Modeling and optimization of populations subject to time-dependent mutation.

It has become clear that many organisms possess the ability to regulate their mutation rate in response to environmental conditions. So the question of finding an optimal mutation rate must be replaced by that of finding an optimal mutation schedule. We show that this task cannot be accomplished with standard population-dynamic models. We then develop a "hybrid" model for populations experiencing time-dependent mutation that treats population growth as deterministic but the time of first appearance of new variants as stochastic. We show that the hybrid model agrees well with a Monte Carlo simulation. From this model, we derive a deterministic approximation, a "threshold" model, that is similar to standard population dynamic models but differs in the initial rate of generation of new mutants. We use these techniques to model antibody affinity maturation by somatic hypermutation. We had previously shown that the optimal mutation schedule for the deterministic threshold model is phasic, with periods of mutation between intervals of mutation-free growth. To establish the validity of this schedule, we now show that the phasic schedule that optimizes the deterministic threshold model significantly improves upon the best constant-rate schedule for the hybrid and Monte Carlo models.

Control of time-dependent biological processes by temporally patterned input

Temporal patterning of biological variables, in the form of oscillations and rhythms on many time scales, is ubiquitous. Altering the temporal pattern of an input variable greatly affects the output of many biological processes. We develop here a conceptual framework for a quantitative understanding of such pattern dependence, focusing particularly on nonlinear, saturable, time-dependent processes that abound in biophysics, biochemistry, and physiology. We show theoretically that pattern dependence is governed by the nonlinearity of the input–output transformation as well as its time constant. As a result, only patterns on certain time scales permit the expression of pattern dependence, and processes with different time constants can respond preferentially to different patterns. This has implications for temporal coding and decoding, and allows differential control of processes through pattern. We show how pattern dependence can be quantitatively predicted using only information from steady, unpatterned input. To apply our ideas, we analyze, in an experimental example, how muscle contraction depends on the pattern of motorneuron firing.

Time-dependent vascular regression and permeability changes in established human tumor xenografts induced by an anti-vascular endothelial growth factor/vascular permeability factor antibody

The hyperpermeability of tumor vessels to macromolecules, compared with normal vessels, is presumably due to vascular endothelial growth factor/vascular permeability factor (VEGF/VPF) released by neoplastic and/or host cells. In addition, VEGF/VPF is a potent angiogenic factor. Removal of this growth factor may reduce the permeability and inhibit tumor angiogenesis. To test these hypotheses, we transplanted a human glioblastoma (U87), a human colon adenocarcinoma (LS174T), and a human melanoma (P-MEL) into two locations in immunodeficient mice: the cranial window and the dorsal skinfold chamber. The mice bearing vascularized tumors were treated with a bolus (0.2 ml) of either a neutralizing antibody (A4.6.1) (492 μg/ml) against VEGF/VPF or PBS (control). We found that tumor vascular permeability to albumin in antibody-treated groups was lower than in the matched controls and that the effect of the antibody was time-dependent and influenced by the mode of injection. Tumor vascular permeability did not respond to i.p. injection of the antibody until 4 days posttreatment. However, the permeability was reduced within 6 h after i.v. injection of the same amount of antibody. In addition to the reduction in vascular permeability, the tumor vessels became smaller in diameter and less tortuous after antibody injections and eventually disappeared from the surface after four consecutive treatments in U87 tumors. These results demonstrate that tumor vascular permeability can be reduced by neutralization of endogenous VEGF/VPF and suggest that angiogenesis and the maintenance of integrity of tumor vessels require the presence of VEGF/VPF in the tissue microenvironment. The latter finding reveals a new mechanism of tumor vessel regression—i.e., blocking the interactions between VEGF/VPF and endothelial cells or inhibiting VEGF/VPF synthesis in solid tumors causes dramatic reduction in vessel diameter, which may block the passage of blood elements and thus lead to vascular regression.

Temperature, ordering, and equilibrium with time-dependent confining forces

The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures, whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher. Simulations with 1,000 ions reach equilibrium between the degrees of freedom when only aperiodic displacements (secular motion) are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.

Apolipoprotein E competitively inhibits receptor-dependent low density lipoprotein uptake by the liver but has no effect on cholesterol absorption or synthesis in the mouse.

