A Viscoelastic Traction Layer Model of Muco-Ciliary Transport

A new mathematical model of the transport of mucus and periciliary liquid (PCL) in the airways by cilia is presented. Mucus is represented by a linearly viscoelastic fluid, the mat of cilia is modelled as an ‘active porous medium.’ The propulsive effect of the cilia is modelled by a time-dependent force acting in a shear-thinned ‘traction layer’ between the mucus and the PCL. The effects of surface and interface tension are modelled by constraining the mucus free surface and mucus–PCL interface to be flat. It is assumed that the epithelium is impermeable to fluid. Using Fourier series, the system is converted into ODEs and solved numerically. We calculate values for mean mucus speed close to those observed by Matsui et~al. [{J. Clin. Invest.}, 102(6):1125–1131, 1998], (∽40 μms^-1). We obtain more detail regarding the dynamics of the flow and the nonlinear relationships between physical parameters in healthy and diseased states than in previously published models. Pressure gradients in the PCL caused by interface and surface tension are vital to ensuring efficient transport of mucus, and the role of the mucus–PCL interface appears to be to support such pressure gradients, ensuring efficient transport. Mean transport of PCL is found to be very small, consistent with previous analyses, providing insight into theories regarding the normal tonicity of PCL. An erratum to this article can be found at     

Targeting an anti-viral CD8+ T cell response to a growing tumor facilitates its rejection

 We demonstrate in a murine model that targeting an anti-viral T cell response to a growing tumor facilitates priming of a tumor-associated antigen (TAA)-specific, rejecting T cell response. Murine P815 mastocytoma cells grow aggressively in a syngeneic host. Transfected P815/S cells (expressing the hepatitis B surface antigen, HBsAg) also grow as subcutaneous tumors, but occasional ‘spontaneous’ rejections after transient growth are observed. Growth of P815/S tumors (but not of P815 tumors) is efficiently suppressed by a CD8⁺ cytotoxic T lymphocyte (CTL)-dependent immune mechanism in mice primed to HBsAg by DNA–immunization. In hosts immunized against HBsAg by DNA vaccination, HBsAg-specific CTL are generated. This specific CTL reactivity was targeted to s.c.-growing P815 tumors by intra tumor injections of either HBsAg-encoding plasmid DNA or viable P815/S cells; this treatment led to tumor rejection in 70–80% of the tumor-bearing animals. All rejecting animals showed a CD8⁺ CTL-dependent resistance to subsequent challenges by native, non-transfected P815 tumors. Targeting an established anti-viral (‘strong’) CTL response to a growing tumor hence is an efficient strategy to facilitate priming of a rejecting CTL response against (‘weak’) TAA in this system. Received: 18 December 1996 / Accepted: 6 February 1997     

Nonlinear simulation of tumor growth

 We study solid tumor (carcinoma) growth in the nonlinear regime using boundary-integral simulations. The tumor core is nonnecrotic and no inhibitor chemical species are present. A new formulation of the classical models [18,24,8,3] is developed and it is demonstrated that tumor evolution is described by a reduced set of two dimensionless parameters and is qualitatively unaffected by the number of spatial dimensions. One parameter describes the relative rate of mitosis to the relaxation mechanisms (cell mobility and cell-to-cell adhesion). The other describes the balance between apoptosis (programmed cell-death) and mitosis. Both parameters also include the effect of vascularization. Our analysis and nonlinear simulations reveal that the two new dimensionless groups uniquely subdivide tumor growth into three regimes associated with increasing degrees of vascularization: low (diffusion dominated, e.g., in vitro), moderate and high vascularization, that correspond to the regimes observed in vivo. We demonstrate that critical conditions exist for which the tumor evolves to nontrivial dormant states or grows self-similarly (i.e., shape invariant) in the first two regimes. This leads to the possibility of shape control and of controlling the release of tumor angiogenic factors by restricting the tumor volume-to-surface-area ratio. Away from these critical conditions, evolution may be unstable leading to invasive fingering into the external tissues and to topological transitions such as tumor breakup and reconnection. Interestingly we find that for highly vascularized tumors, while they grow unbounded, their shape always stays compact and invasive fingering does not occur. This is in agreement with recent experimental observations [30] of in vivo tumor growth, and suggests that the invasive growth of highly-vascularized tumors is associated to vascular and elastic anisotropies, which are not included in the model studied here. Received: 1 May 2002 / Revised version: 26 August 2002 / Published online: 18 December 2002 Current address: Department of Biomedical Engineering, and Department of Mathematics, University of California at Irvine, Irvine CA 92697. e-mail: cristini@math.uci.edu; lowengrb@math.umn.edu. Key words or phrases: Tumor growth – Linear stability analysis – Self-similarity – Boundary-integral simulations     

