Diffusion of antibiotics through a biofilm in the presence of diffusion and absorption barriers

Quorum Quenching Approaches against Bacterial-Biofilm-Induced Antibiotic Resistance

With the widespread phenomenon of antibiotic resistance and the diffusion of multiple drug-resistant bacterial strains, enormous efforts are being conducted to identify suitable alternative agents against pathogenic microorganisms. Since an association between biofilm formation and antibiotic resistance phenotype has been observed, a promising strategy pursued in recent years focuses on controlling and preventing this formation by targeting and inhibiting the Quorum Sensing (QS) system, whose central role in biofilm has been extensively demonstrated. Therefore, the research and development of Quorum Quenching (QQ) compounds, which inhibit QS, has gradually attracted the attention of researchers and has become a new strategy for controlling harmful microorganisms. Among these, a number of both natural and synthetic compounds have been progressively identified as able to interrupt the intercellular communication within a microbial community and the adhesion to a surface, thus disintegrating mature/preformed biofilms. This review describes the role played by QS in the formation of bacterial biofilms and then focuses on the mechanisms of different natural and synthetic QS inhibitors (QSIs) exhibiting promising antibiofilm ability against Gram-positive and Gram-negative bacterial pathogens and on their applications as biocontrol strategies in various fields.

Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous transport

The purpose of this paper is to study the fundamental solution of the time-space bi-fractional diffusion equation incorporating an additional kinetic source term in semi-infinite space. The equation is a generalization of the integer-order model∂ t ρ ( x , t ) = ∂ x 2 ρ ( x , t ) - ρ ( x , t ) (also known as the Debye-Falkenhagen equation) by replacing the first-order time derivative with the Caputo fractional derivative of order 0 < α < 1 , and the second-order space derivative with the Riesz-Feller fractional derivative of order 0 < β < 2 . Using the Laplace-Fourier transforms method, it is shown that the parametric solutions are expressed in terms of the Fox's H-function that we evaluate for different values of α and β .

BacteSign: Building a Findable, Accessible, Interoperable, and Reusable (FAIR) Database for Universal Bacterial Identification

With the increasing incidence of diverse global bacterial outbreaks, it is important to build an immutable decentralized database that can capture regional changes in bacterial resistance with time. Herein, we investigate the use of a rapid 3D printed µbiochamber with a laser-ablated interdigitated electrode developed for biofilm analysis of Pseudomonas aeruginosa, Acinetobacter baumannii and Bacillus subtilis using electrochemical biological impedance spectroscopy (EBIS) across a 48 h spectrum, along with novel ladder-based minimum inhibitory concentration (MIC) stencil tests against oxytetracycline, kanamycin, penicillin G and streptomycin. Furthermore, in this investigation, a search query database has been built demonstrating the deterministic nature of the bacterial strains with real and imaginary impedance, phase, and capacitance, showing increased bacterial specification selectivity in the 9772.37 Hz range.

A growing battlefield in the war against biofilm-induced antimicrobial resistance: insights from reviews on antibiotic resistance

Biofilms are a common survival strategy employed by bacteria in healthcare settings, which enhances their resistance to antimicrobial and biocidal agents making infections difficult to treat. Mechanisms of biofilm-induced antimicrobial resistance involve reduced penetration of antimicrobial agents, increased expression of efflux pumps, altered microbial physiology, and genetic changes in the bacterial population. Factors contributing to the formation of biofilms include nutrient availability, temperature, pH, surface properties, and microbial interactions. Biofilm-associated infections can have serious consequences for patient outcomes, and standard antimicrobial therapies are often ineffective against biofilm-associated bacteria, making diagnosis and treatment challenging. Novel strategies, including antibiotics combination therapies (such as daptomycin and vancomycin, colistin and azithromycin), biofilm-targeted agents (such as small molecules (LP3134, LP3145, LP4010, LP1062) target c-di-GMP), and immunomodulatory therapies (such as the anti-PcrV IgY antibodies which target Type IIIsecretion system), are being developed to combat biofilm-induced antimicrobial resistance. A multifaceted approach to diagnosis, treatment, and prevention is necessary to address this emerging problem in healthcare settings.

