Mathematical modelling of tumour acidity

Acid-mediated tumour invasion is receiving increasing experimental and clinical attention. Previous models proposed to describe this phenomenon failed to capture key properties of the system, such as the existence of the benign steady state, or predicted incorrectly the size of the inter-tissue gap. Here we show that taking proper account of quiescence ameliorates these drawbacks as well as revealing novel behaviour. The simplicity of the model allows us to fully identify the key parameters controlling different aspects of behaviour.     

The role of acidity in solid tumour growth and invasion

Acidic pH is a common characteristic of human tumours. It has a significant impact on tumour progression and response to therapies. In this paper, we develop a simple model of three-dimensional tumour growth to examine the role of acidosis in the interaction between normal and tumour cell populations. Both vascular and avascular tumour dynamics are investigated, and a number of different behaviours are observed. Whilst an avascular tumour always proceeds to a benign steady state, a vascular tumour may display either benign or invasive dynamics, depending on the value of a critical parameter. Analysis of the model allows us to assess novel therapies directed towards changing the level of acidity within the tumour.     

Computational analysis of the influence of the microenvironment on carcinogenesis

The tumour microenvironment is known to play an important role in determining the sequence of acquired phenotypic traits that characterise cancer evolution. A more precise understanding of this role could have a major influence in the understanding of cancer growth and development, and potentially in the optimisation of innovative anti-cancer treatments delivery. However, to lead such an analysis in the basis of traditional biological experiments and observations is almost utopian given the complexity of the underlying biological processes and the typical time scales involved. In this context, computer models constitute a complementary exploratory tool.In this paper we introduce a two-dimensional cellular automaton that models key cancer cell capabilities. The model has been especially designed to mimic the behaviour of a cancer colony growing in vitro and to analyse the effect of different environmental conditions on the sequence of acquisition of phenotypic traits. Our results indicate that microenvironmental factors such as the local concentration of oxygen or nutrients and cell overcrowding may determine the expansion of the tumour colony. The results also show that tumour cells evolve and that their phenotypes adapt to the microenvironment so that environmental stress determines the dominance of particular phenotypical traits.     

Spontaneous behavioural changes in response to epidemics

We study how spontaneous reduction in the number of contacts could develop, as a defensive response, during an epidemic and affect the course of infection events. A model is proposed which couples an SIR model with selection of behaviours driven by imitation dynamics. Therefore, infection transmission and population behaviour become dynamical variables that influence each other. In particular, time scales of behavioural changes and epidemic transmission can be different. We provide a full qualitative characterization of the solutions when the dynamics of behavioural changes is either much faster or much slower than that of epidemic transmission. The model accounts for multiple outbreaks occurring within the same epidemic episode. Moreover, the model can explain “asymmetric waves”, i.e., infection waves whose rising and decaying phases differ in slope. Finally, we prove that introduction of behavioural dynamics results in the reduction of the final attack rate.     

Overexpression of PDGFA and its receptor during carcinogenesis of Opisthorchis viverrini-associated cholangiocarcinoma

Cholangiocarcinoma (CCA) is a crucial health problem in northeastern part of Thailand, which is caused by a combination of Opisthorchis viverrini infection and nitrosamine. A better understanding of its molecular mechanism is an important step to discover and develop the new diagnostics and therapies for CCA. To reveal the involvement of potential genes in the development of CCA, the present study investigated the expression kinetics of platelet-derived growth factor alpha (Pdgfa) and its receptor (Pdgfra) during the tumorigenesis of CCA induced by O. viverrini infection with quantitative RT-PCR, and confirmed the expression with immunohistological staining. The results showed that in the hamster model of opisthorchiasis-associated CCA, the expression of Pdgfa was increased after infection plus N-nitrosodimethylamine (NDMA) administration, reached its peak at 2 months post infection, and remained at the high level until 6 months. Similarly, the expression of Pdgfra was increased time-dependently. The positive immunostaining for PDGFA proteins was observed in the cytoplasm of epithelial tumor cells of hamster CCA. Moreover, the analysis of the expression of these genes in 10 cases of human opisthorchiasis-associated CCA showed that Pdgfa was overexpressed in 80%, and Pdgfra was overexpressed in 40% cases (> 3.0 folds, compared with the expressions of adjacent normal tissues). This result suggests that PDGFA is likely involved in the tumorigenesis of opisthorchiasis-associated CCA, and may be a promising candidate biomarker for diagnosis and treatment strategies of CCA.     

