A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease

A previously published mathematical model, governing tumour growth with mixed immunotherapy and chemotherapy treatments, is modified and studied. The search time, which is assumed to be neglectable in the previously published model, is incorporated into the functional response for tumour-cell lysis by effector cells. The model exhibits bistability where a tumour-cell population threshold exists. A tumour with an initial cell population below the threshold can be controlled by the immune system and remains microscopic and asymptomatic called cancer without disease while that above the threshold grows to lethal size. Bifurcation analysis shows that (a) the chemotherapy-induced damage may cause a microscopic tumour, which would never grow to become lethal if untreated, to grow to lethal size, (b) applying chemotherapy alone requires a large dosage to be successful, (c) immunotherapy is ineffective, and (d) a combination of chemotherapy and immunotherapy can produce a synergistic effect on the outcome of a treatment.     

The concepts of ‘plant functional types’ and ‘functional diversity’ in lake phytoplankton – a new understanding of phytoplankton ecology?

1. This is a discussion of the applicability to the phytoplankton of the concepts of ‘plant functional types’ (PFTs) and ‘functional diversity’ (FD), which originated in terrestrial plant ecology. 2. Functional traits driving the performance of phytoplankton species reflect important processes such as growth, sedimentation, grazing losses and nutrient acquisition. 3. This paper presents an objective, mathematical way of assigning PFTs and measuring FD. Ecologists can use this new approach to investigate general hypotheses [e.g. the intermediate disturbance hypothesis (IDH), the insurance hypothesis and synchronicity phenomena] as, for example, in its original formulation the IDH makes its predictions based on FD rather than species diversity.     

Competition patterns among phytoplankton functional groups: How useful are the complex mathematical models?

Simple models have significant contribution to the development of ecological theory. However, these minimalistic modeling approaches usually focus on a small subset of the causes of a phenomenon and neglect important aspects of system dynamics. In this study, we use a complex aquatic biogeochemical model to examine competition patterns and structural shifts in the phytoplankton community under nutrient enrichment conditions. Our model simulates multiple elemental cycles (org. C, N, P, Si, O), multiple functional phytoplankton (diatoms, green algae and cyanobacteria) and zooplankton (copepods and cladocerans) groups. It also takes into account recent advances in stoichiometric nutrient recycling theory, and the zooplankton grazing term is reformulated to include algal food quality effects on zooplankton assimilation efficiency. The model provided a realistic platform to examine the functional properties (e.g., kinetics, growth strategies, intracellular storage capacity) and the abiotic conditions (temperature, nutrient loading) under which the different phytoplankton groups can dominate or can be competitively excluded in oligo, meso and eutrophic environments. Based on the results of our analysis, the intergroup variability in the minimum cell quota and maximum transport rate at the cell surface for phosphorus along with the group-specific metabolic losses can shape the structure of plankton communities. We also use classification tree analysis to elucidate aspects (e.g., relative differences in the functional group properties, critical values of the abiotic conditions, levels of the other plankton community residents) of the complex interplay among physical, chemical and biological factors that drive epilimnetic plankton dynamics. Finally, our study highlights the importance of improving the mathematical representation of phytoplankton adaptive strategies for resources procurement (e.g., regulation of transport kinetics, effects of transport kinetics on the kinetics of assimilation, relationship between assimilation and growth) to effectively link variability at the organismal level with ecosystem-scale patterns.     

Dynamics of variable-yield nutrient–phytoplankton–zooplankton models with nutrient recycling and self-shading

 Several nutrient–phytoplankton–zooplankton models with internal nutrient storage by phytoplankton are derived and analyzed. It is shown that there are thresholds beyond which the system is uniformly persistent. Variable-yield models with self-shading of phytoplankton are also considered. With respect to uniform persistence, our result demonstrates that the global dynamics of the system with shading are the same as those for which the self-shading mechanism is ignored. Received: 16 March 1999     

Global analysis of a stoichiometric producer–grazer model with Holling type functional responses

Cells, the basic units of organisms, consist of multiple essential elements such as carbon, nitrogen, and phosphorus. The scarcity of any of these elements can strongly restrict cellular and organismal growth. During recent years, ecological models incorporating multiple elements have been rapidly developed in many studies, which form a new research field of mathematical and theoretical biology. Among these models, the one proposed by Loladze et al. (Bull Math Biol 62:1137–1162, 2000) is prominent and has been highly cited. However, the global analysis of this nonsmooth model has never been done. The aim of this paper is to provide the complete global analysis for the model with Holling type I functional response and perform a bifurcation analysis for the model with Holling type II functional response.     

