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PubMed2004

Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour.

In this paper a mathematical model describing the growth of a solid tumour in the presence of an immune system response is presented. In particular, attention is focused upon the attack of tumour cells by so-called tumour-infiltrating cytotoxic lymphocytes (TICLs), in a small, multicellular tumour, without necrosis and at some stage prior to (tumour-induced) angiogenesis. At this stage the immune cells and the tumour cells are considered to be in a state of dynamic equilibrium--cancer dormancy--a phenomenon which has been observed in primary tumours, micrometastases and residual disease after ablation of the primary tumour. Nonetheless, the precise biochemical and cellular mechanisms by which TICLs control cancer dormancy are still poorly understood from a biological and immunological point of view. Therefore we focus on the analysis of the spatio-temporal dynamics of tumour cells, immune cells and chemokines in an immunogenic tumour. The lymphocytes are assumed to migrate into the growing solid tumour and interact with the tumour cells in such a way that lymphocyte-tumour cell complexes are formed. These complexes result in either the death of the tumour cells (the normal situation) or the inactivation (sometimes even the death) of the lymphocytes. The migration of the TICLs is determined by a combination of random motility and chemotaxis in response to the presence of chemokines. The resulting system of four nonlinear partial differential equations (TICLs, tumour cells, complexes and chemokines) is analysed and numerical simulations are presented. We consider two different tumour geometries--multi-layered cell growth and multi-cellular spheroid growth. The numerical simulations demonstrate the existence of cell distributions that are quasi-stationary in time and heterogeneous in space. A linear stability analysis of the underlying (spatially homogeneous) ordinary differential equation (ODE) kinetics coupled with a numerical investigation of the ODE system reveals the existence of a stable limit cycle. This is verified further when a subsequent bifurcation analysis is undertaken using a numerical continuation package. These results then explain the complex heterogeneous spatio-temporal dynamics observed in the partial differential equation (PDE) system. Our approach may lead to a deeper understanding of the phenomenon of cancer dormancy and may be helpful in the future development of more effective anti-cancer vaccines.

Cell Division↗
PubMed1993

[The stability of antibiotics administered in and with a parenteral nutrition mixture enriched with branched-chain amino acids. I. Amikacin and gentamycin].

The combined infusion of antibiotics and parenteral nutrition makes it possible to maintain plasmatic nutrient concentrations over time, in turn facilitating the administration of the antibiotics in the dilution and infusion time recommended according to their pharmacokinetic parameters. On the other hand, this type of administration has care benefits for the patient, reducing the risk of infections, and adding to comfort. The technique is also cost-effective, reducing the cost of drug administration, saving on administrative personnel and nursing staff time. The stability of amikacin and gentamicin are determined in vitro at therapeutic concentrations jointly infused with a mixture of parenteral nutrition with polyols and enriched in ramified chain amino acids. A microbiological stability analysis was carried out of the antibiotics in the parenteral nutrition, along with an HPLC aminogram, in order to determine the concentration of amino acids in the combined infusion with the antibiotic. pH measurements were also taken, along with osmolarity and colour change. Both of the antibiotics and the parenteral nutrition employed, and of the combined infusion mixtures. Amikacin and Gentamicin are stable at a concentration of 5 mg/ml and 1.6 mg/ml respectively in a parenteral nutrition mixture enriched in ramified chain amino acids.

Amikacin↗
PubMed1990

A model study of stability and oscillations in the myocardial cell membrane.

As a step towards an improved understanding of cardiac arrhythmias caused by abnormal automaticity, we perform a stability analysis of a Hodgkin-Huxley model of the myocardial cell membrane (modified Beeler-Reuter, MBR). The bifurcation structure of the model is obtained as a function of three parameters: the intensity of an applied constant current; the potassium equilibrium potential representing the accumulation of K+ ions in the external medium; and the maximum conductance of the slow inward current mimicking the local application of catecholamines on the membrane. For a range of parameter values, the model exhibits either stable automaticity or bistability between two quiescent states or between a quiescent state and an oscillatory state. These transformations of the bifurcation structure are shown to depend on the interrelationship between three elements: the activation of the slow inward current, the region of high slope conductance of the time-independent potassium current functions, and the slow variables controlling the activation of the potassium current and the inactivation of the slow inward current. Reduced two- and three-dimensional models are shown to reproduce the main stability properties of the full MBR model and to facilitate the understanding of its dynamic behavior. The onset of instability and the oscillatory features of the MBR model are in good agreement with relevant experimental results, and possible sources of disagreement on certain points are discussed.

Arrhythmias, Cardiac↗
PubMed2003

Quantification of crystalline forms in active pharmaceutical ingredient and tablets by X-ray powder diffraction.

