
Nanopores lined with hydrophobic groups function as switches for water and all dissolved species, such that transport is allowed only when applying a sufficiently high transmembrane pressure difference or voltage. Here we show a hydrophobic nanopore system whose wetting and ability to transport water and ions is rectified and can be controlled with salt concentration. The nanopore we study contains a junction between a hydrophobic zone and a positively charged hydrophilic zone. The nanopore is closed for transport at low salt concentrations and exhibits finite current only when the concentration reaches a threshold value that is dependent on the pore opening diameter, voltage polarity and magnitude, and type of electrolyte. The smallest nanopore studied here had a 4 nm diameter and did not open for transport in any concentration of KCl or KI examined. A 12 nm nanopore was closed for all KCl solutions but conducted current in KI at concentrations above 100 mM for negative voltages and opened for both voltage polarities at 500 mM KI. Nanopores with a hydrophobic/hydrophilic junction can thus function as diodes, such that one can identify a range of salt concentrations where the pores transport water and ions for only one voltage polarity. Molecular dynamics simulations together with continuum models provided a multiscale explanation of the observed phenomena and linked the salt concentration dependence of wetting with an electrowetting model. Results presented are crucial for designing next-generation chemical and ionic separation devices as well as understanding fundamental properties of hydrophobic interfaces under nanoconfinement.
... The mass is 8 × 10 −20 . The Stokes drag formula for a radius of 3.5 nm (to a physicist a kinesin head is approximately a sphere [9]) is = 7 × 10 −8 . These values imply a diffusion constant of = = 4 7 × 10 −6 2 . ...
Almost 25 years ago, Jarzynski published a paper in which it was asserted: the work done, W, in driving a system from state A to state B, characterized by the Helmholtz free energies FA and FB, satisfies an equality in which an average over an ensemble of measurements for W determines the difference in Free energy. Several features of this result require more detailed description, to be given in the text. The equality is significant and unexpected. So is the statement that the equality is independent of the rate of change from state A to state B. A few years ago, I had presented three papers in which the contraction of the description from full phase space to coordinate space only was made. This was motivated by the large difference in time scales for momenta relaxation and coordinate relaxation. The Jarzynski equality (JE) will be shown here to be correct only in the limit of slow processes. The proposed example is for a macromolecular harmonic oscillator with a Hooke's spring constant, k, that during the time interval linearly changes from k1 to k2. When performed slowly, we obtain JE in a form in which the free energy is related to the ratio of the k's. However, when the transition is performed more rapidly the equality is lost. Jarzynski has suggested to me that Hummer and Szabo have shown that JE follows directly from the Feynman-Kac formula. We show here that F-K does not reproduce the direct calculation executed in this paper and that it has been misapplied in earlier papers.
The cell surface proteome, or surfaceome, is encoded by more than 4000 genes, but we are only beginning to understand the complexes they form. Rapid proximity labeling around specific membrane targets allows for capturing weak and transient interactions expected in the crowded and dynamic environment of the surfaceome. Recently, a high-resolution approach called μMap has been described (Geri, J. B., Oakley, J. V., Reyes-Robles, T., Wang, T., McCarver, S. J., White, C. H., Rodriguez-Rivera, F. P., Parker, D. L., Hett, E. C., Fadeyi, O. O., Oslund, R. C., and MacMillan, D. W. C. (2020) Science 367 , 1091–1097) in which an iridium (Ir)-based photocatalyst is attached to a specific antibody to target labeling of neighbors utilizing light-activated generation of carbenes from diazirine compounds via Dexter Energy Transfer (DET). Here we studied and optimized the spatial resolution for the method using an oncoprotein complex between the antibody drug, trastuzumab (Traz), and its target HER2. A set of eight single site-specific Ir-catalytic centers were engineered into Traz to study intra- and inter-molecular labeling in vitro and on cells by mass spectrometry. From this structurally well-characterized complex we observed a maximum distance of ∼110 Å for labeling. Labeling occurred almost uniformly over the full range of amino acids, unlike the residue specific labeling of other techniques. To examine on cell labeling that is specific to HER2 as opposed to simply being on the membrane, we compared the labeling patterns for the eight Traz-catalyst species to random labeling of membrane proteins using a metabolically integrated fatty acid catalyst. Our results identified 20 high confidence HER2 neighbors, many novel, that were more than 6-fold enriched compared to the non-specific membrane tethered catalyst. These studies define distance labeling parameters from single-site catalysts placed directly on the membrane target of interest, and more accurately compare to non-specific labeling to identify membrane complexes with higher confidence.
