Mathematical models for optimizing tumour radiotherapy. I: A simple two compartment cell-kinetic model for the unperturbed growth of transplantable tumours

Tumour growth kinetics has been analysed on the basis of interactions between two compartments comprising the proliferating and non-proliferating cells. Starting from the differential equations of growth of the cell-populations in the two compartments and assuming the process of intercompartmental cell transfers to be linear, an analytic expression on the variation of growth-fraction with the age of the tumour is obtained. The restricted conditions on the cell-cycle time and cell-loss-rate, under which these differential equations lead to a Gompertzian growth of the tumour, are critically analysed. The formalism permits the estimation of some important cell-kinetic parameters, like growth-fraction or cell-loss-factor, from a knowledge of the tumour-growth curve, cell-cycle-time and a single measurement of the cell-loss-rate of the matured tumour, provided the tumour follows a Gompertzian growth. The validity of the model has been verified with the experimental data on 4 different transplantable murine tumour systems. Usefulness of the model has been demonstrated by making some interesting predictions regarding the radiation response of the tumours from the cell-kinetic parameters.     

Biodiversity effects and transgressive overyielding

Aims The potential for mixtures of plant species to produce more biomass than every one of their constituent species in monoculture is still controversially discussed in the literature. Here we tested how this so-called transgressive overyielding is affected by variation between and within species in monoculture yields in biodiversity experiments.Methods We use basic statistical principles to calculate expected maximum monoculture yield in a species pool used for a biodiversity experiment. Using a real example we show how between- and within-species variance components in monoculture yields can be obtained. Combining the two components we estimate the importance of sampling bias in transgressive overyielding analysis.Important findings The net biodiversity effect (difference between mixture and average monoculture yield) needed to achieve transgressive overyielding increases with the number of species in a mixture and with the variation between constituent species in monoculture yields. If there is no significant variation between species, transgressive overyielding should not be calculated using the best monoculture, because in this case the difference between this species and the other species could exclusively reflect a sampling bias. The sampling bias decreases with increasing variation between species. Tests for transgressive overyielding require replicated species' monocultures. However, it can be doubted whether such an emphasis on monocultures in biodiversity experiments is justified if an analysis of transgressive overyielding is not the major goal.     

Inhibition of Hb Binding to GP1bα Abrogates Hb-Mediated Thrombus Formation on Immobilized VWF and Collagen under Physiological Shear Stress

BackgroundReports including our own describe that intravascular hemolysis increases the risk of thrombosis in hemolytic disorders. Our recent study shows that plasma Hb concentrations correlate directly with platelet activation in patients with paroxysmal nocturnal hemoglobinuria (PNH). The binding of Hb to glycoprotein1bα (GP1bα) increases platelet activation. A peptide AA1-50, designed from N-terminal amino acid sequence of GP1bα significantly inhibits the Hb binding to GP1bα as well as Hb-induced platelet activation. This study further examined if the Hb-mediated platelet activation plays any significant role in thrombus formation on subendothelium matrix under physiological flow shear stresses and the inhibition of Hb-platelet interaction can abrogate the above effects of Hb.

Methods and Results

Study performed thrombus formation assay in vitro by perfusing whole blood over immobilized VWF or collagen type I in presence of Hb under shear stresses simulating arterial or venous flow. The Hb concentrations ranging from 5 to 10 μM, commonly observed level in plasma of the hemolytic patients including PNH, dose-dependently increased thrombus formation on immobilized VWF under higher shear stress of 25 dyne/cm², but not at 5 dyne/cm². The above Hb concentrations also increased thrombus formation on immobilized collagen under both shear stresses of 5 and 25 dyne/cm². The peptide AA1-50 abrogated invariably the above effects of Hb on thrombus formation.

Conclusions and Significance

This study therefore indicates that the Hb-induced platelet activation plays a crucial role in thrombus formation on immobilized VWF or collagen under physiological flow shear stresses. Thus suggesting a probable role of this mechanism in facilitating thrombosis under hemolytic conditions.     

Protective Role of Taurine against Arsenic-Induced Mitochondria-Dependent Hepatic Apoptosis via the Inhibition of PKCδ-JNK Pathway

Background

Oxidative stress-mediated hepatotoxic effect of arsenic (As) is mainly due to the depletion of glutathione (GSH) in liver. Taurine, on the other hand, enhances intracellular production of GSH. Little is known about the mechanism of the beneficial role of taurine in As-induced hepatic pathophysiology. Therefore, in the present study we investigated its beneficial role in As-induced hepatic cell death via mitochondria-mediated pathway.

