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1.
Bacterial chemotaxis may have a significant impact on the structure and function of bacterial communities. Quantification of chemotactic motion is necessary to identify chemoeffectors and to determine the bacterial transport parameters used in predictive models of chemotaxis. When the chemotactic bacteria consume the chemoeffector, the chemoeffector gradient to which the bacteria respond may be significantly perturbed by the consumption. Therefore, consumption of the chemoeffector can confound chemotaxis measurements if it is not accounted for. Current methods of quantifying chemotaxis use bacterial concentrations that are too high to preclude chemoeffector consumption or involve ill-defined conditions that make quantifying chemotaxis difficult. We developed a method of quantifying bacterial chemotaxis at low cell concentrations (~105 CFU/ml), so metabolism of the chemoeffector is minimized. The method facilitates quantification of bacterial-transport parameters by providing well-defined boundary conditions and can be used with volatile and semivolatile chemoeffectors.  相似文献   

2.
A rapid method for bacterial chemotaxis in a spatial gradient of chemoeffectors has been developed. The method is based on turbidimetric measurement of bacteria movement in a chemoeffector gradient created in a spectrophotometer cuvette. The method was verified onEscherichia coli mutants with known chemotactic properties.  相似文献   

3.
Chemotaxis is the migration of cells in gradients of chemoeffector molecules. Although multiple, competing gradients must often coexist in nature, conventional approaches for investigating bacterial chemotaxis are suboptimal for quantifying migration in response to gradients of multiple signals. In this work, we developed a microfluidic device for generating precise and stable gradients of signaling molecules. We used the device to investigate the effects of individual and combined chemoeffector gradients on Escherichia coli chemotaxis. Laminar flow-based diffusive mixing was used to generate gradients, and the chemotactic responses of cells expressing green fluorescent protein were determined using fluorescence microscopy. Quantification of the migration profiles indicated that E. coli was attracted to the quorum-sensing molecule autoinducer-2 (AI-2) but was repelled from the stationary-phase signal indole. Cells also migrated toward higher concentrations of isatin (indole-2,3-dione), an oxidized derivative of indole. Attraction to AI-2 overcame repulsion by indole in equal, competing gradients. Our data suggest that concentration-dependent interactions between attractant and repellent signals may be important determinants of bacterial colonization of the gut.Bacteria sense chemoeffectors using cell surface receptors (13, 29). Cells constantly monitor the concentration of specific molecules, comparing the current concentration to the concentration detected a few seconds earlier. This comparison determines the net direction of movement (6, 22). Chemotaxis allows bacteria to approach sources of attractant chemicals or to avoid sources of repellent chemicals. Natural habitats for Escherichia coli, such as the gastrointestinal (GI) tract, are typically heterogeneous and contain multiple chemoeffectors with potentially opposing effects. The integrated chemotactic response in such environments is thus likely to be an important factor in bacterial colonization.Conventional approaches for investigating bacterial chemotaxis, such as the swim plate and capillary (1) assays, are not ideal for quantifying bacterial migration. Chemotactic-ring formation in semisolid agar requires metabolizable attractants and is subject to multiple factors, and both it and the traditional capillary assay are poorly designed to investigate repellent taxis. Mao et al. (23) were the first to investigate bacterial taxis in a microfluidic flow cell. In their device, a concentration gradient is formed by the diffusive mixing of two inlet streams. However, the exposure to a fully developed gradient in this device is limited because it takes time for the gradient to develop.Variations of this technique, such as three-channel microfluidic devices (7, 8) in which a linear gradient is generated in the absence of flow or a T-channel device that monitors chemotaxis perpendicular to the direction of fluid flow (18), were developed subsequently. The T-channel system has many of the limitations of the device developed by Mao et al. (23), and nonflow systems, like the capillary assay (1), suffer from a lack of temporal stability of the gradients.Here, we report a flow-based microfluidic chemotaxis device that is coupled to a gradient generator. Bacteria are exposed to precise and temporally stable concentration gradients of chemoeffectors over the length of the microfluidic channel. This device was used to quantify E. coli chemotaxis in response to the canonical chemoeffectors l-aspartate and Ni2+. The device was also used to investigate chemotaxis toward cell-cell communication signals such as autoinducer-2 (AI-2), indole, and isatin that are likely to be present in the in vivo microenvironment in which E. coli is present (e.g., the human GI tract). The data obtained reinforce the idea that concentration-dependent interactions between different chemical signals could be important determinants of bacterial colonization in natural environments.  相似文献   