The error function solution of the diffusion equation with the constant surface concentration was derived by the heat kernel to determine the constant diffusion coefficient for diffusion satisfying the infinite dye-bath condition. For the sublimation diffusion of disperse dye in paste into PET film using the film-roll method, the constant surface concentration was determined from the concentration distribution, and the diffusion coefficients of each layer were obtained by the constant surface concentration from the error function solution. When comparing the diffusion coefficients between the layers and comparing the mean diffusion coefficients for different times at a specific temperature, the constant surface concentrations determined from the quadratic regression curves for concentration–distance plots were more appropriate than those determined from the steady-state concentration distributions, which was also confirmed by the plots of concentrations obtained from the error function solution. At a specific temperature, the average of the mean diffusion coefficients obtained by the constant surface concentration of the quadratic regression curve at three specific times matched well with the constant total-amount diffusion coefficient obtained by the slope of the linear regression line for the plot of total amount against square root of time, which was confirmed by their Arrhenius plots.
Physical forces that arise due to bacterial motility and growth play a significant role in shaping the biogeography of the human oral microbiota. Bacteria of the genus Capnocytophaga are abundant in the human oral microbiota and yet very little is known about their physiology. The human oral isolate Capnocytophaga gingivalis exhibits robust gilding motility that is driven by the rotary type 9 secretion system (T9SS), and cells of C. gingivalis transport nonmotile oral microbes as cargo. Phages, i.e., viruses that infect bacteria, are found in abundance within the microbiota. By tracking fluorescently labeled lambda phages that do not infect C. gingivalis, we report active phage transportation by C. gingivalis swarms. Lambda phage-carrying C. gingivalis swarms were propagated near an Escherichia coli colony. The rate of disruption of the E. coli colony increased 10 times compared with a control where phages simply diffused to the E. coli colony. This finding suggests a mechanism where fluid flows produced by motile bacteria increase the rate of transport of phages to their host bacterium. Additionally, C. gingivalis swarms formed tunnel-like structures within a curli fiber-containing E. coli biofilm that increased the efficiency of phage penetration. Our data suggest that invasion by a C. gingivalis swarm changes the spatial structure of the prey biofilm and further increases the penetration of phages. IMPORTANCE Dysbiosis of the human oral microbiota is associated with several diseases, but the factors that shape the biogeography of the oral microbiota are mostly opaque. Biofilms that form in the human supragingival and subgingival regions have a diverse microbial community where some microbes form well-defined polymicrobial structures. C. gingivalis, a bacterium abundant in human gingival regions, has robust gliding motility that is powered by the type 9 secretion system. We demonstrate that swarms of C. gingivalis can transport phages through a complex biofilm which increases the death rate of the prey biofilm. These findings suggest that C. gingivalis could be used as a vehicle for the transportation of antimicrobials and that active phage transportation could shape the spatial structure of a microbial community.
When motile algal cells are exposed to gyrotactic torques, their swimming directions are guided to form radial accumulation, well known as hydrodynamic focusing. The origin of hydrodynamic focusing from the effects of active swimming, ambient flow and particle anisotropy is elucidated in the present study on the pre-asymptotic dispersion of active particles through a vertical pipe. With an extension of the Galerkin method to pipe flows, time-dependent solutions directly from the Smoluchowski equation in the position and orientation space are derived by series expansions of spherical harmonics and Bessel functions. Ballistic and diffusive scaling laws are examined with the predominance of self-propelled swimming, and computation is validated against an explicit benchmark solution and Lagrangian particle simulation. In the limit of extreme shear, the competitive roles of shear dispersion and Brownian rotation are reflected concretely in the pre-asymptotic phase of hydrodynamic focusing. For flows with various shear strengths, a concentration peak in near-wall regions with a smooth transition to hydrodynamic focusing is illustrated with richer phenomena in upwelling and downwelling flows. A newly observed regime through a vertical pipe, named transient effective trapping, is revealed as a transitional mode towards hydrodynamic focusing. The pre-asymptotic approach to hydrodynamic focusing is elaborated intensively through extensive solutions of concentration moments and macroscopic transport coefficients characterised by swimming and flow Péclet numbers. The unique findings for the origin of hydrodynamic focusing could provide insight into related micro-algae reactor technology and contribute to flow control and biomass transfer in confined environments.
