Modeling the bacterial self-organization in a circular container along the contact line as detected by bioluminescence imaging

This paper presents a one-dimensional-in-space mathematical model of a bacterial selforganization in a circular container along the contact line as detected by quasi-one-dimensional bioluminescence imaging. The pattern formation in a luminous Escherichia coli colony was modeled by the nonlinear reaction-diffusion-chemotaxis equations in which the reaction term for the cells is a logistic (autocatalytic) growth function. By varying the input parameters the output results were analyzed with a special emphasis on the influence of the model parameters on the pattern formation. The numerical simulation at transition conditions was carried out using the finite difference technique. The mathematical model and the numerical solution were validated by experimental data

Computational modeling of the bacterial self-organization in a rounded container: The effect of dimensionality

A bacterial self-organization in a rounded container as detected by bioluminescence imaging is mathematically modeled by applying the the Keller–Segel approach with logistic growth. The pattern formation in a colony of luminous Escherichia coli is numerically simulated by the nonlinear reaction-advection-diffusion equations. In this work, the pattern formation is studied in 3D and the results are compared with previous and new 2D and 1D simulations. The numerical simulation at transition conditions was carried out using the finite difference technique. The simulation results showed that the developed 3D model captures fairly well the sophisticated patterns observed in the experiments. Since the numerical simulation based on the 3D model is very time-consuming, the reduction of spatial dimension of the model for simulating 1D spatiotemporal patterns is discussed. Due to the accumulation of luminous cells near the top three-phase contact line the experimental patterns of the bioluminescence can be qualitatively described by 1D and 2D models by adjusting values of the diffusion coefficient and/or chemotactic sensitivity

Nusistovėjusios srovės porėtame biojutiklio elektrode kompiuterinis modeliavimas

Reaction-diffusion in porous enzyme-doped carbon paste electrode has been analyzed. The plate-gap model of such electrode has been proposed. The steady state current was calculated for the wide range of given parameters. The apparent parameters (apparent maximal currents and apparent Michaelis constants) of the modelled electrode were calculated. Relationships between apparent and given parameters were derived.Išnagrinėti reakcijos-difuzijos procesai porėtame anglies pastos elektrode, kuris yra impregnuotas fermetu. Parodyta, kad procesai tokiame elektrode yra panašūs procesams teoriniame stačiakampio profilio plyšio elektrode. Pasiūlytas atitinkamas porėto elektrodo modelis (plyšio elektrodo modelis). Apskaičiuotos plyšio elektrodo srovės plačiame duotų parametrų diapazone. Apskaičiuoti šio teorinio elektrodo tariamieji parametrai (tariamoji maksimali srovė ir tariamoji Michaelio konstanta). Gauti sąryšiai tarp užduotų ir tariamųjų parametrų

Phenomenological model of bacterial aerotaxis with a negative feedback

A phenomenological model for the suspension of the aerotactic swimming microorganisms placed in a chamber with its upper surface open to air is presented. The model was constructed to embody some complexity of the aerotaxis phenomenon, especially, changes in the average bacteria drift velocity under changing environmental conditions. It was assumed that effective forces applied to the cell (gravitational, drag, and thrust) should be essential for the overall system dynamics; and that bacterial propulsion force, but not their swimming velocity, is proportional to the gradient of the oxygen concentration. Mathematically, the model consists of three coupled equations for the oxygen dynamics; for the cell conservation; and for the balance of forces acting on bacteria. An analytical steady-state solution is given for the shallow and deep layers and numerical results are given for the steady-state and initial value problems which are compared with corresponding ones to the Keller–Segel model

Computational modeling of luminous bacteria self-organization on the cylindrical container side surface

This paper deals with the computational modeling of the pattern formation of luminous bacteria. Two bacterial self-organization models are investigated – Keller-Segel diffusion-advection-reaction type equations and the model with additional oxygen equation. These models were applied for the modeling of fluid cultures of lux-gene engineered Escherichia coli in the cylindrical container as seen from the side in 2 dimensions and in quasi-1 dimension along the top three phase contact line. The spatiotemporal patterns were simulated by using the finite difference technique. By applying these models the influence of the cylindrical container depth on the pattern formation was investigated

Computational modeling of luminous bacteria self-organization on the cylindrical container side surface

This paper deals with the computational modeling of the pattern formation of luminous bacteria. Two bacterial self-organization models are investigated – Keller-Segel diffusion-advection-reaction type equations and the model with additional oxygen equation. These models were applied for the modeling of fluid cultures of lux-gene engineered Escherichia coli in the cylindrical container as seen from the side in 2 dimensions and in quasi-1 dimension along the top three phase contact line. The spatiotemporal patterns were simulated by using the finite difference technique. By applying these models the influence of the cylindrical container depth on the pattern formation was investigated

Phoretic interactions and oscillationsin active suspensions of growing Escherichia coli

Bioluminescence imaging experiments were carried out to characterize spatio-temporal patterns of bacterial selforganization in active suspensions (cultures) of bioluminescent Escherichia coli and its mutants. An analysis of the effects of mutations shows that spatio-temporal patterns formed in standard microtitre plates are not related to the chemotaxis system of bacteria. In fact, these patterns are strongly dependent on the properties of mutants that characterize them as self-phoretic (non-flagellar) swimmers. In particular, the observed patterns are essentially dependent on the efficiency of proton translocation across membranes and the smoothness of the cell surface. These characteristics can be associated, respectively, with the surface activity and the phoretic mobility of a colloidal swimmer. An analysis of the experimental data together with mathematical modelling of pattern formation suggests the following: (1) pattern-forming processes can be described by Keller–Segel-type models of chemotaxis with logistic cell kinetics; (2) active cells can be seen as biochemical oscillators that exhibit phoretic drift and alignment; and (3) the spatio-temporalpatternsinasuspensionofgrowingE.coliform due to phoretic interactions between oscillating cells of high metabolic activity

Video S1 from Phoretic interactions and oscillations in active suspensions of growing <i>Escherichia coli</i>

Time-lapse video of bioluminescence images of the cultures of E. coli (first column from the left) and its mutants deficient in NhaA (second column), NhaB (third column), ChaA (fourth column)