4.
Involvement of transport in Rhodobacter sphaeroides chemotaxis.   总被引:11,自引:9,他引:2       下载免费PDF全文
The chemotactic response to a range of chemicals was investigated in the photosynthetic bacterium Rhodobacter sphaeroides, an organism known to lack conventional methyl-accepting sensory transduction proteins. Strong attractants included monocarboxylic acids and monovalent cations. Results suggest that the chemotactic response required the uptake of the chemoeffector, but not its metabolism. If a chemoeffector could block the uptake of another attractant, it also inhibited chemotaxis to that attractant. Sodium benzoate was not an attractant but was a competitive inhibitor of the propionate uptake system. Binding in an active uptake system was therefore insufficient to cause a chemotactic response. At different concentrations, benzoate either blocked propionate chemotaxis or reduced the sensitivity of propionate chemotaxis, an effect consistent with its role as a competitive inhibitor of uptake. Bacteria only showed chemotaxis to ammonium when grown under ammonia-limited conditions, which derepressed the ammonium transport system. Both chemotaxis and uptake were sensitive to the proton ionophore carbonyl cyanide m-chlorophenylhydrazone, suggesting an involvement of the proton motive force in chemotaxis, at least at the level of transport. There was no evidence for internal pH as a sensory signal. These results suggest a requirement for the uptake of attractants in chemotactic sensing in R. sphaeroides.  相似文献   

5.
Adaptability is an essential property of many sensory systems, enabling maintenance of a sensitive response over a range of background stimulus levels. In bacterial chemotaxis, adaptation to the preset level of pathway activity is achieved through an integral feedback mechanism based on activity-dependent methylation of chemoreceptors. It has been argued that this architecture ensures precise and robust adaptation regardless of the ambient ligand concentration, making perfect adaptation a celebrated property of the chemotaxis system. However, possible deviations from such ideal adaptive behavior and its consequences for chemotaxis have not been explored in detail. Here we show that the chemotaxis pathway in Escherichia coli shows increasingly imprecise adaptation to higher concentrations of attractants, with a clear correlation between the time of adaptation to a step-like stimulus and the extent of imprecision. Our analysis suggests that this imprecision results from a gradual saturation of receptor methylation sites at high levels of stimulation, which prevents full recovery of the pathway activity by violating the conditions required for precise adaptation. We further use computer simulations to show that limited imprecision of adaptation has little effect on the rate of chemotactic drift of a bacterial population in gradients, but hinders precise accumulation at the peak of the gradient. Finally, we show that for two major chemoeffectors, serine and cysteine, failure of adaptation at concentrations above 1 mM might prevent bacteria from accumulating at toxic concentrations of these amino acids.  相似文献   

6.
Chemotactic movement of Escherichia coli is one of the most thoroughly studied paradigms of simple behavior. Due to significant competitive advantage conferred by chemotaxis and to high evolution rates in bacteria, the chemotaxis system is expected to be strongly optimized. Bacteria follow gradients by performing temporal comparisons of chemoeffector concentrations along their runs, a strategy which is most efficient given their size and swimming speed. Concentration differences are detected by a sensory system and transmitted to modulate rotation of flagellar motors, decreasing the probability of a tumble and reorientation if the perceived concentration change during a run is positive. Such regulation of tumble probability is of itself sufficient to explain chemotactic drift of a population up the gradient, and is commonly assumed to be the only navigation mechanism of chemotactic E. coli. Here we use computer simulations to predict existence of an additional mechanism of gradient navigation in E. coli. Based on the experimentally observed dependence of cell tumbling angle on the number of switching motors, we suggest that not only the tumbling probability but also the degree of reorientation during a tumble depend on the swimming direction along the gradient. Although the difference in mean tumbling angles up and down the gradient predicted by our model is small, it results in a dramatic enhancement of the cellular drift velocity along the gradient. We thus demonstrate a new level of optimization in E. coli chemotaxis, which arises from the switching of several flagellar motors and a resulting fine tuning of tumbling angle. Similar strategy is likely to be used by other peritrichously flagellated bacteria, and indicates yet another level of evolutionary development of bacterial chemotaxis.  相似文献   