Communication between cells enables the coordination that drives structural and functional complexity in biological systems. Both single and multicellular organisms have evolved diverse communication systems for a range of purposes, including synchronization of behavior, division of labor, and spatial organization. Synthetic systems are also increasingly being engineered to utilize cell–cell communication. While research has elucidated the form and function of cell–cell communication in many biological systems, our knowledge is still limited by the confounding effects of other biological phenomena at play and the bias of the evolutionary background. In this work, our goal is to push forward the context-free understanding of what impact cell–cell communication can have on cellular and population behavior to more fully understand the extent to which cell–cell communication systems can be utilized, modified, and engineered. We use an in silico model of 3D multiscale cellular populations, with dynamic intracellular networks interacting via diffusible signals. We focus on two key communication parameters: the effective interaction distance at which cells are able to interact and the receptor activation threshold. We found that cell–cell communication can be divided into six different forms along the parameter axes, three asocial and three social. We also show that cellular behavior, tissue composition, and tissue diversity are all highly sensitive to both the general form and specific parameters of communication even when the cellular network has not been biased towards that behavior.
Sinking or sedimentation of biological aggregates plays a critical role in carbon sequestration in the ocean and in vertical material fluxes in wastewater treatment plants. In both these contexts, the sinking aggregates are 'active', since they are biological hot-spots and are densely colonized by microorganisms including bacteria and sessile protists, some of which generate feeding currents. However, the effect of these feeding currents on the sinking rates, trajectories and mass transfer to these 'active sinking particles' has not previously been studied. Here, we use a novel scale-free vertical tracking microscope (a.k.a. gravity machine; Krishnamurthy et al. 2020 Nat. Methods 17, 1040-1051 (doi:10.1038/s41592-020-0924-7)) to follow model sinking aggregates (agar spheres) with attached protists (Vorticella convallaria), sinking over long distances while simultaneously measuring local flows. We find that activity due to attached V. convallaria causes significant changes to the flow around aggregates in a dynamic manner and reshapes mass transport boundary layers. Further, we find that activity-mediated local flows along with sinking modify the encounter and plume cross-sections of the aggregate and induce sustained aggregate rotations. Overall, our work shows the important role of biological activity in shaping the near-field flows around aggregates with potentially important effects on aggregate fate and material fluxes.
Understanding the mechanism by which cells coordinate their differentiation and migration is critical to our understanding of many fundamental processes such as wound healing, disease progression, and developmental biology. Mathematical models have been an essential tool for testing and developing our understanding, such as models of cells as soft spherical particles, reaction-diffusion systems that couple cell movement to environmental factors, and multi-scale multi-physics simulations that combine bottom-up rule-based models with continuum laws. However, mathematical models can often be loosely related to data or have so many parameters that model behaviour is weakly constrained. Recent methods in machine learning introduce new means by which models can be derived and deployed. In this review, we discuss examples of mathematical models of aspects of developmental biology, such as cell migration, and how these models can be combined with these recent machine learning methods.
Sonosensitive perfluorocarbon F8TAC18-PFOB emulsion is under development to enhance heating, increase thermal contrast, and reduce treatment times during focused ultrasound tumor ablation of highly perfused tissue. The emulsion previously showed enhanced heating during ex vivo and in vitro studies. Experiments were designed to observe the response in additional scenarios by varying focused ultrasound conditions, emulsion concentrations, and surfactants. Most notably, changes in acoustic absorption were assessed with MR-ARFI. Phantoms were developed to have thermal, elastic, and relaxometry properties similar to those of ex vivo pig tissue. The phantoms were embedded with varying amounts of F8TAC18-PFOB emulsion or lecithin-PFOB emulsion, between about 0.0-0.3% v:w, in 0.05% v:w increments. MR-ARFI measurements were performed using a FLASH-ARFI-MRT sequence to obtain simultaneous displacement and temperature measurements. A Fabry-Perot hydrophone was utilized to observe the acoustic emissions. Susceptibility-weighted imaging and relaxometry mapping were performed to observe concentration-dependent effects. ¹⁹F diffusion-ordered spectroscopy NMR was used to measure the diffusion coefficient of perfluorocarbon droplets in a water emulsion. Increased displacement and temperature were observed with higher emulsion concentration. In semi-rigid MR-ARFI phantoms, a linear response was observed with low-duty cycle MR-ARFI sonications and a mono-exponential saturating response was observed with sustained sonications. The emulsifiers did not have a significant effect on acoustic absorption in semi-rigid gels. Stable cavitation might also contribute to enhanced heating.
