Older plasma lipoproteins are more susceptible to oxidation: a linking mechanism for the lipid and oxidation theories of atherosclerotic cardiovascular disease.

Increases in plasma cholesterol are associated with progressive increases in the risk of atherosclerotic cardiovascular disease. In humans plasma cholesterol is contained primarily in apolipoprotein B-based low density lipoprotein (LDL). Cells stop making the high-affinity receptor responsible for LDL removal as they become cholesterol replete; this slows removal of LDL from plasma and elevates plasma LDL. As a result of this delayed uptake, hypercholesterolemic individuals not only have more LDL but have significantly older LDL. Oxidative modification of LDL enhances their atherogenicity. This study sought to determine whether increased time spent in circulation, or aging, by lipoprotein particles altered their susceptibility to oxidative modification. Controlled synchronous production of distinctive apolipoprotein B lipoproteins (yolk-specific very low density lipoproteins; VLDLy) with a single estrogen injection into young turkeys was used to model LDL aging in vivo. VLDLy remained in circulation for at least 10 days. Susceptibility to oxidation in vitro was highly dependent on lipoprotein age in vivo. Oxidation, measured as hexanal release from n-6 fatty acids in VLDLy, increased from 13.3 +/- 5.5 nmol of 2-day-old VLDLy per ml, to 108 +/- 17 nmol of 7-day-old VLDLy per ml. Oxidative instability was not due to tocopherol depletion or conversion to a more unsaturated fatty acid composition. These findings establish mathematically describable linkages between the variables of LDL concentration and LDL oxidation. The proposed mathematical models suggest a unified investigative approach to determine the mechanisms for acceleration of atherosclerotic cardiovascular disease risk as plasma cholesterol rises.

The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

A model of excitation and adaptation in bacterial chemotaxis

Bacterial chemotaxis is widely studied because of its accessibility and because it incorporates processes that are important in a number of sensory systems: signal transduction, excitation, adaptation, and a change in behavior, all in response to stimuli. Quantitative data on the change in behavior are available for this system, and the major biochemical steps in the signal transduction/processing pathway have been identified. We have incorporated recent biochemical data into a mathematical model that can reproduce many of the major features of the intracellular response, including the change in the level of chemotactic proteins to step and ramp stimuli such as those used in experimental protocols. The interaction of the chemotactic proteins with the motor is not modeled, but we can estimate the degree of cooperativity needed to produce the observed gain under the assumption that the chemotactic proteins interact directly with the motor proteins.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

Fusigenic viral liposome for gene therapy in cardiovascular diseases.

To improve the efficiency of liposome-mediated DNA transfer as a tool for gene therapy, we have developed a fusigenic liposome vector based on principles of viral cell fusion. The fusion proteins of hemagglutinating virus of Japan (HVJ; also Sendai virus) are complexed with liposomes that encapsulate oligodeoxynucleotide or plasmid DNA. Subsequent fusion of HVJ-liposomes with plasma membranes introduces the DNA directly into the cytoplasm. In addition, a DNA-binding nuclear protein is incorporated into the HVJ-liposome particle to enhance plasmid transgene expression. The fusigenic viral liposome vector has proven to be efficient for the intracellular introduction of oligodeoxynucleotide, as well as intact genes up to 100 kbp, both in vitro and in vivo. Many animal tissues have been found to be suitable targets for fusigenic viral liposome DNA transfer. In the cardiovascular system, we have documented successful cytostatic gene therapy in models of vascular proliferative disease using antisense oligodeoxynucleotides against cell cycle genes, double-stranded oligodeoxynucleotides as "decoys" to trap the transcription factor E2F, and expression of a transgene encoding the constitutive endothelial cell form of nitric oxide synthase. Similar strategies are also effective for the genetic engineering of vein grafts and for the treatment of a mouse model of immune-mediated glomerular disease.

Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models.

Most models of tumorigenesis assume that the tumor grows by increased cell division. In these models, it is generally supposed that daughter cells behave as do their parents, and cell numbers have clear potential for exponential growth. We have constructed simple mathematical models of tumorigenesis through failure of programmed cell death (PCD) or differentiation. These models do not assume that descendant cells behave as their parents do. The models predict that exponential growth in cell numbers does sometimes occur, usually when stem cells fail to die or differentiate. At other times, exponential growth does not occur: instead, the number of cells in the population reaches a new, higher equilibrium. This behavior is predicted when fully differentiated cells fail to undergo PCD. When cells of intermediate differentiation fail to die or to differentiate further, the values of growth parameters determine whether growth is exponential or leads to a new equilibrium. The predictions of the model are sensitive to small differences in growth parameters. Failure of PCD and differentiation, leading to a new equilibrium number of cells, may explain many aspects of tumor behavior--for example, early premalignant lesions such as cervical intraepithelial neoplasia, the fact that some tumors very rarely become malignant, the observation of plateaux in the growth of some solid tumors, and, finally, long lag phases of growth until mutations arise that eventually result in exponential growth.