A Merck development compound was known to exist in several polymorphic forms, hydrates and solvates. The polymorphic forms were characterized and the most thermodynamically stable form at room temperature was identified and taken into development. During routine stability analysis it became apparent that the crystalline form of the compound was converting from one form to another in tablets that were stored at 40 degrees C/75% relative humidity in open containers. This form conversion did not occur when the active pharmaceutical ingredient (API) alone was stored under these conditions. This paper describes the development and application of an X-ray powder diffraction method for the determination of the relative content of the two crystalline forms in API and within the final formulation. Results of monitoring the crystalline form conversion are reported and a possible mechanism of conversion is postulated.

Crystallization↗
PubMed1985

Molecular properties of the oxytocin/bovine neurophysin biosynthetic precursor. Studies using a semisynthetic precursor.

An oxytocin/bovine neurophysin I biosynthetic precursor, [N epsilon-diacetimidyl-30,71, des-His106]pro-OT/BNPI, was synthesized from a synthetic oxytocinyl peptide, 1/2Cys-Tyr-Ile-Gln-Asn-1/2Cys-Pro-Leu-Gly-Gly-Lys-Arg, and native neurophysin by chemical semisynthesis. The semisynthetic precursor contains the entire sequence of the biosynthetic precursor deduced from the complementary DNA structure except for omission of the carboxyl-terminal histidine residue. The covalent structure of the semisynthetic product was verified by amino acid analysis and amino-terminal analysis. Analytical affinity chromatography was employed to evaluate noncovalent binding properties of the precursor. The precursor does not bind significantly to immobilized Met-Tyr-Phe, a hormone binding site ligand. In contrast, the acetimidated precursor binds to immobilized bovine neurophysin II, with a 13-fold higher affinity than does acetimidated neurophysin itself. When a hormonal ligand, [Lys8]vasopressin, was added to the elution buffer at the concentration of 0.1 mM so that a major portion of the immobilized BNPII was liganded, the affinity between the immobilized liganded BNPII and the precursor was enhanced 8-fold and approached the affinity for the liganded (bovine neurophysin I-immobilized BNPII) interaction. The data imply that the precursor can self-associate and that this self-association is closely related to that of liganded neurophysin. The tripeptide affinity matrix data argue that, in the precursor, the ligand binding site of the neurophysin domain is occupied intramolecularly by the hormone domain. The data verify the view that both the self-association surface and hormone binding site are established upon precursor folding. A disulfide stability analysis showed the resistance, to disulfide interchange by dithiothreitol, of semisynthetic precursor but not of neurophysin, as judged by protein association and peptide ligand binding activities, respectively. The results argue that the molecular structure of the precursor is established upon precursor folding and before enzymatic processing that produces mature hormone and neurophysin.

Amino Acid Sequence↗
PubMed1997

Metalloelastase expression in a mouse macrophage cell line--regulation by 4beta-phorbol 12-myristate 13-acetate, lipopolysaccharide and dexamethasone.

The regulation of the expression of mouse macrophage elastase (MME) was investigated using the murine tumor cell line P388D1. The effects of three factors were studied: a phorbol ester (4beta-phorbol 12-myristate 13-acetate, PMA), an endotoxin (lipopolysaccharide, LPS) and a corticosteroid (dexamethasone). Both in situ hybridization and northern blot analysis showed that P388D1 cells constitutively express the MME gene. Quantification of the MME mRNA by northern blot analysis showed that only PMA and dexamethasone significantly regulate MME gene expression in a time-dependent and dose-dependent manner. After PMA treatment, the MME mRNA level was maximal between 4 h and 9 h (medium-term response), and the mean amplitude of the response to a concentration of 100 nM was 2.5-fold (P<0.01). LPS did not induce any significant change in MME mRNA level even when 1% serum was added to the cultures. Following dexamethasone treatment, the MME mRNA level was minimal between 21 h and 33 h (long-term response), and the mean amplitude of the response to a concentration of 100 nM was 0.49-fold (P < 0.05). Using actinomycin D, it appeared that the inhibition of RNA synthesis reduces the ulterior stimulating effect of PMA from 184% to 121%, and that MME mRNA has a half-life longer than 8 h, which is not diminished by dexamethasone. These results strongly suggest that the two factors modify MME mRNA level by stimulating (PMA) or inhibiting (dexamethasone) the transcription of the gene, rather than by modifying the transcript stability. Analysis of the cell-conditioned media by elastin zymography showed the MME as a lysis band in the 22-kDa region, the intensity of which varied with the treatments. The MME secretion is stimulated by PMA, inhibited by dexamethasone and does not show any variation after LPS treatment.

