A two-phase thin-film model for cell-induced gel contraction incorporating osmotic effects.

We present a mathematical model of an experiment in which cells are cultured within a gel, which in turn floats freely within a liquid nutrient medium. Traction forces exerted by the cells on the gel cause it to contract over time, giving a measure of the strength of these forces. Building upon our previous work (Reoch et al. in J Math Biol 84(5):31, 2022), we exploit the fact that the gels used frequently have a thin geometry to obtain a reduced model for the behaviour of a thin, two-dimensional cell-seeded gel. We find that steady-state solutions of the reduced model require the cell density and volume fraction of polymer in the gel to be spatially uniform, while the gel height may vary spatially. If we further assume that all three of these variables are initially spatially uniform, this continues for all time and the thin film model can be further reduced to solving a single, non-linear ODE for gel height as a function of time. The thin film model is further investigated for both spatially-uniform and varying initial conditions, using a combination of analytical techniques and numerical simulations. We show that a number of qualitatively different behaviours are possible, depending on the composition of the gel (i.e., the chemical potentials) and the strength of the cell traction forces. However, unlike in the earlier one-dimensional model, we do not observe cases where the gel oscillates between swelling and contraction. For the case of initially uniform cell and gel density, our model predicts that the relative change in the gels' height and length are equal, which justifies an assumption previously used in the work of Stevenson et al. (Biophys J 99(1):19-28, 2010). Conversely, however, even for non-uniform initial conditions, we do not observe cases where the length of the gel changes whilst its height remains constant, which have been reported in another model of osmotic swelling by Trinschek et al. (AIMS Mater Sci 3(3):1138-1159, 2016; Phys Rev Lett 119:078003, 2017).

A mathematical model for cell-induced gel contraction incorporating osmotic effects.

Biological tissues are composed of cells surrounded by the extracellular matrix (ECM). The ECM can be thought of as a fibrous polymer network, acting as a natural scaffolding to provide mechanical support to the cells. Reciprocal mechanical and chemical interactions between the cells and the ECM are crucial in regulating the development of tissues and maintaining their functionality. Hence, to maintain in vivo-like behaviour when cells are cultured in vitro, they are often seeded in a gel, which aims to mimic the ECM. In this paper, we present a mathematical model that incorporates cell-gel interactions together with osmotic pressure to study the mechanical behaviour of biological gels. In particular, we consider an experiment where cells are seeded within a gel, which gradually compacts due to forces exerted on it by the cells. Adopting a one-dimensional Cartesian geometry for simplicity, we use a combination of analytical techniques and numerical simulations to investigate how cell traction forces interact with osmotic effects (which can lead to either gel swelling or contraction depending on the gel's composition). Our results show that a number of qualitatively different behaviours are possible, depending on the composition of the gel (i.e. its chemical potentials) and the strength of the cell traction forces. A novel prediction of our model is that there are cases where the gel oscillates between swelling and contraction; to our knowledge, this behaviour has not been reported in experiments. We also consider how physical parameters like drag and viscosity affect the manner in which the gel evolves.

Follicle structure influences the availability of oxygen to the oocyte in antral follicles.

The ability of an oocyte to successfully mature is highly dependent on intrafollicular conditions, including the size and structure of the follicle. Here we present a mathematical model of oxygen transport in the antral follicle. We relate mean oxygen concentration in follicular fluid of bovine follicles to the concentration in the immediate vicinity of the cumulus-oocyte complex (COC). The model predicts that the oxygen levels within the antral follicle are dependent on the size and structure of the follicle and that the mean level of dissolved oxygen in follicular fluid does not necessarily correspond to that reaching the COC.

Estimation of glucose uptake by ovarian follicular cells.