7.
Local chemical gradients can have a significant impact on bacterial population distributions within subsurface environments by evoking chemotactic responses. These local gradients may be created by consumption of a slowly diffusing nutrient, generation of a local food source from cell lysis, or dissolution of nonaqueous phase liquids trapped within the interstices of a soil matrix. We used a random walk simulation algorithm to study the effect of a local microscopic gradient on the swimming behavior of bacteria in a porous medium. The model porous medium was constructed using molecular dynamics simulations applied to a fluid of equal-sized spheres. The chemoattractant gradient was approximated with spherical symmetry, and the parameters for the swimming behavior of soil bacterium Pseudomonas putida were based on literature values. Two different mechanisms for bacterial chemotaxis, one in which the bacteria responded to both positive and negative gradients, and the other in which they responded only to positive gradients, were compared. The results of the computer simulations showed that chemotaxis can increase migration through a porous medium in response to microscopic-scale gradients. The simulation results also suggested that a more significant role of chemotaxis may be to increase the residence time of the bacteria in the vicinity of an attractant source.  相似文献   

8.
Swimming bacteria sense and respond to chemical signals in their environment. Chemotaxis is the directed migration of a bacterial population toward increasing concentrations of a chemical that they perceive to be beneficial to their survival. Bacteria that are indigenous to groundwater environments exhibit chemotaxis toward chemical contaminants such as hydrocarbons, which they are also able to degrade. This phenomenon may facilitate bioremediation processes by bringing bacteria into closer proximity to these contaminants. A microfluidic device was assembled to study chemotaxis transverse to advective flow. Using a T-shaped channel design (T-sensor), two fluid streams were brought into contact by impinging flow. They then flowed adjacent to each other along a transparent channel. An advantage to this design is that it allows real-time visualization of bacterial distributions within the channel. Under laminar flow conditions a chemotactic driving force was created perpendicular to the direction of flow by diffusion of the chemical attractant from one input stream to the other. A comparison of the chemotactic band behavior in the absence and presence of flow showed that fluid velocity did not significantly impede chemotactic migration in the transverse direction.  相似文献   

9.
Chemotactic bacteria can be attracted to electron donors they consume. In systems where donor is heterogeneously distributed, chemotaxis can lead to enhanced removal of donor relative to that achieved in the absence of chemotaxis. However, simultaneous consumption of an electron acceptor may result in the formation of an acceptor gradient to which the bacteria also respond, thus diminishing the positive effect of chemotaxis. Depletion of an electron acceptor can also reduce the rate of electron donor consumption in addition to its effect on chemotaxis. In this study, we examined the effect of oxygen on chemotaxis to naphthalene and on naphthalene consumption by Pseudomonas putida G7. The organism was able to move up an oxygen gradient when there was a naphthalene gradient in the opposite direction. In the absence of an oxygen gradient, low levels of oxygen attenuated chemotaxis to naphthalene but did not affect random motility. The rate of naphthalene consumption decreased at dissolved oxygen concentrations similar to those at which chemotaxis was attenuated. These results suggest that low dissolved oxygen concentrations can reduce naphthalene removal by P. putida G7 in systems where naphthalene is heterogeneously distributed by simultaneously attenuating chemotactic motion toward naphthalene and decreasing the rate of naphthalene degradation.  相似文献   

10.
The luciferase protein fragment complementation assay is a powerful tool for studying protein-protein interactions. Two inactive fragments of luciferase are genetically fused to interacting proteins, and when these two proteins interact, the luciferase fragments can reversibly associate and reconstitute enzyme activity. Though this technology has been used extensively in live eukaryotic cells, split luciferase complementation has not yet been applied to studies of dynamic protein-protein interactions in live bacteria. As proof of concept and to develop a new tool for studies of bacterial chemotaxis, fragments of Renilla luciferase (Rluc) were fused to the chemotaxis-associated response regulator CheY3 and its phosphatase CheZ in the enteric pathogen Vibrio cholerae. Luciferase activity was dependent on the presence of both CheY3 and CheZ fusion proteins, demonstrating the specificity of the assay. Furthermore, enzyme activity was markedly reduced in V. cholerae chemotaxis mutants, suggesting that this approach can measure defects in chemotactic signaling. However, attempts to measure changes in dynamic CheY3-CheZ interactions in response to various chemoeffectors were undermined by nonspecific inhibition of the full-length luciferase. These observations reveal an unexpected limitation of split Rluc complementation that may have implications for existing data and highlight the need for great caution when evaluating small molecule effects on dynamic protein-protein interactions using the split luciferase technology.  相似文献   