This paper investigates the channel impulse response (CIR), i.e., the molecule hitting rate, of a molecular communication (MC) system employing an absorbing receiver (RX) covered by multiple non-overlapping receptors. In this system, receptors are heterogeneous, i.e., they may have different sizes and arbitrary locations. Furthermore, we consider two types of transmitter (TX), namely a point TX and a membrane fusion (MF)-based spherical TX. We assume the point TX or the center of the MF-based TX has a fixed distance to the center of the RX. Given this fixed distance, the TX can be at different locations and the CIR of the RX depends on the exact location of the TX. By averaging over all possible TX locations, we analyze the expected molecule hitting rate at the RX as a function of the sizes and locations of the receptors, where we assume molecule degradation may occur during the propagation of the signaling molecules. Notably, our analysis is valid for different numbers, a wide range of sizes, and arbitrary locations of the receptors, and its accuracy is confirmed via particle-based simulations. Exploiting our numerical results, we show that the expected number of absorbed molecules at the RX increases with the number of receptors, when the total area on the RX surface covered by receptors is fixed. Based on the derived analytical expressions, we compare different geometric receptor distributions by examining the expected number of absorbed molecules at the RX. We show that evenly distributed receptors result in a larger number of absorbed molecules than other distributions. We further compare three models that combine different types of TXs and RXs. Compared to the ideal model with a point TX and a fully absorbing RX, the practical model with an MF-based TX and an RX with heterogeneous receptors yields a lower peak CIR, suffers from more severe inter-symbol interference, and gives rise to a higher average bit error rate (BER). This underlines the importance of our analysis of practical TX-RX models since the existing CIR and BER analyses based on the ideal model do not reflect the performance achievable in practice. Numerical results show that different vesicle generation rate results in the same number of molecules harvested by the TX, but a different peak received signal at the RX.
Each government is looking for to provide the best services to establish efficiency and quality of performance. This goal could be accomplished by improving the service performance of entire sectors in society. The government of Syria has realized the importance of moving in the direction of information technology. Therefore, E-governance initiatives were launched in Syria as a part of overall country information technology in 20 s century. Each government sector has since upgraded the performance by having its websites and e-services application. However, there are gaps and loose connections exist among the sectors, which has accordingly tarnished the image of Syrian E-governance. This has led to significant questions about the requirement of modification and enhancement of such service. Hence, the purpose of this research is to investigate and explore the factors that drive the E-governance implementation and affect government performance as well as the government-citizen relationship in Syria.KeywordsE-governanceGovernment of SyriaGovernment-Citizen
Atherosclerosis is one of the major cardiovascular disorder which causes severe health issues in human body. It also ends with patient death, when improper therapy takes place. Conventional therapy measures includes oral statin therapy, skin mode application, Inhalation mode of therapy etc., has their own advantages. But they cannot fully exploit the inflammation because of lower systemic bioavailability. Nowadays, Nano molecular communication provides numerous solutions in the field of targeted drug delivery system. The aim of this article is to propose a new analytical model for the propagation process of molecules based on Brownian motion mechanism by formulating the probability density of the Latency in blood medium. This model is analyzed based on crucial parameters such as radius of the propagating molecules, blood viscosity, drift velocity, distance between Nano-Tx and Nano-Rx, temperature of the fluid medium with respect to various blood shear rates. Based on simulation results, the latency is highly affected with molecular radius, distance temperature, shear rate and drift velocity. Our future work is to apply this model for various drug carrying molecules used in the treatment of the cardiovascular diseases and to assess its propagation capacity under various conditions of blood medium.KeywordsAtherosclerosisMolecular communicationDrug deliveryNano-TxNano-Rx
Random motion in disordered media is sensitive to the presence of obstacles which prevent atoms, molecules, and other particles from moving freely in space. When obstacles are static, a sharp transition between confined motion and free diffusion occurs at a critical obstacle density: the percolation threshold. Surprisingly, this conventional wisdom breaks in the presence of simple interactions. To show this, we introduce the Sokoban random walk which -- akin to the protagonist of an eponymous video game -- has some limited ability to push away obstacles that block its path. While one expects that this added capacity would allow the walk to venture further away, we find that this is only true above the percolation threshold. Indeed, we show that the Sokoban always confines itself to a finite region whose mean size is uniquely determined by the initial obstacle density. The observed relation obeys an equation that we derive based on a conservative rule for the onset of confinement and by accounting for the emergent fractal nature of Sokoban trajectories. Our findings depart markedly from the ruling "ant in a labyrinth" paradigm, and vividly illustrate that even weak and localized particle-media interactions cannot be neglected when coming to understand transport phenomena.