A differential scanning calorimetry study of the interaction of α-tocopherol with mixtures of phospholipids

(1) When α-tocopherol was included in multibilayer vesicles of dimyristoylphosphatidylcholine, dipalmitoylphosphatidylcholine and distearoylphosphatidylcholine it induced a broadening of the main transition and a displacement of this transition to lower temperatures, as seen by differential scanning calorimetry. This effect was quantitatively more important in the samples of distearoylphosphatidylcholine than in those of the other phosphatidylcholines. (2) α-Tocopherol when present in equimolar mixtures of dimyristoylphosphatidylcholine and diastearoylphosphatidylcholine, which show monotectic behaviour, preferentially partitions in the most fluid phase. (3) The effect of α-tocopherol on the phase transition of dilauroylphosphatidylethanolamine and dipalmitoylphosphatidylethanolamine is qualitatively different of that observed on phosphatidylcholines, and several peaks are observed in the calorimetric profile, probably indicating the formation of separated phases with different contents in α-tocopherol. The effect was more apparent in dipalmitoylphosphatidylethanolamine than in dilauroylphosphatidylethanolamine. (4) The inclusion of α-tocopherol in equimolar mixtures of dilauroylphosphatidylethanolamine and dipalmitoylphosphatidylcholine, which show cocrystallization, only produced a broadening of the phase transition and a shift to lower temperatures. However, in the case of equimolar mixtures of dipalmitoylphosphatidylcholine which also show cocrystallization, the effect was to cause lateral phase separation with the formation of different mixtures of phospholipids and α-tocopherol. (5) α-Tocopherol was also included in equimolar mixtures of phosphatidylethanolamine and phosphatidylcholine showing monotectic behaviour, and in this case α-tocopherol preferentially partitioned in the most fluid phase, independently of whether this was composed mainly of phosphatidylcholine or of phosphatidylethanolamine.     

TG–FTIR study on co-pyrolysis of municipal solid waste with biomass

Co-pyrolysis of cotton stalk, a representative agricultural biomass in China, mixed with municipal solid waste (MSW) with high ash content and low calorific value was carried out using a thermogravimetric analyzer (TGA) coupled with a Fourier transform infrared (FTIR) spectrometer in Ar atmosphere. Pyrolysis characteristic and pollutant emission performance from MSW and stalk blends at different mass proportions were studied. The results show that as the mass proportion of stalk added increases, the total weight loss of the blend during pyrolysis increases. The addition of stalk has substantial effects on the N-selectivity to HCN, NH₃ and HNCO. In the presence of stalk, lower concentrations of HCl are detected.     

Bone marrow–mesenchymal stromal cell infusion in patients with chronic kidney disease: A safety study with 18 months of follow-up

Background

Chronic kidney disease (CKD) is a progressive loss of kidney function and structure that affects approximately 13% of the population worldwide. A recent meta-analysis revealed that cell-based therapies improve impaired renal function and structure in preclinical models of CKD. We assessed the safety and tolerability of bone marrow–mesenchymal stromal cell (MSC) infusion in patients with CKD.

Permanence of a predator–prey discrete system with Holling-IV functional response and distributed delays

A predator–prey discrete-time model with Holling-IV functional response and distributed delays is investigated in this paper. By using the comparison theorem of the difference equation and some analysis technique, some sufficient conditions are obtained for the permanence of the discrete predator–prey system. Two examples are given to illustrate the feasibility of the obtained result.     

On the dynamics of one-prey-n-predator impulsive reaction-diffusion predator–prey system with ratio-dependent functional response

In this paper, a one-prey-n-predator impulsive reaction-diffusion periodic predator–prey system with ratio-dependent functional response is investigated. On the basis of the upper and lower solution method and comparison theory of differential equation, sufficient conditions on the ultimate boundedness and permanence of the predator–prey system are established. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Examples and numerical simulations are presented to verify the feasibility of our results. A discussion is conducted at the end.     

Anticancer activity of natural cytokinins: A structure–activity relationship study

Cytokinin ribosides (N⁶-substituted adenosine derivatives) have been shown to have anticancer activity both in vitro and in vivo. This study presents the first systematic analysis of the relationship between the chemical structure of cytokinins and their cytotoxic effects against a panel of human cancer cell lines with diverse histopathological origins. The results confirm the cytotoxic activity of N⁶-isopentenyladenosine, kinetin riboside, and N⁶-benzyladenosine and show that the spectrum of cell lines that are sensitive to these compounds and their tissues of origin are wider than previously reported. The first evidence that the hydroxylated aromatic cytokinins (ortho-, meta-, para-topolin riboside) and the isoprenoid cytokinin cis-zeatin riboside have cytotoxic activities is presented.Most cell lines in the panel showed greatest sensitivity to ortho-topolin riboside (IC₅₀ = 0.5–11.6 μM). Cytokinin nucleotides, some synthesized for the first time in this study, were usually active in a similar concentration range to the corresponding ribosides. However, cytokinin free bases, 2-methylthio derivatives and both O- and N-glucosides showed little or no toxicity. Overall the study shows that structural requirements for cytotoxic activity of cytokinins against human cancer cell lines differ from the requirements for their activity in plant bioassays. The potent anticancer activity of ortho-topolin riboside (GI₅₀ = 0.07–84.60 μM, 1st quartile = 0.33 μM, median = 0.65 μM, 3rd quartile = 1.94 μM) was confirmed using NCI₆₀, a standard panel of 59 cell lines, originating from nine different tissues. Further, the activity pattern of oTR was distinctly different from those of standard anticancer drugs, suggesting that it has a unique mechanism of activity. In comparison with standard drugs, oTR showed exceptional cytotoxic activity against NCI₆₀ cell lines with a mutated p53 tumour suppressor gene. oTR also exhibited significant anticancer activity against several tumour models in in vivo hollow fibre assays.     