11.
Rhodobacter sphaeroides exhibits two behavioral responses when exposed to some compounds: (i) a chemotactic response that results in accumulation and (ii) a sustained increase in swimming speed. This latter chemokinetic response occurs without any apparent long-term change in the size of the electrochemical proton gradient. The results presented here show that the chemokinetic response is separate from the chemotactic response, although some compounds can induce both responses. Compounds that caused only chemokinesis induced a sustained increase in the rate of flagellar rotation, but chemoeffectors which were also chemotactic caused an additional short-term change in both the stopping frequency and the duration of stops and runs. The response to a change in chemoattractant concentration was a transient increase in the stopping frequency when the concentration was reduced, with adaptation taking between 10 and 60 s. There was also a decrease in the stopping frequency when the concentration was increased, but adaptation took up to 60 min. The nature and duration of both the chemotactic and chemokinetic responses were concentration dependent. Weak organic acids elicited the strongest chemokinetic responses, and although many also caused chemotaxis, there were conditions under which chemokinesis occurred in the absence of chemotaxis. The transportable succinate analog malonate caused chemokinesis but not chemotaxis, as did acetate when added to a mutant able to transport but not grow on acetate. Chemokinesis also occurred after incubation with arsenate, conditions under which chemotaxis was lost, indicating that phosphorylation at some level may have a role in chemotaxis. Aspartate was the only chemoattractant amino acid to cause chemokinesis. Glutamate caused chemotaxis but not chemokinesis. These data suggest that (i) chemotaxis and chemokinesis are separate responses, (ii) metabolism is required for chemotaxis but not chemokinesis, (iii) a reduction in chemoattractant concentration may cause the major chemotactic signal, and (iv) a specific transport pathway(s) may be involved in chemokinetic signalling in R. sphaeroides.  相似文献   

12.
Phagocyte motility and chemotaxis are included in a distributed mathematical model for the inflammatory response to bacterial invasion of tissue. Both uniform and non-uniform steady state solutions may occur for the model equations governing bacteria and phagocyte densities in a macroscopic tissue region. The non-uniform states appear to be more dangerous because they allow large bacteria densities concentrated in local foci, and in some cases greater total bacteria and phagocyte populations. Using a linear stability analysis, it is shown that a phagocyte chemotactic response smaller than a critical value can lead to a non-uniform state, while a chemotactic response greater than this critical value stabilizes the uniform state. This result is the opposite of that found for the role of chemotaxis in aggregation of slimemold amoebae because, in the inflammatory response, the chemotactic population serves as an inhibitor rather than an activator. We speculate that these non-uniform steady states could be related to the localized cell aggregation seen in chronic granulomatous inflammation. The formation of non-uniform states is not necessarily a consequence of defective phagocyte chemotaxis, however. Rather, certain values of the kinetic parameters can yield values for the critical chemotactic response which are greater than the normal response.Numerical computations of the transient inflammatory response to bacterial challenge are presented, using parameter values estimated from the experimental literature wherever possible.  相似文献   

13.
Complex networks of interacting molecular components of living cells are responsible for many important processes, such as signal processing and transduction. An important challenge is to understand how the individual properties of these molecular interactions and biochemical transformations determine the system-level properties of biological functions. Here, we address the issue of the accuracy of signal transduction performed by a bacterial chemotaxis system. The chemotaxis sensitivity of bacteria to a chemoattractant gradient has been measured experimentally from bacterial aggregation in a chemoattractant-containing capillary. The observed precision of the chemotaxis depended on environmental conditions such as the concentration and molecular makeup of the chemoattractant. In a quantitative model, we derived the chemotactic response function, which is essential to describing the signal transduction process involved in bacterial chemotaxis. In the presence of a gradient, an analytical solution is derived that reveals connections between the chemotaxis sensitivity and the characteristics of the signaling system, such as reaction rates. These biochemical parameters are integrated into two system-level parameters: one characterizes the efficiency of gradient sensing, and the other is related to the dynamic range of chemotaxis. Thus, our approach explains how a particular signal transduction property affects the system-level performance of bacterial chemotaxis. We further show that the two parameters can be derived from published experimental data from a capillary assay, which successfully characterizes the performance of bacterial chemotaxis.  相似文献   