Explicit Separation of Growth and Motility in a New Tumor Cord Model

We investigate a new model of tumor growth in which cell motility is considered an explicitly separate process from growth. Bulk tumor expansion is modeled by individual cell motility in a density-dependent diffusion process. This model is implemented in the context of an in vivo system, the tumor cord. We investigate numerically microscale density distributions of different cell classes and macroscale whole tumor growth rates as functions of the strength of transitions between classes. Our results indicate that the total tumor growth follows a classical von Bertalanffy growth profile, as many in vivo tumors are observed to do. This provides a quick validation for the model hypotheses. The microscale and macroscale properties are both sensitive to fluctuations in the transition parameters, and grossly adopt one of two phenotypic profiles based on their parameter regime. We analyze these profiles and use the observations to classify parameter regimes by their phenotypes. This classification yields a novel hypothesis for the early evolutionary selection of the metastatic phenotype by selecting against less motile cells which grow to higher densities and may therefore induce local collapse of the vascular network.     

Reconstructing parameters of the FitzHugh–Nagumo system from boundary potential measurements

We consider distributed parameter identification problems for the FitzHugh–Nagumo model of electrocardiology. The model describes the evolution of electrical potentials in heart tissues. The mathematical problem is to reconstruct physical parameters of the system through partial knowledge of its solutions on the boundary of the domain. We present a parallel algorithm of Newton–Krylov type that combines Newton’s method for numerical optimization with Krylov subspace solvers for the resulting Karush–Kuhn–Tucker system. We show by numerical simulations that parameter reconstruction can be performed from measurements taken on the boundary of the domain only. We discuss the effects of various model parameters on the quality of reconstructions. Action Editor: David Terman     

Surface Plasmon Enhancement at a Liquid–Metal–Liquid Interface

Herein, we report the first experimental demonstration of surface plasmon enhancement at a liquid–metal–liquid interface using a pseudo-Kretschmann geometry. Pumping gold nanoparticle clusters at the interface of a p-xylene–water mixture, we were able to measure a fluorescence enhancement of three orders of magnitude in Rose Bengal at an excitation wavelength of 532 nm. The observed increase is due to the local electric field enhancement and the reduction of the fluorescence lifetime of dye molecules in the close vicinity of the metal surface. Theoretical modeling using the T-matrix method of the electric field intensity enhancement of emulated surfaces supports the experimental results. This new approach will open a new road for the study of dynamic systems using plasmonics.     

The composition and importance of the phytoneuston in two floodplain lakes in south-eastern Australia

Normans Lagoon and 3-Gum pond are small floodplain water bodies adjacent to the Murray River, south-eastern Australia, and often have a visible film/sheen across their surface. Since few studies have provided quantitative comparisons of the surface and subsurface layer communities of shallow freshwater lakes, we determined the contributions of the surface and subsurface populations to overall algal biomass when a surface film was visible, and when it was not visible. We examined the algae and cyanobacteria present at the air–water interface of each water body, and compared the findings with those for the water immediately below the surface, and for the overall water column. The algal groupings Trachelomonas spp., other Euglenophyceae (principally Euglena spp.), Chlorophyceae and Cyanobacteria usually comprised >95% of the measured biovolume within all samples. Samples from the air–water interface were considerably enriched (up to 200-fold) with respect to algal biovolume, whether or not a visible surface film was present, and elevated cell counts were observed within the air–water interface for motile organisms such as Trachelomonas spp. and green unicellular flagellates. The reverse was true for the cyanobacterium Planktolyngbya however, with greater concentrations occurring at depth. In terms of its contribution to the overall algal/cyanobacterial populations within each water body, the surface layer was found to be responsible for <1–20% of the biovolume over the entire water column. Multivariate statistical analysis confirmed there were significant differences between the communities of the air–water interface and those of the water below, and that these differences occurred both in the presence and absence of a visible surface film/sheen. Handling editor: D. Ryder     

Using pseudo amino acid composition to predict transmembrane regions in protein: cellular automata and Lempel-Ziv complexity