Animals↗
PubMed2001

Knowledge-based potential defined for a rotamer library to design protein sequences.

A knowledge-based potential for a rotamer library was developed to design protein sequences. Protein side-chain conformations are represented by 56 templates. Each of their fitness to a given structural site-environment is evaluated by a combined function of the three knowledge-based terms, i.e. two-body side-chain packing, one-body hydration and local conformation. The number of matches between the native sequence and the structural site-environment in the database and that of the virtually settled mismatches, counted in advance, were transformed into the energy scores. In the best-14 test (assessment for the reproduction ability of the native rotamer on its structural site within a quarter of 56 fitness rank positions), the structural stability analysis on mutants of human and T4 lysozymes and the inverse-folding search by a structure profile against the sequence database, this function performs better than the function deduced with the conventional normalization and our previously developed function. Targeting various structural motifs, de novo sequence design was conducted with the function. The sequences thus obtained exhibit reasonable molecular masses and hydrophobic/hydrophilic patterns similar to the native sequences of the target and act as if they were the homologs to the target proteins in BLASTP search. This significant improvement is discussed in terms of the reference state for normalization and the crucial role of short-range repulsion to prohibit residue bumps.

Amino Acid Sequence↗
PubMed2004

Optimized dose delivery of the peptide cyclosporine using hydrofluoroalkane-based metered dose inhalers.

The goal of this study was to illustrate the potential to deliver relatively high doses of a therapeutic peptide using hydrofluoroalkane (HFA) metered dose inhaler (MDI) drug delivery systems. For the purposes of this study, cyclosporine was used as the model compound. Cyclosporine formulations, varying in peptide concentration, ethanol cosolvent concentration, and propellant type, were evaluated and optimized for product performance. As ethanol concentration was decreased from 10 to 3% by weight, fine particle fraction (the mass of cyclosporine which passes through a 4.7-micron cut point divided by the total mass of cyclosporine delivered ex-valve) increased from 34 to 68% for 227 and 33 to 52% for 134a formulations. Because of the excellent solubility properties of cyclosporine in HFA-based systems, minimal or no ethanol was needed as a cosolvent to achieve cyclosporine concentrations of 1.5% w/w. With these formulations, it was possible to obtain a fine particle mass (mass of particles <4.7 microns) greater than 500 microg per actuation. In addition, one formulation was chosen for stability analysis: 0.09% w/w cyclosporine, 10% w/w ethanol, 134a. Three different types of container closure systems (stainless steel, aluminum, and epoxy-coated canisters) and two storage configurations (upright and inverted) were evaluated. Cyclosporine was determined to be stable in HFA 134a-based MDI systems, regardless of container closure system and configuration, over a 2-year period. Cyclosporine represents a compelling example of how significant peptide doses are attainable through the use of solution-based MDIs. It has been shown that through formulation optimization, 2-3 mg of the peptide, cyclosporine, may be delivered in five actuations to the lung for local or systemic therapy.

Administration, Inhalation↗
PubMed2001

Stability of modulated-gravity-induced thermal convection in magnetic fields.

A stability analysis is presented of modulated-gravity-induced thermal convection in a heated fluid layer subject to an applied magnetic field. The nearest correction to the critical Rayleigh number for both single and multiple frequency oscillating-gravity components is obtained by solving the linearized magnetohydrodynamic equations using the small parameter perturbation technique. The correction depends on both the applied magnetic field and the oscillating frequency. In the absence of an applied magnetic field, the correction depends on the Prandtl number only when the exciting frequency is small. However, it asymptotically approaches zero as the frequency increases, with or without the presence of a magnetic field. The heated fluid layer is more stable with gravity modulation than with any type of wall temperature modulation. The difference becomes smaller with decreasing Prandtl number Pr. This finding is of critical importance in that ground-based experiments with appropriate wall temperature modulations may be conducted to simulate the oscillating-gravity effects on the onset of thermal convection in lower-Prandtl-number fluids. For conducting melts considered for microgravity applications, it is possible to apply an external magnetic field to further inhibit the onset of modulated-gravity-induced thermal convection. This effectiveness increases with the Hartmann number Ha. For large Ha, the nearest correction term R02 approximately Ha2 as the magnetic Prandtl number Pm<<1. However, R02 approximately Ha(4/3) for Ha>>1 and Pm>>1, provided that Ha<0.5pi(Pm/Pr(3/2)), which is satisfied by a majority of space melt experiments. Thus, under normal laboratory conditions applied magnetic fields are more effective in stabilizing a conducting fluid subject to an oscillating-gravity field than one subject to a constant field. If Ha>0.5pi(Pm/Pr(3/2)), R02 approximately -Ha2 for Ha>>1 and Pm>>1 and the magnetic field becomes less effective in stabilizing thermal convection driven by oscillating gravity than that driven by the constant gravity. This is in contrast with the existing studies on thermal convection stability in a magnetic field, which show that marginal stability is independent of Pm and always increases with increasing applied field.