Evaluation of mitochondrial function and metabolic reprogramming during tumor progression in a cell model of skin carcinogenesis

Metabolic reprogramming from mitochondrial aerobic respiration to aerobic glycolysis is a hallmark of cancer. However, whether it is caused by a dysfunction in the oxidative phosphorylation pathway is still under debate. In this work, we have analyzed the bioenergetic cellular (BEC) index and the relative cell ability to grow in the presence of either galactose or glucose as sources of sugar (Gal/Glu index) of a system formed by four epidermal cell lines with increasing tumorigenic potentials, ranging from nontumorigenic to highly malignant. We find that the BEC index gradually decreases whereas the Gal/Glu index increases with tumorigenicity, indicating that a progressive metabolic adaptation to aerobic glycolysis occurs in tumor cells associated with malignancy. Interestingly, this metabolic adaptation does not appear to be caused by damaged respiration, since the expression and activity of components of the respiratory chain complexes were unchanged in the cell lines. Moreover, the corresponding mitochondrial ATP synthetic abilities of the cell lines were found similar. The production of reactive oxygen species was also measured. A shift in ROS generation was found when compared nontumorigenic with tumorigenic cell lines, the latter exhibiting about threefold higher ROS levels than nontumorigenic cells. This result indicates that oxidative stress is an early event during tumor progression.     

Mechanism of arsenic carcinogenesis: an integrated approach

Epidemiological evidence shows an association between inorganic arsenic in drinking water and increased risk of skin, lung and bladder cancers. The lack of animal models has hindered mechanistic studies of arsenic carcinogenesis in the past, but some promising new models for these cancers are now available. The various forms of arsenic to which humans are exposed, either directly or via metabolism of inorganic arsenic to various methylated forms, further complicate the issue of mechanism, since these compounds can have different effects, both genotoxic and non-genotoxic. This review will try to integrate all of these issues, with a strong bias toward effects that are produced by environmentally relevant arsenic concentrations.     

Store-operated Ca channels in prostate cancer epithelial cells: function, regulation, and role in carcinogenesis

Ca²⁺ homeostasis mechanisms, in which the Ca²⁺ entry pathways play a key role, are critically involved in both normal function and cancerous transformation of prostate epithelial cells. Here, using the lymph node carcinoma of the prostate (LNCaP) cell line as a major experimental model, we characterize prostate-specific store-operated Ca²⁺ channels (SOCs)—a primary Ca²⁺ entry pathway for non-excitable cells—for the first time. We show that prostate-specific SOCs share major store-dependent, kinetic, permeation, inwardly rectifying, and pharmacological (including dual, potentiation/inhibition concentration-dependent sensitivity to 2-APB) properties with “classical” Ca²⁺ release-activated Ca²⁺ channels (CRAC), but have a higher single channel conductance (3.2 and 12 pS in Ca²⁺- and Na⁺-permeable modes, respectively). They are subject to feedback inhibition via Ca²⁺-dependent PKC, CaMK-II and CaM regulatory pathways and are functionally dependent on caveolae integrity. Caveolae also provide a scaffold for spatial co-localization of SOCs with volume-regulated anion channels (VRAC) and their Ca²⁺-mediated interaction. The TRPC1 and TRPV6 members of the transient receptor potential (TRP) channel family are the most likely molecular candidates for the formation of prostate-specific endogenous SOCs. Differentiation of LNCaP cells to an androgen-insensitive, apoptotic-resistant neuroendocrine phenotype downregulates SOC current. We conclude that prostate-specific SOCs are important determinants in the transition to androgen-independent prostate cancer.     

The CD95/CD95L signaling pathway: A role in carcinogenesis

Apoptosis is a fundamental process that contributes to tissue homeostasis, immune responses, and development. The receptor CD95, also called Fas, is a member of the tumor necrosis factor receptor (TNF-R) superfamily. Its cognate ligand, CD95L, is implicated in immune homeostasis and immune surveillance, and various lineages of malignant cells exhibit loss-of-function mutations in this pathway; therefore, CD95 was initially classified as a tumor suppressor gene. However, more recent data indicate that in different pathophysiological contexts, this receptor can transmit non-apoptotic signals, promote inflammation, and contribute to carcinogenesis. A comparison with the initial molecular events of the TNF-R signaling pathway leading to non-apoptotic, apoptotic, and necrotic pathways reveals that CD95 is probably using different molecular mechanisms to transmit its non-apoptotic signals (NF-κB, MAPK, and PI3K). As discussed in this review, the molecular process by which the receptor switches from an apoptotic function to an inflammatory role is unknown. More importantly, the biological functions of these signals remain elusive.     