14.
Since the pioneering work by Julius Adler in the 1960's, bacterial chemotaxis has been predominantly studied as metabolism-independent. All available simulation models of bacterial chemotaxis endorse this assumption. Recent studies have shown, however, that many metabolism-dependent chemotactic patterns occur in bacteria. We hereby present the simplest artificial protocell model capable of performing metabolism-based chemotaxis. The model serves as a proof of concept to show how even the simplest metabolism can sustain chemotactic patterns of varying sophistication. It also reproduces a set of phenomena that have recently attracted attention on bacterial chemotaxis and provides insights about alternative mechanisms that could instantiate them. We conclude that relaxing the metabolism-independent assumption provides important theoretical advances, forces us to rethink some established pre-conceptions and may help us better understand unexplored and poorly understood aspects of bacterial chemotaxis.  相似文献   

15.
Bacterial chemotactic responses are initiated when certain small molecules (i.e., carbohydrates, amino acids) interact with bacterial chemoreceptors. Although bacterial chemotaxis has been the subject of intense investigations, few have explored the influence of attractant structure on signal generation and chemotaxis. Previously, we found that polymers bearing multiple copies of galactose interact with the chemoreceptor Trg via the periplasmic binding protein glucose/galactose binding protein (GGBP). These synthetic multivalent ligands were potent agonists of Escherichia coli chemotaxis. Here, we report on the development of a second generation of multivalent attractants that possess increased chemotactic activities. Strikingly, the new ligands can alter bacterial behavior at concentrations 10-fold lower than those required with the original displays; thus, they are some of the most potent synthetic chemoattractants known. The potency depends on the number of galactose moieties attached to the oligomer backbone and the length of the linker tethering these carbohydrates. Our investigations reveal the plasticity of GGBP; it can bind and mediate responses to several carbohydrates and carbohydrate derivatives. These attributes of GGBP may underlie the ability of bacteria to sense a variety of ligands with relatively few receptors. Our results provide insight into the design and development of compounds that can modulate bacterial chemotaxis and pathogenicity.  相似文献   

16.
Bacterial chemotaxis can enhance the bioremediation of contaminants in aqueous and subsurface environments if the contaminant is a chemoattractant that the bacteria degrade. The process can be promoted by traveling bands of chemotactic bacteria that form due to metabolism-generated gradients in chemoattractant concentration. We developed a multiple-relaxation-time (MRT) lattice-Boltzmann method (LBM) to model chemotaxis, because LBMs are well suited to model reactive transport in the complex geometries that are typical for subsurface porous media. This MRT-LBM can attain a better numerical stability than its corresponding single-relaxation-time LBM. We performed simulations to investigate the effects of substrate diffusion, initial bacterial concentration, and hydrodynamic dispersion on the formation, shape, and propagation of bacterial bands. Band formation requires a sufficiently high initial number of bacteria and a small substrate diffusion coefficient. Uniform flow does not affect the bands while shear flow does. Bacterial bands can move both upstream and downstream when the flow velocity is small. However, the bands disappear once the velocity becomes too large due to hydrodynamic dispersion. Generally bands can only be observed if the dimensionless ratio between the chemotactic sensitivity coefficient and the effective diffusion coefficient of the bacteria exceeds a critical value, that is, when the biased movement due to chemotaxis overcomes the diffusion-like movement due to the random motility and hydrodynamic dispersion.  相似文献   

17.
An optical trapping technique is implemented to investigate the chemotactic behavior of a marine bacterial strain Vibrio alginolyticus. The technique takes the advantage that the bacterium has only a single polar flagellum, which can rotate either in the counter-clock-wise or clock-wise direction. The two rotation states of the motor can be readily and instantaneously resolved in the optical trap, allowing the flagellar motor switching rate S(t) to be measured under different chemical stimulations. In this paper the focus will be on the bacterial response to an impulsive change of chemoattractant serine. Despite different propulsion apparati and motility patterns, cells of V. alginolyticus apparently use a similar response as Escherichia coli to regulate their chemotactic behavior. Specifically, we found that the switching rate S(t) of the bacterial motor exhibits a biphasic behavior, showing a fast initial response followed by a slow relaxation to the steady-state switching rate S0. The measured S(t) can be mimicked by a model that has been recently proposed for chemotaxis in E. coli. The similarity in the response to the brief chemical stimulation in these two different bacteria is striking, suggesting that the biphasic response may be evolutionarily conserved. This study also demonstrated that optical tweezers can be a useful tool for chemotaxis studies and should be applicable to other polarly flagellated bacteria.  相似文献   

