Metabolic symbiosis between oxygenated and hypoxic tumour cells: An agent-based modelling study

Deregulated metabolism is one of the hallmarks of cancer. It is well-known that tumour cells tend to metabolize glucose via glycolysis even when oxygen is available and mitochondrial respiration is functional. However, the lower energy efficiency of aerobic glycolysis with respect to mitochondrial respiration makes this behaviour, namely the Warburg effect, counter-intuitive, although it has now been recognized as source of anabolic precursors. On the other hand, there is evidence that oxygenated tumour cells could be fuelled by exogenous lactate produced from glycolysis. We employed a multi-scale approach that integrates multi-agent modelling, diffusion-reaction, stoichiometric equations, and Boolean networks to study metabolic cooperation between hypoxic and oxygenated cells exposed to varying oxygen, nutrient, and inhibitor concentrations. The results show that the cooperation reduces the depletion of environmental glucose, resulting in an overall advantage of using aerobic glycolysis. In addition, the oxygen level was found to be decreased by symbiosis, promoting a further shift towards anaerobic glycolysis. However, the oxygenated and hypoxic populations may gradually reach quasi-equilibrium. A sensitivity analysis using Latin hypercube sampling and partial rank correlation shows that the symbiotic dynamics depends on properties of the specific cell such as the minimum glucose level needed for glycolysis. Our results suggest that strategies that block glucose transporters may be more effective to reduce tumour growth than those blocking lactate intake transporters.

Coupled CFD-DEM modelling to predict how EPS affects bacterial biofilm deformation, recovery and detachment under flow conditions

The deformation and detachment of bacterial biofilm are related to the structural and mechanical properties of the biofilm itself. Extracellular polymeric substances (EPS) play an important role on keeping the mechanical stability of biofilms. The understanding of biofilm mechanics and detachment can help to reveal biofilm survival mechanisms under fluid shear and provide insight about what flows might be needed to remove biofilm in a cleaning cycle or for a ship to remove biofilms. However, how the EPS may affect biofilm mechanics and its deformation in flow conditions remains elusive. To address this, a coupled computational fluid dynamic– discrete element method (CFD‐DEM) model was developed. The mechanisms of biofilm detachment, such as erosion and sloughing have been revealed by imposing hydrodynamic fluid flow at different velocities and loading rates. The model, which also allows adjustment of the proportion of different functional groups of microorganisms in the biofilm, enables the study of the contribution of EPS toward biofilm resistance to fluid shear stress. Furthermore, the stress–strain curves during biofilm deformation have been captured by loading and unloading fluid shear stress to study the viscoelastic properties of the biofilm. Our predicted emergent viscoelastic properties of biofilms were consistent with relevant experimental measurements.

Modelling bacterial twitching in fluid flows: a CFD-DEM approach

Bacterial habitats are often associated with fluid flow environments. Bacterial twitching is important for initial bacterial colonization and biofilm formation. The existing research about bacteria twitching is largely experimental orientated. There is a lack of models of twitching motility of bacteria in shear flows, which could provide fundamental understanding about how bacterial twitching would be affected by bacteria associated properties such as number of pili and their distribution on the cell body and environmental factors such as flow and surface patterns. In this work, a three-dimensional modelling approach of Computational Fluid Dynamics (CFD) coupled with the Discrete Element Method (DEM) proposed to study bacterial twitching on flat and groove surfaces under shear flow conditions. Rod-shaped bacteria are modelled as groups of spherical particles and Type IV pili attached to bacteria are modelled as dynamic springs which can elongate, retract, attach and detach. The CFD-DEM model of rod-shape bacteria is validated against orbiting of immotile bacteria in shear flows. The effects of fluid flow rate and surface topography on twitching motility are studied. The model can successfully predict upstream twitching motility of rod-shaped bacteria in shear flows. Our model can predict that there would be an optimal range of wall shear stress in which bacterial upstream twitching is most efficient. The results also indicate that when bacteria twitch on groove surfaces, they are likely to accumulate around the downstream side of the groove walls.

Regulating, Measuring, and Modeling the Viscoelasticity of Bacterial Biofilms

Biofilms occur in a broad range of environments under heterogeneous physicochemical conditions, such as in bioremediation plants, on surfaces of biomedical implants, and in the lungs of cystic fibrosis patients. In these scenarios, biofilms are subjected to shear forces, but the mechanical integrity of these aggregates often prevents their disruption or dispersal. Biofilms' physical robustness is the result of the multiple biopolymers secreted by constituent microbial cells which are also responsible for numerous biological functions. A better understanding of the role of these biopolymers and their response to dynamic forces is therefore crucial for understanding the interplay between biofilm structure and function. In this paper, we review experimental techniques in rheology, which help quantify the viscoelasticity of biofilms, and modeling approaches from soft matter physics that can assist our understanding of the rheological properties. We describe how these methods could be combined with synthetic biology approaches to control and investigate the effects of secreted polymers on the physical properties of biofilms. We argue that without an integrated approach of the three disciplines, the links between genetics, composition, and interaction of matrix biopolymers and the viscoelastic properties of biofilms will be much harder to uncover.