Effects of selenium on chemical carcinogenesis

Chemical carcinogenesis can be characterized by a sequence of events leading to the development of tumors. Selenium (Se) inhibition of colon, liver, and lung carcinogens is demonstrated. Using the male Sprague Dawley rat model Se inhibited the colon tumor incidence in 1,2-dimethylhydrazine (DMH) treated rats and reduced the total number of colon tumors in methylazoxymethanol (MAM) treated rats. Selenium inhibited 2-acetylaminofluorene (AAF) and 3′-methyl-4-dimethylaminoazobenzene (3′-MeDAB) hepatocarcinogenesis. The hepatic tumor incidence induced by 3′-MeDAB was reduced by both inorganic Se (Na₂SeO₃) and by organic Se (Se-yeast) supplements. In vitro systems have been studied in an effort to decipher the inhibitory properties of Se on the multistage origin of tumors induced by chemical carcinogens. Current studies suggest that the protective effect of Se against AAF hepatocarcinogenesis may be correlated with a change in AAF metabolism. The mutagenicity of AAF and AAF metabolites inSalmonella typhimurium TA1538 is decreased by Se. Additionally, Se reduced N-t-OH−AAF induction of sister chromatid exchange (SCE) frequencies in whole blood cultures, and also reduced aryl hydrocarbon hydroxylase activity using benzo(a) pyrene as substrate. The comparative effects of antioxidants on DMH induction of colon tumors are presented in detail. Supplements of 4 ppm Se to the drinking water, 1.2% ascorbic acid (V _c ) to the diet or 0.5% butylated hydroxytoluene (BHT) to the diet of DMH-treated rats reduced the colon tumor incidence of DMH controls from 64 to 31% (Se), 38% (V _c ), and 43% (BHT). The colon tumor incidence in DMH-treated rats receiving a combination of Se+V _c increased to 83%, while the combination of Se+BHT decreased the colon tumor incidence to 55%. The growth and survival of rats provided long-term supplements of 4 ppm Se in the drinking water are compared with untreated controls.     

Travelling waves and EEG patterns during epileptic seizure: analysis with an integrate-and-fire neural network

Epilepsy is characterized by paradoxical patterns of neural activity. They may cause different types of electroencephalogram (EEG), which dynamically change in shape and frequency content during the temporal evolution of seizure. It is generally assumed that these epileptic patterns may originate in a network of strongly interconnected neurons, when excitation dominates over inhibition. The aim of this work is to use a neural network composed of 50 x 50 integrate-and-fire neurons to analyse which parameter alterations, at the level of synapse topology, may induce network instability and epileptic-like discharges, and to study the corresponding spatio-temporal characteristics of electrical activity in the network. We assume that a small group of central neurons is stimulated by a depolarizing current (epileptic focus) and that neurons are connected via a Mexican-hat topology of synapses. A signal representative of cortical EEG (ECoG) is simulated by summing the membrane potential changes of all neurons. A sensitivity analysis on the parameters describing the synapse topology shows that an increase in the strength and in spatial extension of excitatory vs. inhibitory synapses may cause the occurrence of travelling waves, which propagate along the network. These propagating waves may cause EEG patterns with different shape and frequency, depending on the particular parameter set used during the simulations. The resulting model EEG signals include irregular rhythms with large amplitude and a wide frequency content, low-amplitude high-frequency rapid discharges, isolated or repeated bursts, and low-frequency quasi-sinusoidal patterns. A slow progressive temporal variation in a single parameter may cause the transition from one pattern to another, thus generating a highly non-stationary signal which resembles that observed during ECoG measurements. These results may help to elucidate the mechanisms at the basis of some epileptic discharges, and to relate rapid changes in EEG patterns with the underlying alterations at the network level.     

The impact of demographic changes on the epidemiology of herpes zoster: Spain as a case study

Varicella zoster virus (VZV) causes varicella upon first exposure and may reactivate later in life into herpes zoster (HZ), with a risk that is thought to be reduced by re-exposures to VZV. Given the decades-long time scales of reactivation and its dependence on the accumulation of re-exposure episodes, adopting a long-term perspective may be useful to correctly interpret current epidemiological trends of VZV. In this study, we investigate the possible impact of demographic changes on varicella and HZ in Spain, using an age-structured mathematical model informed with historical demographic data and calibrated against age-specific profiles of varicella seroprevalence and HZ incidence data. The model qualitatively reproduces the remarkable growth of HZ incidence observed in Spain between 1997 and 2004, before the introduction of varicella vaccination programmes. We demonstrate that this growth may be partially ascribed to the reduction of varicella circulation that followed the overall decline of the birth rate in the twentieth century. Model predictions further suggest that, even under the most optimistic projections, HZ incidence will continue its rise until at least 2040. Considering the effect of demographic changes can help interpreting variations in epidemiological trends of HZ, contributing to a more accurate evaluation of vaccination programmes against VZV.     

Viral defense, carcinogenesis and ISG15: novel roles for an old ISG

Recent studies have established that type I interferon modulates expression of large number of cellular genes. While the proteins encoded by some of these genes have a direct antiviral activity, the functions of the majority of the others have not yet been determined. One of the first identified IFN stimulated gene, encodes ubiquitin like protein ISG15 that is also expressed in response to different stress stimuli. Although it was shown that ISG15 functions as protein modifier, it has been only recently that the targets of ISG15 conjugation were identified. Recent studies have also revealed mechanism of ISG15 conjugation and its interaction with the ubiquitin conjugation pathway. This review is focused on the possible role of ISG15 in the antiviral response, regulation of cell growth and carcinogenesis.     