Journal Article↗
PubMed2003

A review of drainage and spontaneous rupture in free standing thin films with tangentially immobile interfaces.

A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Frenkel criterion and is obtained from the zeroth order approximation of the H3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H3 term in the evolution equation and is dependent on the film thinning velocity. A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semi-empirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams.

Journal Article↗
PubMed1976

Time delay in simple chemostat models.

The models of Monod and Williams, for the growth of unicellular organisms in chemostats, give strongly damped transients in the biomass and cell number when the flow rate of the chemostat is changed. A simple trick is used to incorporate time delay in these models while still allowing a conventional stability analysis. For long enough time delays the equilibrium point is unstable and limit cycles can be compared. Results obtained using Williams' model, with weakly damped transients as a result of using moderately long time delay, are compared with his data in which cell numbers show weak damping but biomass shows strong damping.

Cells, Cultured↗
PubMed2003

Stability properties of elementary dynamic models of membrane transport.

Living cells are characterized by their capacity to maintain a stable steady state. For instance, cells are able to conserve their volume, internal ionic composition and electrical potential difference across the plasma membrane within values compatible with the overall cell functions. The dynamics of these cellular variables is described by complex integrated models of membrane transport. Some clues for the understanding of the processes involved in global cellular homeostasis may be obtained by the study of the local stability properties of some partial cellular processes. As an example of this approach, I perform, in this study, the neighborhood stability analysis of some elementary integrated models of membrane transport. In essence, the models describe the rate of change of the intracellular concentration of a ligand subject to active and passive transport across the plasma membrane of an ideal cell. The ligand can be ionic or nonionic, and it can affect the cell volume or the plasma membrane potential. The fundamental finding of this study is that, within the physiological range, the steady states are asymptotically stable. This basic property is a necessary consequence of the general forms of the expressions employed to describe the active and passive fluxes of the transported ligand.

Biological Transport↗
PubMed1996

Calcium functions as a transcriptional and mitogenic repressor in Syrian hamster embryo cells: roles of intracellular pH and calcium in controlling embryonic cell differentiation and proliferation.

We have investigated the role played by the growth and differentiation factor (GDF)-induced calcium ion second messenger signal in the control of cellular differentiation and proliferation in Syrian hamster embryo (SHE) cells. Blocking the platelet-derived growth factor (PDGF)-induced calcium ion signal with either extracellular/intracellular acidification or pharmacological agents resulted in increased immediate early gene expression and mitogenesis. The increase in immediate early gene expression resulted from a change in the level of immediate early gene transcription and not immediate early gene mRNA stability. Analysis of the promoter elements that control immediate early gene expression indicated that the calcium ion effect is mediated through the CaRE/CRE and AP1 promoter elements. The calcium signal-mediated reduction in PDGF A/B-stimulated SHE cell immediate early gene expression resulted in a reduction in PDGF A/B-induced cellular proliferation. These results demonstrate that in SHE cells, calcium functions to suppress mitogen-induced proliferation at the level of immediate early gene expression, an effect related to the control of cellular proliferation and differentiation by GDFs through the calcium ion second messenger.

Animals↗
PubMed1997

A Theoretical Study of Instabilities at the Advancing Front of Thermally Driven Coating Films

A thin liquid coating can spread vertically beyond the equilibrium meniscus position by the application of a temperature gradient to the adjacent substrate. So called super-meniscus films experience a surface shear stress which drives flow toward regions of higher surface tension located at the cooler end of the substrate. The Marangoni stresses responsible for this spreading process can also be used to coat horizontal surfaces rapidly and efficiently. Experiments in the literature have shown that in either geometry, the advancing front can develop a pronounced ridge with lateral undulations that develop into long slender rivulets. These rivulets, which prevent complete surface coverage, display a remarkable regularity in height, width, and spacing which suggests the presence of a hydrodynamic instability. We have performed a linear stability analysis of such thermally driven films to determine the most dangerous wavenumber. Our numerical solutions indicate the presence of an instability at the advancing front of films which develop a sufficiently thick capillary ridge. Our results for the film thickness profiles and spreading velocities, as well as the wavenumber corresponding to the most unstable mode, compare favorably with recent experimental measurements. An energy analysis of the perturbed flow reveals that the increased mobility in the thickened portions of the films strongly promotes unstable flow, in analogy with other coating processes using gravitational or centrifugal forces. Copyright 1997Academic Press

Journal Article↗
PubMed1998

Stationary Solutal Marangoni Instability in a Two-Layer System.