Summary. Transmembrane (TM) proteins represent about 20–30% of the protein sequences in higher eukaryotes, playing important roles across a range of cellular functions. Moreover, knowledge about topology of these proteins often provides crucial hints toward their function. Due to the difficulties in experimental structure determinations of TM protein, theoretical prediction methods are highly preferred in identifying the topology of newly found ones according to their primary sequences, useful in both basic research and drug discovery. In this paper, based on the concept of pseudo amino acid composition (PseAA) that can incorporate sequence-order information of a protein sequence so as to remarkably enhance the power of discrete models (Chou, K. C., Proteins: Structure, Function, and Genetics, 2001, 43: 246–255), cellular automata and Lempel-Ziv complexity are introduced to predict the TM regions of integral membrane proteins including both α-helical and β-barrel membrane proteins, validated by jackknife test. The result thus obtained is quite promising, which indicates that the current approach might be a quite potential high throughput tool in the post-genomic era. The source code and dataset are available for academic users at liml@scu.edu.cn. Authors’ address: Menglong Li, College of Chemistry, Sichuan University, Chengdu, Sichuan 610064, P.R. China     

Growth, ageing and death of a photoautotrophic plant cell culture

 Batch cultures of photoautotrophic cell suspensions of Chenopodiumrubrum L., growing in an inorganic medium on CO₂ under a daily balanced light–dark regime of 16 : 8 h could be maintained for approximately 100 d without subcultivation. The long-lived cultures showed an initial cell division phase of 4 weeks, followed by a stationary phase of another 4 weeks, after which ageing and progressive cell death reduced the number of living cells and the cultures usually expired after another 3–4 weeks. These developmental phases of the cell culture were characterised with respect to photosynthetic performance, dark respiration, content of phytohormones and capacity of cell division. Cell division of the majority of the cells finished in the G1- or G0-phase of the cell cycle, caused by a pronounced decline in the endogenous levels of auxin and cytokinins. Supply of these growth factors to resting cells resulted in resumption of cytokinesis, at least by some of the cells. However, responsiveness to the phytohomones declined during the stationary phase, and subcultivation was no longer possible beyond day 60 when the phases of ageing and death commenced. Ageing was characterised by a further decline in the photosynthetic capacity of the cells, by a climacteric enhancement of dark respiration, but also by a slight increase in the level of IAA and cytokinins concomitant with a decrease in ethylene. Similarities and differences between the development of batch-cultured photoautotrophic cells of C. rubrum and that of a leaf are discussed with respect to using the cell culture as a model for a leaf. Received: 30 April 1999 / Accepted: 21 August 1999     

A Riemannian manifold analysis of endothelial cell monolayer impedance parameter precision

Endothelial cell adhesion and barrier function play a critical role in many biological and pathophysiological processes. The decomposition of endothelial cell adhesion and barrier function into cell–cell and cell–matrix components using frequency dependent cellular micro-impedance measurements has, therefore, received widespread application. Few if any studies, however, have examined the precision of these model parameters. This study presents a parameter sensitivity analysis of a representative cellular barrier function model using a concise geometric formulation that includes instrumental data acquisition settings. Both model state dependence and instrumental noise distributions are accounted for within the framework of Riemannian manifold theory. Experimentally acquired microimpedance measurements of attached endothelial cells define the model state domain, while experimentally measured noise statistics define the data space Riemannian metric based on the Fisher information matrix. The results of this analysis show that the sensitivity of cell–cell and cell–matrix impedance components are highly model state dependent and several well defined regions of low precision exist. The results of this study further indicate that membrane resistive components can significantly reduce the precision of the remaining parameters in these models. This work was supported by a National Science Foundation CAREER Award (AE), BES-0238905, and in part by the American Heart Association under Grant 0265029B (AE).     

Somatostatin analogues, a series of tissue transglutaminase inducers, as a new tool for therapy of mesenchimal tumors of the gastrointestinal tract

Summary. Imatinib, a tyrosine kinase inhibitor directed against the enzymatic domain of KIT protein, was found to produce dramatic clinical responses in metastatic gastrointestinal stromal tumors (GISTs). However, resistance usually develops thus determining treatment failure. The present study was performed to analyse the expression of somatostatin receptor (SSTR) subtypes, modulators of tissue transglutaminase, in a series of GISTs and leiomyosarcomas by immunohistochemistry to identify a new potential therapeutic target. Sixteen cases (8 males and 8 females, age range: 38–73; 11 GISTs, 4 leiomyosarcomas, 1 leiomyoma) were studied. Immunohistochemical detection of the relevant SSTRs was performed on paraffin-embedded tissue sections, stained with polyclonal antibodies directed against the five somatostatin receptor subtypes. We found 7 out of 16 (44%) tumors expressing all SSTRs and 14 out of 16 (87%) tumors positive for at least 3 subtypes. SSTR2_A was the most represented subtype in the tumors studied, being expressed in approximately 70% of cases exhibiting an intense labeling in most of these cases. The significant expression of SSTRs shown in this series of GISTs and gastrointestinal leiomyosarcomas suggests a potential therapeutic target to be explored alone and/or in combination with other therapeutic agents in the setting of refractory GI stromal tumors.     