Hollow Fiber Membrane Contactor Modules comprise a technology that is considered promising for mobile carbon capture due to its high surface area per unit volume and low pressure drop. Although experimental, theoretical, and numerical studies have been devoted to understanding and improving performance, no study has so far used numerical simulations to show how the system scales with flow rate, reactivity, solubility, etc. in full generality. The present study addresses this scaling by solving the so called reactive Graetz problem: a canonical partial differential equation system coupling gas and liquid flow domains, including solubility and reactivity effects unlike the original Graetz problem. It is found that the Peclet number of the liquid, the aspect ratio of the fiber, and the Damkohler number of the liquid solvent, all play decisive roles in the mass transfer of CO2 and the work exerted per molecule captured.
This paper proposes a novel imperfect transmitter (TX) model, namely the membrane fusion (MF)-based TX, that adopts MF between a vesicle and the TX membrane to release molecules encapsulated within the vesicle. For the MF-based TX, the molecule release probability and the fraction of molecules released from the TX membrane are derived. Incorporating molecular degradation and a fully-absorbing receiver (RX), the channel impulse response (CIR) is derived for two scenarios: 1) Both TX and RX are static, and 2) both TX and RX are diffusion-based mobile. Moreover, a sequence of bits transmitted from the TX to the RX is considered. The average bit error rate (BER) is obtained for both scenarios, wherein the probability mass function (PMF) of the number of molecules absorbed in the mobile scenario is derived. Furthermore, a simulation framework is proposed for the MF-based TX, based on which the derived analytical expressions are validated. Simulation results show that a low MF probability or low vesicle mobility slows the release of molecules and reduces the molecule hitting probability at the RX. Simulation results also indicate the difference between the MF-based TX and an ideal point TX in terms of the inter-symbol interference (ISI).
In recent years, there have been more and more research on molecular communication (MC). Because the deployment of mobile nanomachines may be required in some applications of MC, research on mobile MC has become a trend. The signal detection schemes for static MC are no longer applicable due to the time varying channel impulse response (IR), which is caused by the mobile characteristics of nanomachines. In this paper, a low complexity and non-coherent detection scheme is proposed for mobile scenario, which is based on the energy difference between two adjacent symbols. Most of the existing signal detection methods do not consider inter-symbol interference (ISI). Compared with those methods, the proposed scheme can achieve signal detection utilizing ISI without knowing channel state information (CSI). The bit error rate (BER) performance of the proposed method is investigated under different conditions through simulations. Besides, the influence of mobility features of nanomachines on the signal detection accuracy is also investigated in detail. The simulation results demonstrate that the BER performance of the proposed scheme outperforms the latest signal detection scheme for short-distance mobile MC system with high velocity. Consequently, the detection scheme proposed in this paper can reduce the influence of nanomachines' mobility and has the potential to be used in mobile MC systems.
In this paper, we propose a bio-inspired receiver, which detects the electrons transmitted through a nanowire, then, it converts the detected information to blue light using bioluminescence. We simulate the construction of the nanowire, present its electrical characteristics and calculate its maximum capacity for a better design of the receiver. The designed receiver contains two parts; a part that detects the transmitted electrons, which we model by using an equivalent circuit, and a part that converts the detected electrons to blue light. We derive the analytical expressions of the components of the equivalent circuit and give an approximation of their values. We calculate the probability of photons emission for each electrical pulse detected. We also determine the optimal threshold for Integrate Sample and Dump (ISD) receiver. We calculate the error probability of bits detection and present analytical and simulation results to evaluate the performance of the designed receiver. The results of this study show that the designed receiver can accurately detect the electrons sent through a conductive nanowire. Thus providing, to the best of our knowledge, the first technical solution that leads towards integrated wired electrical and optical nanonetworks.
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