18.
In many natural environments, bacterial populations experience suboptimal growth due to the competition with other microorganisms for limited resources. The chemotactic response provides a mechanism by which bacterial populations can improve their situation by migrating toward more favorable growth conditions. For bacteria cultured under suboptimal growth conditions, evidence for an enhanced chemotactic response has been observed previously. In this article, for the first time, we have quantitatively characterized this behavior in terms of two macroscopic transport coefficients, the random motility and chemotactic sensitivity coefficients, measured in the stopped-flow diffusion chamber assay. Escherichia coli cultured over a range of growth rates in a chemostat exhibits a dramatic increase in the chemotactic sensitivity coefficient for D-fucose at low growth rates, while the random motility coefficient remains relatively constant by comparison. The change in the chemotactic sensitivity coefficient is accounted for by an independently measured increase in the number of galactose-binding proteins which mediate the chemotactic signal. This result is consistent with the relationship between macroscopic and microscopic parameters for chemotaxis, which was proposed in the mathematical model of Rivero and co-workers. (c) 1993 John Wiley & Sons, Inc.  相似文献   

19.
One of the most common methods of tracking movement of bacteria in groundwater environments involves a priori fluorescent staining. A major concern in using these stains to label bacteria in subsurface injection-and-recovery studies is the effect they may have on the bacterium's transport properties. Previous studies investigated the impact of fluorophores on bacterial surface properties (e.g. zeta potential). However, no previous study has looked at the impact of fluorescent staining on swimming speed and chemotaxis. It was found that DAPI lowered the mean population swimming speed of Pseudomonas putida F1 by 46% and Pseudomonas stutzeri by 55%. DAPI also inhibited the chemotaxis in both strains. The swimming speeds of P. putida F1 and P. stutzeri were diminished slightly by CFDA/SE, but not to a statistically significant extent. CFDA/SE had no effect on chemotaxis of either strain to acetate. SYBR(?) Gold had no effect on swimming speed or the chemotactic response to acetate for either strain. This research indicates that although DAPI may not affect sorption to grain surfaces, it adversely affects other potentially important transport properties such as swimming and chemotaxis. Consequently, bacterial transport studies conducted using DAPI are biased to nonchemotactic conditions and do not appear to be suitable for monitoring the effect of chemotaxis on bacterial transport in shallow aquifers.  相似文献   

20.
Quantitative analysis of experiments on bacterial chemotaxis to naphthalene   总被引:6,自引:0,他引:6  
A mathematical model was developed to quantify chemotaxis to naphthalene by Pseudomonas putida G7 (PpG7) and its influence on naphthalene degradation. The model was first used to estimate the three transport parameters (coefficients for naphthalene diffusion, random motility, and chemotactic sensitivity) by fitting it to experimental data on naphthalene removal from a discrete source in an aqueous system. The best-fit value of naphthalene diffusivity was close to the value estimated from molecular properties with the Wilke-Chang equation. Simulations applied to a non-chemotactic mutant strain only fit the experimental data well if random motility was negligible, suggesting that motility may be lost rapidly in the absence of substrate or that gravity may influence net random motion in a vertically oriented experimental system. For the chemotactic wild-type strain, random motility and gravity were predicted to have a negligible impact on naphthalene removal relative to the impact of chemotaxis. Based on simulations using the best-fit value of the chemotactic sensitivity coefficient, initial cell concentrations for a non-chemotactic strain would have to be several orders of magnitude higher than for a chemotactic strain to achieve similar rates of naphthalene removal under the experimental conditions we evaluated. The model was also applied to an experimental system representing an adaptation of the conventional capillary assay to evaluate chemotaxis in porous media. Our analysis suggests that it may be possible to quantify chemotaxis in porous media systems by simply adjusting the model's transport parameters to account for tortuosity, as has been suggested by others.  相似文献   

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