Prediction of upper extremity impact forces during falls on the outstretched hand

Among the most common causes of upper extremity fracture is a fall on the outstretched hand. Yet few data exist on the biomechanical factors which affect injury risk during this event. In this study, we measured impact forces during low-height (0–5 cm), forward falls onto the outstretched hand, and found that these are governed by an initial high-frequency peak and a subsequent, lower-frequency oscillation. This behavior was well-simulated by a two-degree-of-freedom, lumped-parameter mathematical model. Increases in body mass caused greater increases in the peak magnitude of the low-frequency component (F_max2) than the high-frequency component (F_max1). However, increases in fall height more strongly influenced F_max1, which exceeded F_max2 for all but very low fall heights. Model predictions suggest that fall heights greater than 0.6 m carry significant risk for wrist fracture, since above this height, peak forces surpass the average fracture force of the distal radius. Finally, while the shoulder experiences lower peak force than the wrist (since F_max1 is not transmitted proximally), it undergoes considerably greater deflection, and thereby absorbs the majority of impact energy during a fall.     

Differential survival of Venus gallina and Scapharca inaequivalvis during anoxic stress: Covalent modification of phosphofructokinase and glycogen phosphorylase during anoxia

Summary Biochemical mechanisms underlying anaerobiosis were assessed in two Mediterranean bivalve species, Scapharca inaequivalvis and Venus gallina, with widely differing tolerances for oxygen lack. These species displayed LT₅₀ values for anoxic survival at 17–18°C of 17 and 4 d, respectively. Succinate and alanine were the major products of 24 h anaerobic metabolism in both species but only S. inaequivalvis further metabolized succinate to propionate. Both species reduced metabolic rate while anoxic but metabolic arrest was more pronounced in S. inaequivalvis. Calculated ATP turnover rate (MATP) during exposure to N₂-bubbled seawater was only 4.51% of the aerobic rate in S. inaequivalvis but was 12.68% in V. gallina. To counteract a greater load of acid end products, V. gallina foot showed a significantly greater buffering capacity, 23.38±0.20 slykes, compared to 19.6±0.79 slykes in S. inaequivalvis. The two species also differed distinctly in the enzymatic regulation of anaerobiosis. In V. gallina anoxia exposure caused only a small change in PFK kinetic parameters (a decrease in K_a AMP) and had no effect on glycogen phosphorylase. By contrast, S. inaequivalvis foot showed a strong modification of enzyme properties in anoxia. The percentage of glycogen phosphorylase in the a form dropped significantly only in S. inaequivalvis. Other changes included alterations in the properties of PFK leading to a less active enzyme form in anoxia. Compared to the aerobic enzyme form, PFK from anoxic foot showed a reduced affinity for fructose-6-P (K_m increased 2.4-fold), greater inhibition by ATP (I₅₀ decreased 6.8-fold), and an increase in sensitivity to AMP activation (K_a decreased by 50%). These enzyme changes appear to be key to a glycolytic rate depression during anaerobiosis in S. inaequivalvis foot muscle.Abbreviations EDTA ethylenediaminetetraacetic acid - EGTA ethyleneglycol-bis-(2-aminoethyl)-tetraacetic acid - Fructose-2,6-P ₂ fructose-2,6-bisphosphate - Fructose-6-P fructose-6-phosphate - K _a AMP Activation constant (concentration of AMP required to increase the reaction to twice the rate it shows in the absence of AMP) - MATP ATP turnover rate - P _i inorganic phosphate - PCA Perchloric acid - PFK 6-phosphofructo-1-kinase - TCA Trichloroacetic acid     

Triose phosphate isomerase from the blood fluke Schistosoma mansoni: Biochemical characterisation of a potential drug and vaccine target

The glycolytic enzyme triose phosphate isomerase from Schistosoma mansoni is a potential target for drugs and vaccines. Molecular modelling of the enzyme predicted that a Ser-Ala-Asp motif which is believed to be a helminth-specific epitope is exposed. The enzyme is dimeric (as judged by gel filtration and cross-linking), resistant to proteolysis and highly stable to thermal denaturation (melting temperature of 82.0 °C). The steady-state kinetic parameters are high (K_m for dihydroxyacetone phosphate is 0.51 mM; K_m for glyceraldehyde 3-phosphate is 1.1 mM; k_cat for dihydroxyacetone phosphate is 7800 s⁻¹ and k_cat for glyceraldehyde 3-phosphate is 6.9 s⁻¹).