The effect of different mass transfer mechanisms on the Marangoni instability in a two-layer system of finite width is studied. A dilute soluble surfactant is transferred across the interface between two immiscible fluid phases. A linear stability analysis is developed, and the corresponding eigenvalue problem is solved analytically for the onset of monotonic instability. Mass transfer is assumed to be controlled by bulk diffusion or/and by the adsorption-desorption mechanism. The influences of the diffusivity ratio and the layer width ratio on the instability of the system are examined. Copyright 1998 Academic Press.

Journal Article↗
PubMed1999

Dynamics of Drop Formation in an Electric Field.

The effect of an electric field on the formation of a drop of an inviscid, perfectly conducting liquid from a capillary which protrudes from the top plate of a parallel-plate capacitor into a surrounding dynamically inactive, insulating gas is studied computationally. This free boundary problem which is comprised of the surface Bernoulli equation for the transient drop shape and the Laplace equation for the velocity potential inside the drop and the electrostatic potential outside the drop is solved by a method of lines incorporating the finite element method for spatial discretization. The finite element algorithm employed relies on judicious use of remeshing and element addition to a two-region adaptive mesh to accommodate large domain deformations, and allows the computations to proceed until the thickness of the neck connecting an about to form drop to the rest of the liquid in the capillary is less than 0.1% of the capillary radius. The accuracy of the computations is demonstrated by showing that in the absence of an electric field predictions made with the new algorithm are in excellent agreement with boundary integral calculations (Schulkes, R. M. S. M. J. Fluid Mech. 278, 83 (1994)) and experimental measurements on water drops (Zhang, X., and Basaran, O. A. Phys. Fluids 7(6), 1184 (1995)). In the presence of an electric field, the algorithm predicts that as the strength of the applied field increases, the mode of drop formation changes from simple dripping to jetting to so-called microdripping, in accordance with experimental observations (Cloupeau, M., and Prunet-Foch, B. J. Aerosol Sci. 25(6), 1021 (1994); Zhang, X., and Basaran, O. A. J. Fluid Mech. 326, 239 (1996)). Computational predictions of the primary drop volume and drop length at breakup are reported over a wide range of values of the ratios of electrical, gravitational, and inertial forces to surface tension force. In contrast to previously mentioned cases where both the flow rate in the tube and the electric field strength are nonzero, situations are also considered in which the flow rate is zero and the dynamics are initiated by impulsively changing the field strength from a certain value to a larger value. When the magnitude of the step change in field strength is small, the results of the new transient calculations accord well with those of an earlier stability analysis (Basaran, O. A., and Scriven, L. E. J. Colloid Interface Sci. 140(1), 10 (1990)) and thereby provide yet another testament to the accuracy of the new algorithm. Copyright 1999 Academic Press.

Journal Article↗
PubMed1999

An Approach of a Nonlinear Dynamic Model for Micellar Effects on Bimolecular Reactions.

The effects of micellar solutions on bimolecular reactions were studied in detail using a newly established nonlinear dynamic model with a far-from-equilibrium reaction scheme, by which the incorporation of organic substrates with the micellar phase was imitated. Through the linear stability analysis of the steady state solutions given by the rate equation of the change of substrate concentration within a micellar phase with time, it leads to some explicit relationships between the incorporated substrate concentration and the relevant parameters. Based on this model the micellar effects on the kinetics of the alkaline hydrolysis of esters have been interpreted. Copyright 1999 Academic Press.

Journal Article↗
PubMed2001

Marangoni Flow Driven Instabilities and Marginal Regeneration.

Fingering instabilities in films moving along wetted surfaces, dimpling in horizontal liquid films, and the drainage of vertical soap films by marginal regeneration are caused by surface tension gradients along the perimeter of the thin film. These gradients lead to a mechanical instability which involves Marangoni type liquid flow. It is possible to describe the conditions for the onset of marginal regeneration with a critical number of the ratio between the driving force for the Marangoni flow and the friction of film elements that move relative to their surroundings. This ratio is called the Mysels number. A linear stability analysis leads to a scaling relation lambda approximately h(Ca)(-1/3) between the wavelength lambda of the instability and the capillary number Ca (Ca=/etaV(s)/gamma. In experiments with several Marangoni-driven instabilities this scaling relation has been found; it illustrates the general applicability in the understanding of flow phenomena of this type. Copyright 2001 Academic Press.

Journal Article↗