Parameter estimation in a generalized discrete-time model of density dependence

Flexible discrete-time per-capita-growth-rate models accommodating a variety of density-dependent relationships offer parsimonious explanations for the variation of population abundance through time. However, the accuracy of standard approaches to parameter estimation and confidence interval construction for such models has not been explored in a generalized setting or with consideration of limited sample sizes typical for ecology. Here, we use simulated data to quantify the relative effects of sample size, population perturbations, and environmental stochasticity on statistical inference. We focus on the key parameters that inform population dynamic predictions in a generalized Beverton–Holt model. We find that reliable parameter estimation requires data spanning ranges where both low and high density dependence act. However, the asymptotic distribution of the likelihood ratio test statistic can be fairly accurate for constructing confidence regions even when point estimation is poor. Consideration of the joint profile likelihood surface is shown to be useful for assessing reliability of point estimates and dynamical population predictions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A new MAGE-4 antigenic peptide recognized by cytolytic T lymphocytes on HLA–A24 carcinoma cells

“Cancer-germline” genes such as those of the MAGE family are expressed in many tumors and in male germline cells, but are silent in other normal tissues. They encode tumor specific antigens that are used in cancer immunotherapy trials. MAGE-4 antigens represent promising targets for cancer immunotherapy because gene MAGE-4 is expressed in more than 50% of carcinomas of the esophagus, lung, bladder, and head and neck. To identify new MAGE-4 antigenic peptides, we have folded HLA–A*2402 soluble molecules with candidate peptide NYKRCFPVI, which corresponds to amino acids 143 to151 of the MAGE-4 protein. A24/MAGE-4 multimers were used to isolate a cytolytic T cell clone that recognized the MAGE-4 peptide from the blood cells of a donor without cancer. This clone lysed specifically A24 carcinoma cells expressing MAGE-4. The antigenic peptide is processed more efficiently in tumor cells pre-treated with IFN-γ. This MAGE-4 peptide could represent an interesting target for immunotherapy because it is presented by HLA–A24 molecules, which are widely expressed in different ethnic groups.     

The generation of anti-tumoral cells using dentritic cells from the peripheral bloood of patients with malignant brain tumors

 Dendritic cells (DCs) can be the principal initiators of antigen-specific immune responses. We analyzed the in vitro-responses against brain tumor cells using DCs from the peripheral blood of patients with brain tumors. Peripheral blood mononuclear cells (PBMC) were obtained from 19 patients with malignant brain tumors: 12 metastatic brain tumors of lung adenocarcinoma, 7 high-grade astrocytomas. PBMC were cultured with 100 ng/ml of GM-CSF and 10 ng/ml of IL-4 for 5–7 days in order to produce mature DCs. The autologous tumor lysate (5 mg/ml, containing 1 × 10⁶ cells) was then added to the cultured DCs. Using the DCs generated by these treatments, we assessed the changes that occurred in their immune responses against brain tumor via ⁵¹Cr-release and lymphocyte proliferation assays. We found that the matured DCs displayed the typical surface phenotype of CD3⁺, CD45⁺, CD80⁺ and CD86⁺. After the pulsation treatment with tumor lysate, DCs were found to have strong cytotoxic T lymphocyte activity, showing 42.5 ± 12.7% killing of autologous tumor cells. We also found an enhancement of allogeneic T cell proliferation after pulsing the DC with tumor lysate. These data support the efficacy of DC-based immunotherapy for patients with malignant brain tumors. Received: 2 October 2000 / Accepted: 26 April 2001     

Calcium and the role of motoneuronal doublets in skeletal muscle control

This work presents a novel structural model of skeletal muscle activation, providing a physiologically based account of frequency-dependent muscle responses like the catch-like effect. Numerous Ca²⁺ reservoirs within muscle fibers are considered, and a simplified analysis of the allocation of Ca²⁺ resources and the dynamics of calcium transport is proposed. The model correctly accounts for catch-like effects in slow and fast-twitch fibers during long-train stimulations and force–frequency relations in different muscle types. Results obtained from the model compare favorably to experiments showing that prolonged increases in force characteristic of the catch-like effect are not accompanied by sustained increases in free myoplasmic Ca²⁺. Also, in agreement with early experiments, the interspike interval in catch-inducing doublets is seen to be an important parameter for regulating the precise onset amplitude of the catch-like effect. This suggests that a plausible physiological function for the inclusion of doublets or the exclusion of individual spikes within a regular motor-neuronal spike-train is to rapidly bring skeletal muscles to predefined target forces according to prespecified motor programs in the central nervous system. This is a potentially very useful property directly mediated by the catch-like process modeled here. One further prediction of the model is that the slope of the frequency–tension profile of a given muscle is highly sensitive to changes in the efficiency and temporal characteristics of the dihydropyridine–ryanodine receptor complex. Interestingly, this is consistent with findings made on cardiac muscles, and might incidentally explain some instances of cardiac failure.     