Accommodation of tmRNA–SmpB into stalled ribosomes: A cryo-EM study

In eubacteria, translation of defective messenger RNAs (mRNAs) produces truncated polypeptides that stall on the ribosome. A quality control mechanism referred to as trans-translation is performed by transfer-messenger RNA (tmRNA), a specialized RNA acting as both a tRNA and an mRNA, associated with small protein B (SmpB). So far, a clear view of the structural movements of both the protein and RNA necessary to perform accommodation is still lacking. By using a construct containing the tRNA-like domain as well as the extended helix H2 of tmRNA, we present a cryo-electron microscopy study of the process of accommodation. The structure suggests how tmRNA and SmpB move into the ribosome decoding site after the release of EF-Tu·GDP. While two SmpB molecules are bound per ribosome in a preaccommodated state, our results show that during accommodation the SmpB protein interacting with the small subunit decoding site stays in place while the one interacting with the large subunit moves away. Relative to canonical translation, an additional movement is observed due to the rotation of H2. This suggests that the larger movement required to resume translation on a tmRNA internal open reading frame starts during accommodation.     

A causal C–A mutation in the second exon of GS3 highly associated with rice grain length and validated as a functional marker

Comparative sequencing of GS3, the most important grain length (GL) QTL, has shown that differentiation of rice GL might be principally due to a single nucleotide polymorphism (SNP) between C and A in the second exon. A total of 180 varieties representing a wide range of rice germplasm were used for association analysis between C–A mutation and GL in order to confirm the potential causal mutation. A cleaved amplified polymorphic sequence (CAPS) marker, SF28, was developed based on the C–A polymorphism in the GS3 gene. A total of 142 varieties carried allele C with GL from 6.4 to 8.8 mm, while the remaining 38 varieties carried allele A with GL from 8.8 to 10.7 mm. Twenty-four unlinked SSR markers were selected to genotype 180 varieties for population structure analysis. Population structure was observed when the population was classified to three subpopulations. Average GL of either genotype A or genotype C within japonica among the three subpopulations had no significant difference from that in indica, respectively, although indica rice had longer grains on average than japonica in the 180 varieties. However, genotype C always had longer grain length on average than genotype A among three subpopulations. The mutation could explain 79.1, 66.4 and 34.7% of GL variation in the three subpopulations, respectively. These results clearly confirmed the mutation between C and A was highly associated with GL. The SF28 could be a functional marker for improvement of rice grain length.     

Density functional study of H<Subscript>2</Subscript>O molecule adsorption on α-U(001) surface

Periodic density functional theory (DFT) calculations were performed to investigate the adsorption of H₂O on U(001) surface. The metallic nature of uranium atom and different adsorption sites of U(001) surface play key roles in the H₂O molecular dissociate reaction. The long-bridge site is the most favorable site of H₂O-U(001) adsorption configuration. The triangle-center site of the H atom is the most favorable site of HOH-U(001) adsorption configuration. The interaction between H₂O and U surface is more evident on the first layer than that on any other two sub-layers. The dissociation energy of one hydrogen atom from H₂O is ?1.994 to ?2.215 eV on U(001) surface, while the dissociating energy decreases to ?3.351 to ?3.394 eV with two hydrogen atoms dissociating from H₂O. These phenomena also indicate that the O_ads can promote the dehydrogenation of H₂O. A significant charge transfer from the first layer of the uranium surface to the H and O atoms is also found to occur, making the bonding partly ionic.     

Strength of phytoplankton–nutrient relationship: evidence from 13 biomanipulated ponds

Phytoplankton biomass–nutrient relationship is widely used by lake managers to assess the eutrophication impact and to set the nutrient targets. Submerged vegetation and large zooplankton grazing have long been identified as factors weakening the relationship by decoupling phytoplankton from nutrients. Proving this decoupling unambiguously is difficult because, in natural systems, many factors act together, blurring each other’s effect. In this article, we present the results of continuous monitoring of 13 ponds where the effects of submerged vegetation and zooplankton grazing were enhanced by biomanipulation (fish removal). The monitoring allowed these effects to be assessed and compared with the pre-biomanipulation situations when phytoplankton biomass was mainly nutrient driven. The comparison showed a strong weakening effect of submerged vegetation and large zooplankton grazing on the chlorophyll a–total phosphorus relationship suggesting that a considerable degree of ecological quality of ponds affected by eutrophication can be restored even when nutrient-loading reduction is not feasible.