In vitro maturation (IVM) of mammalian oocytes provides an alternative to traditional in vitro fertilization techniques for clinical treatment of infertility or animal breeding. IVM involves the collection of oocytes from the ovary prior to ovulation, with maturation occurring in a laboratory environment. The success of IVM is highly sensitive to the in vitro nutrient environment. The nurse cells surrounding the oocyte, known as cumulus cells, regulate this environment and removal of these cells reduces the ability of the oocyte to develop following insemination. Determining the nature of the interaction between the oocyte and cumulus cells, collectively called the cumulus-oocyte complex (COC), is a difficult task experimentally. Here we use a combination of experimental and mathematical techniques to investigate glucose transport within bovine COCs and find quantitative estimates of the glucose uptake rates of the oocyte and cumulus cells. Surprisingly, our modeling shows the rate of uptake of glucose by the oocyte to increase and then decrease with concentration, a result that needs further experimental investigation but which supports the expectation that high and low glucose concentrations are detrimental to oocyte development. The methodology described is suitable for use across species and for investigating the transport of other important nutrients within the COC.

Mathematical modelling of oxygen concentration in bovine and murine cumulus-oocyte complexes.

Immature oocytes benefit from nutrient modification of the follicular environment by the surrounding cumulus mass. However, the oxygen concentration that the oocyte may be exposed to could be lower than the antral follicular concentration due to the metabolism of surrounding cumulus cells. Using metabolic data previously determined, we have developed a mathematical model of O(2) diffusion across the bovine and murine cumulus-oocyte complex. From this we have determined that across a physiological range of external pO(2), less than 0.25% and 0.5% O(2) is removed by cumulus cells within the bovine and murine cumulus-oocyte complex respectively. Our model differs from others as it: incorporates a term that allows for nonlinear variation of the oxygen consumption rate with oxygen concentration; considers two regions (oocyte and cumulus) sharing a common boundary, both of which consume oxygen at different non linear rates. Cumulus cells therefore remove little O(2), thus sparing this essential gas for the oocyte, which is dependent on ATP generation via oxidative phosphorylation.

Effects of low and high relative molecular protein mass on four methods for total protein determination in urine.

Four commonly used methods for the determination of total protein in urine were compared. These were two biuret methods using different precipitants, a Ponceau S method and a Coomassie Brilliant Blue method. The protein content of the urines was also evaluated by sodium dodecylsulphate polyacrylamide gel electrophoresis. The biuret method with ethanolic phosphotungstic acid as precipitant correlated best with the Coomassie Brilliant Blue method (r = 0.944; p less than 0.001) but less well with the Ponceau S (r = 0.895; p less than 0.001) or biuret-trichloroacetic acid (r = 0.874; p less than 0.001) methods. For urines with normal electrophoretic protein patterns, the imprecise biuret-trichloroacetic acid method (cv = 18.5%) gave the greatest number of false high results (23 in 36 urines) as assessed by electrophoresis. False low results were common in low relative molecular mass (Mr) proteinuria, especially with the biuret-tricholoroacetic acid and Ponceau S methods. High Mr proteinuria rarely caused false low results. Discrepancies between methods appear to have resulted from incomplete precipitation of low Mr protein by trichloroacetic acid.

Type 2 (non-insulin-dependent) diabetes mellitus, migration and westernisation: the Tokelau Island Migrant Study.

The migration of Tokelauans from a traditional atoll in the Pacific to urban New Zealand is associated with an increased prevalence and incidence of Type 2 (non-insulin-dependent) diabetes mellitus over the period 1968-1982. During the same period, a lesser but definite increase is seen among non-migrants in Tokelau. The age standardised prevalence rates rose from 7.5 and 11.7 to 10.8 and 19.9 per 100 respectively in the male and female migrants compared with an increase from 3.0 and 8.7 to 7.0 and 14.3 per 100 in the non-migrant males and females respectively. The incidence of diabetes is shown to be consistently higher in the migrants compared to the non-migrants giving relative risks of 1.5 in males and 1.9 in females. The factors most likely contributing to this difference, are changes to a higher calorie, high protein diet, higher alcohol consumption, a greater weight gain and altered levels of physical activity in the migrants. A number of populations in the Pacific have been shown to have a low rate of diabetes in their traditional setting, but may have a genetic predisposition for diabetes which responds to factors in the urban industrialised environment and life-style. The social and economic changes taking place in Tokelau are also clearly increasing the risk of diabetes. To reverse these trends and prevent the development of complications of Type 2 diabetes, it will be important to institute preventive programmes and to follow up the population in both environments for long-term outcomes, including mortality.