Methodology/Principal Findings

Rats were exposed to NaAsO₂ (2 mg/kg body weight for 6 months) and the hepatic tissue was used for oxidative stress measurements. In addition, the pathophysiologic effect of NaAsO₂ (10 µM) on hepatocytes was evaluated by determining cell viability, mitochondrial membrane potential and ROS generation. As caused mitochondrial injury by increased oxidative stress and reciprocal regulation of Bcl-2, Bcl-xL/Bad, Bax, Bim in association with increased level of Apaf-1, activation of caspase 9/3, cleavage of PARP protein and ultimately led to apoptotic cell death. In addition, As markedly increased JNK and p38 phosphorylation with minimal disturbance of ERK. Pre-exposure of hepatocytes to a JNK inhibitor SP600125 prevented As-induced caspase-3 activation, ROS production and loss in cell viability. Pre-exposure of hepatocytes to a p38 inhibitor SB2035, on the other hand, had practically no effect on these events. Besides, As activated PKCδ and pre-treatment of hepatocytes with its inhibitor, rottlerin, suppressed the activation of JNK indicating that PKCδ is involved in As-induced JNK activation and mitochondrial dependent apoptosis. Oral administration of taurine (50 mg/kg body weight for 2 weeks) both pre and post to NaAsO₂ exposure or incubation of the hepatocytes with taurine (25 mM) were found to be effective in counteracting As-induced oxidative stress and apoptosis.

Conclusions/Significance

Results indicate that taurine treatment improved As-induced hepatic damages by inhibiting PKCδ-JNK signalling pathways. Therefore taurine supplementation could provide a new approach for the reduction of hepatic complication due to arsenic poisoning.     

Induction of necrosis in cadmium-induced hepatic oxidative stress and its prevention by the prophylactic properties of taurine

The present study has been carried out to investigate the protective role of taurine against cadmium (Cd)-induced oxidative impairment in murine liver. Oral administration of cadmium chloride (CdCl₂) at a dose of 4 mg/kg body weight for 6 days increased the accumulation of the Cd in the liver and diminished the liver weight to body weight ratio. The CdCl₂ altered the levels of intracellular trace elements, cofactors of various metalloenzymes and increased the activities of serum marker enzymes related to liver dysfunction. In addition, Cd intoxication also attenuated intracellular antioxidant power, the activities of antioxidant enzymes as well as the levels of cellular metabolites. Moreover, level of hepatic metallothionein, lipid peroxidation, protein carbonylation, DNA fragmentation, concentration of intracellular reactive oxygen species (ROS) and the activities of cytochrome P450s have been increased due to Cd toxicity. In addition to the oxidative impairments, Cd exposure caused hepatic cell death mainly via the necrotic pathway. Oral administration of taurine at a dose of 100 mg/kg body weight for 5 days prior to CdCl₂ intoxication prevented the alterations of all the toxic-induced hepatic damages. Histological studies also supported the beneficial role of taurine against Cd-induced hepatic damages. Combining all, results suggest that taurine could protect hepatic tissues against Cd-induced oxidative stress probably through its antioxidant activity.     

TLR4 and NKT Cell Synergy in Immunotherapy against Visceral Leishmaniasis

NKT cells play an important role in autoimmune diseases, tumor surveillance, and infectious diseases, providing in most cases protection against infection. NKT cells are reactive to CD1d presented glycolipid antigens. They can modulate immune responses by promoting the secretion of type 1, type 2, or immune regulatory cytokines. Pathogen-derived signals to dendritic cells mediated via Toll like Receptors (TLR) can be modulated by activated invariant Natural Killer T (iNKT) cells. The terminal β-(1–4)-galactose residues of glycans can modulate host responsiveness in a T helper type-1 direction via IFN-γ and TLRs. We have attempted to develop a defined immunotherapeutic, based on the cooperative action of a TLR ligand and iNKT cell using a mouse model of visceral leishmaniasis. We evaluated the anti-Leishmania immune responses and the protective efficacy of the β-(1–4)-galactose terminal NKT cell ligand glycosphingophospholipid (GSPL) antigen of L. donovani parasites. Our results suggest that TLR4 can function as an upstream sensor for GSPL and provoke intracellular inflammatory signaling necessary for parasite killing. Treatment with GSPL was able to induce a strong effective T cell response that contributed to effective control of acute parasite burden and led to undetectable parasite persistence in the infected animals. These studies for the first time demonstrate the interactions between a TLR ligand and iNKT cell activation in visceral leishmaniasis immunotherapeutic.