Heterogenous biofilm mass-transport model replicates periphery sequestration of antibiotics in Pseudomonas aeruginosa PAO1 microcolonies

A model for antibiotic accumulation in bacterial biofilm microcolonies utilizing heterogenous porosity and attachment site profiles replicated the periphery sequestration reported in prior experimental studies on Pseudomonas aeruginosa PAO1 biofilm cell clusters. These P. aeruginosa cell clusters are in vitro models of the chronic P. aeruginosa infections in cystic fibrosis patients which display recalcitrance to antibiotic treatments, leading to exacerbated morbidity and mortality. This resistance has been partially attributed to periphery sequestration, where antibiotics fail to penetrate biofilm cell clusters. The physical phenomena driving this periphery sequestration have not been definitively established. This paper introduces mathematical models to account for two proposed physical phenomena driving periphery sequestration: biofilm matrix attachment and volume-exclusion due to variable biofilm porosity. An antibiotic accumulation model which incorporated these phenomena better fit observed periphery sequestration data compared to previous models.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Heterogenous Biofilm Mass-Transport Model Replicates Periphery Sequestration of Antibiotics in P. aeruginosa PAO1 Microcolonies

A spatiotemporal model for antibiotic accumulation in bacterial biofilm microcolonies which leverages heterogenous porosity and attachment site profiles replicated the periphery sequestration phenomena reported in prior experimental studies on Pseudomonas aeruginosa PAO1 biofilm cell clusters. These P. aeruginosa cell clusters are in vitro models of the chronic P. aeruginosa infections found in adult cystic fibrosis patients, which display resistance to antibiotic treatments, leading to exacerbated morbidity and mortality. This resistance has been partially attributed to periphery sequestration, where antibiotics are unable to penetrate biofilm cell clusters. The underlying physical phenomena driving this periphery sequestration have not been definitively established. This paper introduces mathematical models to account for two proposed physical phenomena driving periphery sequestration: biofilm matrix attachment and volume-exclusion due to variable biofilm porosity. An antibiotic accumulation model which incorporated these phenomena was able to better fit observed periphery sequestration data compared to previous models.

Subdiffusion with particle immobilization process described by a differential equation with Riemann-Liouville-type fractional time derivative

An equation describing subdiffusion with possible immobilization of particles is derived by means of the continuous time random walk model. The equation contains a fractional time derivative of Riemann-Liouville type which is a differential-integral operator with the kernel defined by the Laplace transform; the kernel controls the immobilization process. We propose a method for calculating the inverse Laplace transform providing the kernel in the time domain. In the long time limit the subdiffusion-immobilization process reaches a stationary state in which the probability density of a particle distribution is an exponential function.

Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion

We use a subdiffusion equation with fractional Caputo time derivative with respect to another function g (g-subdiffusion equation) to describe a smooth transition from ordinary subdiffusion to superdiffusion. Ordinary subdiffusion is described by the equation with the "ordinary" fractional Caputo time derivative, superdiffusion is described by the equation with a fractional Riesz-type spatial derivative. We find the function g for which the solution (Green's function, GF) to the g-subdiffusion equation takes the form of GF for ordinary subdiffusion in the limit of small time and GF for superdiffusion in the limit of long time. To solve the g-subdiffusion equation we use the g-Laplace transform method. It is shown that the scaling properties of the GF for g-subdiffusion and the GF for superdiffusion are the same in the long time limit. We conclude that for a sufficiently long time the g-subdiffusion equation describes superdiffusion well, despite a different stochastic interpretation of the processes. Then, paradoxically, a subdiffusion equation with a fractional time derivative describes superdiffusion. The superdiffusive effect is achieved here not by making anomalously long jumps by a diffusing particle, but by greatly increasing the particle jump frequency which is derived by means of the g-continuous-time random walk model. The g-subdiffusion equation is shown to be quite general, it can be used in modeling of processes in which a kind of diffusion change continuously over time. In addition, some methods used in modeling of ordinary subdiffusion processes, such as the derivation of local boundary conditions at a thin partially permeable membrane, can be used to model g-subdiffusion processes, even if this process is interpreted as superdiffusion.