Individual Based Model Links Thermodynamics, Chemical Speciation and Environmental Conditions to Microbial Growth

Individual based Models (IbM) must transition from research tools to engineering tools. To make the transition we must aspire to develop large, three dimensional and physically and biologically credible models. Biological credibility can be promoted by grounding, as far as possible, the biology in thermodynamics. Thermodynamic principles are known to have predictive power in microbial ecology. However, this in turn requires a model that incorporates pH and chemical speciation. Physical credibility implies plausible mechanics and a connection with the wider environment. Here, we propose a step toward that ideal by presenting an individual based model connecting thermodynamics, pH and chemical speciation and environmental conditions to microbial growth for 5·105 individuals. We have showcased the model in two scenarios: a two functional group nitrification model and a three functional group anaerobic community. In the former, pH and connection to the environment had an important effect on the outcomes simulated. Whilst in the latter pH was less important but the spatial arrangements and community productivity (that is, methane production) were highly dependent on thermodynamic and reactor coupling. We conclude that if IbM are to attain their potential as tools to evaluate the emergent properties of engineered biological systems it will be necessary to combine the chemical, physical, mechanical and biological along the lines we have proposed. We have still fallen short of our ideals because we cannot (yet) calculate specific uptake rates and must develop the capacity for longer runs in larger models. However, we believe such advances are attainable. Ideally in a common, fast and modular platform. For future innovations in IbM will only be of use if they can be coupled with all the previous advances.

A Bayesian approach to modelling the impact of hydrodynamic shear stress on biofilm deformation

We investigate the feasibility of using a surrogate-based method to emulate the deformation and detachment behaviour of a biofilm in response to hydrodynamic shear stress. The influence of shear force, growth rate and viscoelastic parameters on the patterns of growth, structure and resulting shape of microbial biofilms was examined. We develop a statistical modelling approach to this problem, using combination of Bayesian Poisson regression and dynamic linear models for the emulation. We observe that the hydrodynamic shear force affects biofilm deformation in line with some literature. Sensitivity results also showed that the expected number of shear events, shear flow, yield coefficient for heterotrophic bacteria and extracellular polymeric substance (EPS) stiffness per unit EPS mass are the four principal mechanisms governing the bacteria detachment in this study. The sensitivity of the model parameters is temporally dynamic, emphasising the significance of conducting the sensitivity analysis across multiple time points. The surrogate models are shown to perform well, and produced ≈ 480 fold increase in computational efficiency. We conclude that a surrogate-based approach is effective, and resulting biofilm structure is determined primarily by a balance between bacteria growth, viscoelastic parameters and applied shear stress.

A mechanistic Individual-based Model of microbial communities

Accurate predictive modelling of the growth of microbial communities requires the credible representation of the interactions of biological, chemical and mechanical processes. However, although biological and chemical processes are represented in a number of Individual-based Models (IbMs) the interaction of growth and mechanics is limited. Conversely, there are mechanically sophisticated IbMs with only elementary biology and chemistry. This study focuses on addressing these limitations by developing a flexible IbM that can robustly combine the biological, chemical and physical processes that dictate the emergent properties of a wide range of bacterial communities. This IbM is developed by creating a microbiological adaptation of the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). This innovation should provide the basis for “bottom up” prediction of the emergent behaviour of entire microbial systems. In the model presented here, bacterial growth, division, decay, mechanical contact among bacterial cells, and adhesion between the bacteria and extracellular polymeric substances are incorporated. In addition, fluid-bacteria interaction is implemented to simulate biofilm deformation and erosion. The model predicts that the surface morphology of biofilms becomes smoother with increased nutrient concentration, which agrees well with previous literature. In addition, the results show that increased shear rate results in smoother and more compact biofilms. The model can also predict shear rate dependent biofilm deformation, erosion, streamer formation and breakup.

A mechanistic Individual-based Model of microbial communities

Accurate predictive modelling of the growth of microbial communities requires the credible representation of the interactions of biological, chemical and mechanical processes. However, although biological and chemical processes are represented in a number of Individual-based Models (IbMs) the interaction of growth and mechanics is limited. Conversely, there are mechanically sophisticated IbMs with only elementary biology and chemistry. This study focuses on addressing these limitations by developing a flexible IbM that can robustly combine the biological, chemical and physical processes that dictate the emergent properties of a wide range of bacterial communities. This IbM is developed by creating a microbiological adaptation of the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). This innovation should provide the basis for "bottom up" prediction of the emergent behaviour of entire microbial systems. In the model presented here, bacterial growth, division, decay, mechanical contact among bacterial cells, and adhesion between the bacteria and extracellular polymeric substances are incorporated. In addition, fluid-bacteria interaction is implemented to simulate biofilm deformation and erosion. The model predicts that the surface morphology of biofilms becomes smoother with increased nutrient concentration, which agrees well with previous literature. In addition, the results show that increased shear rate results in smoother and more compact biofilms. The model can also predict shear rate dependent biofilm deformation, erosion, streamer formation and breakup.

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects.