Leaky vessels as a potential source of stromal acidification in tumours

Malignant tumours are characterised by higher rates of acid production and a lower extracellular pH than normal tissues. Previous mathematical modelling has indicated that the tumour-derived production of acid leads to a gradient of low pH in the interior of the tumour extending to a normal pH in the peritumoural tissue. This paper uses mathematical modelling to examine the potential of leaky vessels as an additional source of stromal acidification in tumours. We explore whether and to what extent increasing vascular permeability in vessels can lead to the breakdown of the acid gradient from the core of the tumour to the normal tissue, and a progressive acidification of the peritumoural stroma. We compare our mathematical simulations to experimental results found in vivo with a tumour implanted in the mammary fat pad of a mouse in a window chamber construct. We find that leaky vasculature can cause a net acidification of the normal tissue away from the tumour boundary, though not a progressive acidification over time as seen in the experiments. Only through progressively increasing the leakiness can the model qualitatively reproduce the experimental results. Furthermore, the extent of the acidification predicted by the mathematical model is less than as seen in the window chamber, indicating that although vessel leakiness might be acting as a source of acid, it is not the only factor contributing to this phenomenon. Nevertheless, tumour destruction of vasculature could result in enhanced stromal acidification and invasion, hence current therapies aimed at buffering tumour pH should also examine the possibility of preventing vessel disruption

Speed of reaction diffusion in embryogenesis

Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns formed and the robustness of pattern selection, much less is known about the time scales required for pattern formation. Studies of gradient formation by the diffusion of a single morphogen from a localized source have shown that patterning can occur on realistic time scales over distances of a millimeter or less. Reaction diffusion has the potential to give rise to patterns on a faster time scale, since all points in the domain can act as sources of morphogen. However, the speed at which patterning can occur has hitherto not been explored in depth. In this paper, we investigate this issue in specific reaction diffusion models and address the question of whether patterning via reaction diffusion is fast enough to be applicable to morphogenesis

Complex pattern formation in reaction diffusion systems with spatially-varying parameters

Spontaneous pattern formation in reaction–diffusion systems on a spatially homogeneous domain has been well studied. However, in embryonic development and elsewhere, pattern formation often takes place on a spatially heterogeneous background. We explore the effects of spatially varying parameters on pattern formation in one and two dimensions using the Gierer–Meinhardt reaction–diffusion model. We investigate the effect of the wavelength of a pre-pattern and demonstrate a novel form of moving pattern. We find that spatially heterogeneous parameters can both increase the range and complexity of possible patterns and enhance the robustness of pattern selection

Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling

In many developing tissues, adjacent cells diverge in character so as to create a fine-grained pattern of cells in contrasting states of differentiation. It has been proposed that such patterns can be generated through lateral inhibition—a type cells–cell interaction whereby a cell that adopts a particular fate inhibits its immediate neighbours from doing likewise. Lateral inhibition is well documented in flies, worms and vertebrates. In all of these organisms, the transmembrane proteins Notch and Delta (or their homologues) have been identified as mediators of the interaction—Notch as receptor, Delta as its ligand on adjacent cells. However, it is not clear under precisely what conditions the Delta-Notch mechanism of lateral inhibition can generate the observed types of pattern, or indeed whether this mechanism is capable of generating such patterns by itself. Here we construct and analyse a simple and general mathematical model of such contact-mediated lateral inhibition. In accordance with experimental data, the model postulates that receipt of inhibition (i.e. activation of Notch) diminishes the ability to deliver inhibition (i.e. to produce active Delta). This gives rise to a feedback loop that can amplify differences between adjacent cells. We investigate the pattern-forming potential and temporal behavior of this model both analytically and through numerical simulation. Inhomogeneities are self-amplifying and develop without need of any other machinery, provided the feedback is sufficiently strong. For a wide range of initial and boundary conditions, the model generates fine-grained patterns similar to those observed in living systems

Transitions in bacterial communities across two fermentation-based virgin coconut oil (VCO) production processes

Despite being one of the most used methods of virgin coconut oil (VCO) production, there is no metagenomic study that details the bacterial community shifts during fermentation-based VCO production. The identification and quantification of bacteria associated with coconut milk fermentation is useful for detecting the dominant microbial genera actively involved in VCO production which remains largely undescribed. Describing the constitutive microbial genera involved in this traditional fermentation practice can be used as a preliminary basis for improving industrial practices and developing better fermentation procedures. In this study, we utilized 16S rRNA metagenomic sequencing to trace the transitions in microbial community profiles as coconut milk is fermented to release VCO in two VCO production lines. The results show that difference in the microbiome composition between the different processing steps examined in this work was mainly due to the abundance of the Leuconostoc genus in the raw materials and its decline and transition into the lactic acid bacteria groups Weissella, Enterococcus, Lactobacillus, Lactococcus, and Streptococcus during the latter stages of fermentation. A total of 17 genera with relative abundances greater than 0.01% constitute the core microbiome of the two processing lines and account for 74%-97% of the microbial abundance in all coconut-derived samples. Significant correlations were shown through an analysis of the Spearman\u27s rank between and within the microbial composition and pH at the genus level. The results of the present study show that the dynamics of VCO fermentation rely on the shifts in abundances of various members of the Lactobacillales order

A study of the temperature dependence of bienzyme systems and enzymatic chains

It is known that most enzyme-facilitated reactions are highly temperature dependent processes. In general, the temperature coefficient, Q10, of a simple reaction reaches 2.0-3.0. Nevertheless, some enzyme-controlled processes have much lower Q10 (about 1.0), which implies that the process is almost temperature independent, even if individual reactions involved in the process are themselves highly temperature dependent. In this work, we investigate a possible mechanism for this apparent temperature compensation: simple mathematical models are used to study how varying types of enzyme reactions are affected by temperature. We show that some bienzyme-controlled processes may be almost temperature independent if the modules involved in the reaction have similar temperature dependencies, even if individually, these modules are strongly temperature dependent. Further, we show that in non-reversible enzyme chains the stationary concentrations of metabolites are dependent only on the relationship between the temperature dependencies of the first and last modules, whilst in reversible reactions, there is a dependence on every module. Our findings suggest a mechanism by which the metabolic processes taking place within living organisms may be regulated, despite strong variation in temperature

The Biosorption of Lead from Aqueous Solutions by a Wood-immobilized Fungal Biosorbent

Lead [Pb(II)] biosorption capacities of immobilized Talaromyces macrosporus on Moringa oleifera L. wood were compared against pure fungal and pure M. oleifera biomass. A Pb(II) contact test of 1000 ug/mL show similar Pb(II) removal of non-immobilized fungal biomass (F) and powdered wood colonized with fungi (WP+F), with WP+F producing more biomass. Powdered sorbents had higher Pb(II) uptake compared to whole sorbents analyzed through ICP-AES, possibly due to increased surface area for Pb(II) binding. FTIR analysis of the F, WP, and WP+F identified hydroxyl, amino, carbonyl, and sulfhydryl functional groups which constitute probable Pb(II)-affinitive binding sites. The biosorbents tested in a Continuous Flow Column (CF) adsorbed Pb(II) at 1000, 2000, and 4000 ug/mL in 30 minutes with the Pb(II) uptake of WP+F producing removal efficiencies at 91-95% regardless of initial Pb(II) concentration. WP+F also showed significantly higher q values than powdered wood (WP) at 42.67184.83 mg/g for the Pb(II) test concentrations. Recovery of Pb(II) from WP+F yielded 99.61% of adsorbed ions from 1000 ug/mL Pb(II), proving Pb(II) entrapment in the sorbent. This is the first study to describe biosorption capacities for T. macrosporus and M. oleifera softwood along with the wood’s viability as an immobilization scaffold. These results show the potential of using T. macrosporus immobilized on M. oleifera wood as a tool for removal of Pb(II) in wastewater with high Pb(II) concentrations

Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions

We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain RN,At=2A−A+,x, t>0, ||t=−||+Ardx, t>0 with the Robin boundary condition +aAA=0, x, where aA>0, the reaction rates (p,q,r,s) satisfy 1<p<()+, q>0, r>0, s0, 1<<+, the diffusion constant is chosen such that 1, and the time relaxation constant is such that 0. We rigorously prove the following results on the stability of one-spike solutions: (i) If r=2 and 1<p<1+4/N or if r=p+1 and 1<p<, then for aA>1 and sufficiently small the interior spike is stable. (ii) For N=1 if r=2 and 1<p3 or if r=p+1 and 1<p<, then for 0<aA<1 the near-boundary spike is stable. (iii) For N=1 if 3<p<5 and r=2, then there exist a0(0,1) and µ0>1 such that for a(a0,1) and µ=2q/(s+1)(p−1)(1,µ0) the near-boundary spike solution is unstable. This instability is not present for the Neumann boundary condition but only arises for the Robin boundary condition. Furthermore, we show that the corresponding eigenvalue is of order O(1) as 0. ©2007 American Institute of Physic

Spatial and spatio-temporal patterns in a cell-haptotaxis model

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation

A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics:influenza A as a case study

Multi-scale epidemic forecasting models have been used to inform population-scale predictions with within-host models and/or infection data collected in longitudinal cohort studies. However, most multi-scale models are complex and require significant modelling expertise to run. We formulate an alternative multi-scale modelling framework using a compartmental model with multiple infected stages. In the large-compartment limit, our easy-to-use framework generates identical results compared to previous more complicated approaches. We apply our framework to the case study of influenza A in humans. By using a viral dynamics model to generate synthetic patient-level data, we explore the effects of limited and inaccurate patient data on the accuracy of population-scale forecasts. If infection data are collected daily, we find that a cohort of at least 40 patients is required for a mean population-scale forecasting error below 10%. Forecasting errors may be reduced by including more patients in future cohort studies or by increasing the frequency of observations for each patient. Our work, therefore, provides not only an accessible epidemiological modelling framework but also an insight into the data required for accurate forecasting using multi-scale models