Composite subdiffusion equation that describes transient subdiffusion

A composite subdiffusion equation with fractional Caputo time derivative with respect to another function g is used to describe a process of a continuous transition from subdiffusion with parameters α and D_{α} to subdiffusion with parameters β and D_{β}. The parameters are defined by the time evolution of the mean square displacement of diffusing particle σ^{2}(t)=2D_{i}t^{i}/Γ(1+i), i=α,β. The function g controls the process at intermediate times. The composite subdiffusion equation is more general than the ordinary fractional subdiffusion equation with constant parameters; it has potentially wide application in modeling diffusion processes with changing parameters.

Subdiffusion equation with Caputo fractional derivative with respect to another function in modeling diffusion in a complex system consisting of a matrix and channels

Anomalous diffusion of an antibiotic (colistin) in a system consisting of packed gel (alginate) beads immersed in water is studied experimentally and theoretically. The experimental studies are performed using the interferometric method of measuring concentration profiles of a diffusing substance. We use the g-subdiffusion equation with the fractional Caputo time derivative with respect to another function g to describe the process. The function g and relevant parameters define anomalous diffusion. We show that experimentally measured time evolution of the amount of antibiotic released from the system determines the function g. The process can be interpreted as subdiffusion in which the subdiffusion parameter (exponent) α decreases over time. The g-subdiffusion equation, which is more general than the "ordinary" fractional subdiffusion equation, can be widely used in various fields of science to model diffusion in a system in which parameters, and even a type of diffusion, evolve over time. We postulate that diffusion in a system composed of channels and a matrix can be described by the g-subdiffusion equation, just like diffusion in a system of packed gel beads placed in water.

First-passage time for the g-subdiffusion process of vanishing particles

Subdiffusion equation and molecule survival equation, both with Caputo fractional time derivatives with respect to other functions g_{1} and g_{2}, respectively, are used to describe diffusion of a molecule that can disappear at any time with a constant probability. The process can be interpreted as an "ordinary" subdiffusion and "ordinary" molecule survival process in which timescales are changed by the functions g_{1} and g_{2}. We derive the first-passage time distribution for the process. The mutual influence of subdiffusion and molecule-vanishing processes can be included in the model when the functions g_{1} and g_{2} are related to each other. As an example, we consider the processes in which subdiffusion and molecule survival are highly related, which corresponds to the case of g_{1}≡g_{2}.

Stochastic interpretation of g-subdiffusion process

Recently, we considered the g-subdiffusion equation with a fractional Caputo time derivative with respect to another function g, T. Kosztołowicz et al. [Phys. Rev. E 104, 014118 (2021)2470-004510.1103/PhysRevE.104.014118]. This equation offers different possibilities for modeling diffusion such as a process in which a type of diffusion evolves continuously over time. However, the equation has not been derived from a stochastic model and the stochastic interpretation of g subdiffusion is still unknown. In this Letter, we show the stochastic foundations of this process. We derive the equation by means of a modified continuous time random walk model. An interpretation of the g-subdiffusion process is also discussed.

Subdiffusion equation with Caputo fractional derivative with respect to another function

We show an application of a subdiffusion equation with Caputo fractional time derivative with respect to another function g to describe subdiffusion in a medium having a structure evolving over time. In this case a continuous transition from subdiffusion to other type of diffusion may occur. The process can be interpreted as "ordinary" subdiffusion with fixed subdiffusion parameter (subdiffusion exponent) α in which timescale is changed by the function g. As an example, we consider the transition from "ordinary" subdiffusion to ultraslow diffusion. The g-subdiffusion process generates the additional aging process superimposed on the "standard" aging generated by "ordinary" subdiffusion. The aging process is analyzed using coefficient of relative aging of g-subdiffusion with respect to "ordinary" subdiffusion. The method of solving the g-subdiffusion equation is also presented.

Boundary conditions at a thin membrane for the normal diffusion equation which generate subdiffusion

We consider a particle transport process in a one-dimensional system with a thin membrane, described by the normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators, with time-dependent kernels, which act on the functions and their spatial derivatives defined on both membrane surfaces. We show how boundary conditions at the membrane change the temporal evolution of the first and second moments of particle position distribution (the Green's function) which is a solution to the normal diffusion equation. As these moments define the kind of diffusion, an appropriate choice of boundary conditions generates the moments characteristic for subdiffusion. The interpretation of the process is based on a particle random walk model in which the subdiffusion effect is caused by anomalously long stays of the particle in the membrane.