Effects of sodium dodecylsulphate, dye concentration and paraprotein on coomassie blue dye-binding assays for protein in urine.

Various Coomassie Blue reagents, containing either increased dye concentration or added sodium dodecylsulphate, were compared with a biuret method for the assay of total protein in urine. When immunoglobulin free light chain protein or immunoglobulin paraprotein were present, results from the Coomassie Blue methods were up to 50% lower than with the biuret method; increased dye concentration did not improve comparability substantially, but the addition of sodium dodecylsulphate reduced the bias to about 20%. When neither free light chain protein nor immunoglobulin paraprotein was present, results from the Coomassie Blue methods were only about 30% lower. The addition of sodium dodecylsulphate reduced this bias to 10%. Correlations between the biuret and the Coomassie Blue method were best when the Coomassie Blue reagent contained 40 mg/L sodium dodecylsulphate (r better than 0.98 in all groups; p less than 0.001).

Migration and gout: the Tokelau Island migrant study.

The prevalence and 14 year incidence of clinical gout and its precursors were investigated in the Polynesian population of Tokelauans living in the Pacific basin, non-migrant Tokelauans living in their isolated atoll homeland being compared with migrant Tokelauans living in urban New Zealand. The age standardised prevalence of gout in Tokelauan men in New Zealand was higher than that in non-migrant Tokelauan men, being 21.0 and 19.5/1000 subjects at the beginning of the study and 51.0 and 14.6/1000 at the end of study, respectively. Migrant men in New Zealand aged under 55 had higher mean serum uric acid concentrations than non-migrant men of the same age. The prevalence of gout was low in women in both environments. The age standardised relative risk of developing gout between 1968 and 1982 was 9.0 times higher in the migrant men than in the non-migrant men. Age, serum uric acid concentration, serum cholesterol concentration, and self reported alcohol consumption at entry to the study were the best set of predictors of gout in men. Preventive strategies to change body mass, diet, and patterns of alcohol use need to be developed in this population.

Stability of total cholesterol, high-density-lipoprotein cholesterol, and triglycerides in frozen sera.

When human serum must be stored for extended periods before analysis, conditions must be such that samples give results comparable with those for "fresh" (unstored) samples. In a balanced experiment with statistically pre-determined sample size, we assessed, at three-weekly intervals for 18 weeks, the stability of total cholesterol, high-density-lipoprotein cholesterol, and triglycerides in human serum stored at -15 degrees C. No significant changes were observed.

The health status of fourth form students in Northland.

A random sample of fourth form students throughout Northland was studied. Uncorrected visual defects were found in 4.5% and significant hearing loss in 9.1%. Appreciable numbers were overweight; 6.2% of boys and 22.5% of girls exceeded the desirable bulk index range. Levels of total cholesterol appear decreased compared to earlier New Zealand studies and were significantly lower than the Wairoa College survey levels. There was a strong correlation between total cholesterol and low density lipoprotein cholesterol. High density lipoprotein cholesterol was significantly higher in non-Maori than in Maori girls. Overall systolic blood pressure for boys at 114.3 mmHg (15.2 kPa) was significantly higher than for girls at 109.5 mm Hg (14.56 kPa). One-third of boys exceeded the adult uric acid reference range; a significantly higher proportion than for girls. Fifteen point one percent of boys and 23.5% of girls reported smoking seven or more cigarettes per week; 19.1% of boys and 9% of girls reported taking regular amounts of alcohol at least every weekend.