Gravity-induced absorbance changes in Phycomyces: a novel method for detecting primary responses of gravitropism

 The negative gravitropism of the sporangiophores of Phycomyces blakesleeanus Burgeff is elicited by different sensory inputs, which include flexure of the growing zone, buoyance of lipid globules and sedimentation of paracrystalline proteins, so-called octahedral crystals (C. Schimek et al., 1999a, Planta 210: 132–142). Gravity-induced absorbance changes (GIACs), which are associated with primary events of gravity sensing, were detected in the growing zones of sporangiophores. After placing sporangiophores horizontally, GIACs were detected after a latency of about 5 min, i.e. 15–25 min prior to gravitropic bending. The spectroscopic properties of the GIACs indicate that gravitropic stimulation could imply the reduction of cytochromes. The GIACs were spectrally distinct from light-induced absorbance changes (LIACs), showing that the primary responses of the light and gravity transduction chains are different. A dual stimulation with gravity and light generated GIAC-LIACs which were distinct from the absorbance changes occurring after the single stimuli and which indicate that light and gravity interact early in the respective transduction chains. Received: 2 September 1999 / Accepted: 9 November 1999     

A mathematical model of the stress induced during avascular tumour growth

In this paper a mathematical model is developed to describe the effect of nonuniform growth on the mechanical stress experienced by cells within an avascular tumour. The constitutive law combines the stress-strain relation of linear elasticity with a growth term that is derived by analogy with thermal expansion. To accommodate the continuous nature of the growth process, the law relates the rate of change of the stress tensor to the rate of change of the strain (rather than relating the stress to the strain directly). By studying three model problems which differ in detail, certain characteristic features are identified. First, cells near the tumour boundary, where nutrient levels and cell proliferation rates are high, are under compression. By contrast, cells towards the centre of the tumour, where nutrient levels are low and cell death dominant, are under tension. The implications of these results and possible model developments are also discussed. Received: 15 November 1999 / Published online: 5 May 2000     

A Mathematical Model for the Regulation of Tumor Dormancy Based on Enzyme Kinetics

In this paper we present a two-compartment model for tumor dormancy based on an idea of Zetter [1998, Ann. Rev. Med. 49, 407–422] to wit: The vascularization of a secondary (daughter) tumor can be suppressed by an inhibitor originating from a larger primary (mother) tumor. We apply this idea at the avascular level to develop a model for the remote suppression of secondary avascular tumors via the secretion of primary avascular tumor inhibitors. The model gives good agreement with the observations of [De Giorgi et al., 2003, Derm. Surgery 29, 664–667]. These authors reported on the emergence of a polypoid melanoma at a site remote from a primary polypoid melanoma after excision of the latter. The authors observed no recurrence of the melanoma at the primary site, but did observe secondary tumors at secondary sites 5–7 cm from the primary site within a period of 1 month after the excision of the primary site. We attempt to provide a reasonable biochemical/cell biological model for this phenomenon. We show that when the tumors are sufficiently remote, the primary tumor will not influence the secondary tumor while, if they are too close together, the primary tumor can effectively prevent the growth of the secondary tumor, even after it is removed. It should be possible to use the model as the basis for a testable hypothesis.     

In silico analysis of arginine catabolism as a source of nitric oxide or polyamines in endothelial cells

Summary. We use a modeling and simulation approach to carry out an in silico analysis of the metabolic pathways involving arginine as a precursor of nitric oxide or polyamines in aorta endothelial cells. Our model predicts conditions of physiological steady state, as well as the response of the system to changes in the control parameter, external arginine concentration. Metabolic flux control analysis allowed us to predict the values of flux control coefficients for all the transporters and enzymes included in the model. This analysis fulfills the flux control coefficient summation theorem and shows that both the low affinity transporter and arginase share the control of the fluxes through these metabolic pathways. The first two authors equally contributed to this work. Current address for the second author: ICREA-Complex Systems Laboratory, Universitat Pompeu Fabra, Barcelona, Spain. Authors’ address: Dr. Miguel ángel Medina, Departamento de Biología Molecular y Bioquímica, Facultad de Ciencias, Universidad de Málaga, E-29071 Málaga, Spain