Subdiffusion in a system with a partially permeable partially absorbing wall

We consider subdiffusion of a particle in a one-dimensional system with a thin partially permeable and partially absorbing wall. The system with the wall can be used to filter diffusing particles. Passing through the wall, the particle can be absorbed with a certain probability. Knowing the Green's functions we derive boundary conditions at the wall. The boundary conditions take a specific form in which fractional time derivatives are involved. The temporal evolution of the probability that a diffusing particle has not been absorbed is also considered.

Experimental and Theoretical Analysis of Metal Complex Diffusion through Cell Monolayer

The study of drugs diffusion through different biological membranes constitutes an essential step in the development of new pharmaceuticals. In this study, the method based on the monolayer cell culture of CHO-K1 cells has been developed in order to emulate the epithelial cells barrier in permeability studies by laser interferometry. Laser interferometry was employed for the experimental analysis of nickel(II) and cobalt(II) complexes with 1-allylimidazole or their chlorides’ diffusion through eukaryotic cell monolayers. The amount (mol) of nickel(II) and cobalt(II) chlorides transported through the monolayer was greater than that of metals complexed with 1-allylimidazole by 4.34-fold and 1.45-fold, respectively, after 60 min. Thus, laser interferometry can be used for the quantitative analysis of the transport of compounds through eukaryotic cell monolayers, and the resulting parameters can be used to formulate a mathematical description of this process.

Diffusion profiles in L. lactis biofilms under different conditions

Despite being an important topic in biofilm research, we still know little about diffusion in biofilms. Emerging biofilms of Lactococcus lactis growing in custom-made flow-cells were monitored and diffusion constants across the height of the biofilms recorded. The biofilms showed different diffusional behavior with regard to flow rate and pH variations, despite growing to similar thickness. At a higher flow rate, the biofilm exhibits slower diffusion compared to the reference cultivation at lower flow rate. By increasing pH, the biofilm exhibited fast growth and little difference in diffusion compared to the reference cultivation. Furthermore, the diffusion inside of the biofilms differed depending on the position in the flow-cell. The present study reveals new insights in how external factors can affect structure and density of biofilms. The method can be reliably used for L. lactis biofilms with a thickness up to 120 μm.

Modelling experimentally measured of ciprofloxacin antibiotic diffusion in Pseudomonas aeruginosa biofilm formed in artificial sputum medium

We study the experimentally measured ciprofloxacin antibiotic diffusion through a gel-like artificial sputum medium (ASM) mimicking physiological conditions typical for a cystic fibrosis layer, in which regions occupied by Pseudomonas aeruginosa bacteria are present. To quantify the antibiotic diffusion dynamics we employ a phenomenological model using a subdiffusion-absorption equation with a fractional time derivative. This effective equation describes molecular diffusion in a medium structured akin Thompson's plumpudding model; here the 'pudding' background represents the ASM and the 'plums' represent the bacterial biofilm. The pudding is a subdiffusion barrier for antibiotic molecules that can affect bacteria found in plums. For the experimental study we use an interferometric method to determine the time evolution of the amount of antibiotic that has diffused through the biofilm. The theoretical model shows that this function is qualitatively different depending on whether or not absorption of the antibiotic in the biofilm occurs. We show that the process can be divided into three successive stages: (1) only antibiotic subdiffusion with constant biofilm parameters, (2) subdiffusion and absorption of antibiotic molecules with variable biofilm transport parameters, (3) subdiffusion and absorption in the medium but the biofilm parameters are constant again. Stage 2 is interpreted as the appearance of an intensive defence build-up of bacteria against the action of the antibiotic, and in the stage 3 it is likely that the bacteria have been inactivated. Times at which stages change are determined from the experimentally obtained temporal evolution of the amount of antibiotic that has diffused through the ASM with bacteria. Our analysis shows good agreement between experimental and theoretical results and is consistent with the biologically expected biofilm response. We show that an experimental method to study the temporal evolution of the amount of a substance that has diffused through a biofilm is useful in studying the processes occurring in a biofilm. We also show that the complicated biological process of antibiotic diffusion in a biofilm can be described by a fractional subdiffusion-absorption equation with subdiffusion and absorption parameters that change over time.