This study examines the question of whether apolipoprotein E (apoE) alters steady-state concentrations of plasma cholesterol carried in low density lipoproteins (LDL-C) by acting as a competitive inhibitor of hepatic LDL uptake or by altering the rate of net cholesterol delivery from the intestinal lumen to the liver. To differentiate between these two possibilities, rates of cholesterol absorption and synthesis and the kinetics of hepatic LDL-C transport were measured in vivo in mice with either normal (apoE+/+) or zero (apoE-/-) levels of circulating apoE. Rates of cholesterol absorption were essentially identical in both genotypes and equaled approximately 44% of the daily dietary load of cholesterol. This finding was consistent with the further observation that the rates of cholesterol synthesis in the liver (approximately 2,000 nmol/h) and extrahepatic tissues (approximately 3,000 nmol/h) were also essentially identical in the two groups of mice. However, the apparent Michaelis constant for receptor-dependent hepatic LDL-C uptake was markedly lower in the apoE-/- mice (44 +/- 4 mg/dl) than in the apoE+/+ animals (329 +/- 77 mg/dl) even though the maximal transport velocity for this uptake process was essentially the same (approximately 400 micrograms/h per g) in the two groups of mice. These studies, therefore, demonstrate that apoE-containing lipoproteins can act as potent competitive inhibitors of hepatic LDL-C transport and so can significantly increase steady-state plasma LDL-C levels. This apolipoprotein plays no role, however, in the regulation of cholesterol absorption, sterol biosynthesis, or hepatic LDL receptor number, at least in the mouse.

Epitopes close to the apolipoprotein B low density lipoprotein receptor-binding site are modified by advanced glycation end products

Advanced glycation end products (AGEs) are thought to contribute to the abnormal lipoprotein profiles and increased risk of cardiovascular disease of patients with diabetes and renal failure, in part by preventing apolipoprotein B (apoB)-mediated cellular uptake of low density lipoproteins (LDL) by LDL receptors (LDLr). It has been proposed that AGE modification at one site in apoB, almost 1,800 residues from the putative apoB LDLr-binding domain, may be sufficient to induce an apoB conformational change that prevents binding to the LDLr. To further explore this hypothesis, we used 29 anti-human apoB mAbs to identify other potential sites on apoB that may be modified by in vitro advanced glycation of LDL. Glycation of LDL caused a time-dependent decrease in its ability to bind to the LDLr and in the immunoreactivity of six distinct apoB epitopes, including two that flank the apoB LDLr-binding domain. ApoB appears to be modified at multiple sites by these criteria, as the loss of glycation-sensitive epitopes was detected on both native glycated LDL and denatured, delipidated glycated apoB. Moreover, residues directly within the putative apoB LDLr-binding site are not apparently modified in glycated LDL. We propose that the inability of LDL modified by AGEs to bind to the LDLr is caused by modification of residues adjacent to the putative LDLr-binding site that were undetected by previous immunochemical studies. AGE modification either eliminates the direct participation of the residues in LDLr binding or indirectly alters the conformation of the apoB LDLr-binding site.

A joint hazard and time scaling model to compare survival curves.

To provide a more general method for comparing survival experience, we propose a model that independently scales both hazard and time dimensions. To test the curve shape similarity of two time-dependent hazards, h1(t) and h2(t), we apply the proposed hazard relationship, h12(tKt)/ h1(t) = Kh, to h1. This relationship doubly scales h1 by the constant hazard and time scale factors, Kh and Kt, producing a transformed hazard, h12, with the same underlying curve shape as h1. We optimize the match of h12 to h2 by adjusting Kh and Kt. The corresponding survival relationship S12(tKt) = [S1(t)]KtKh transforms S1 into a new curve S12 of the same underlying shape that can be matched to the original S2. We apply this model to the curves for regional and local breast cancer contained in the National Cancer Institute's End Results Registry (1950-1973). Scaling the original regional curves, h1 and S1 with Kt = 1.769 and Kh = 0.263 produces transformed curves h12 and S12 that display congruence with the respective local curves, h2 and S2. This similarity of curve shapes suggests the application of the more complete curve shapes for regional disease as templates to predict the long-term survival pattern for local disease. By extension, this similarity raises the possibility of scaling early data for clinical trial curves according to templates of registry or previous trial curves, projecting long-term outcomes and reducing costs. The proposed model includes as special cases the widely used proportional hazards (Kt = 1) and accelerated life (KtKh = 1) models.

Visualization of Receptor-mediated Endocytosis in Yeast

We studied the ligand-induced endocytosis of the yeast α-factor receptor Ste2p by immuno-electron microscopy. We observed and quantitated time-dependent loss of Ste2p from the plasma membrane of cells exposed to α-factor. This ligand-induced internalization of Ste2p was blocked in the well-characterized endocytosis-deficient mutant sac6Δ. We provide evidence that implicates furrow-like invaginations of the plasma membrane as the site of receptor internalization. These invaginations are distinct from the finger-like plasma membrane invaginations within actin cortical patches. Consistent with this, we show that Ste2p is not located within the cortical actin patch before and during receptor-mediated endocytosis. In wild-type cells exposed to α-factor we also observed and quantitated a time-dependent accumulation of Ste2p in intracellular, membrane-bound compartments. These compartments have a characteristic electron density but variable shape and size and are often located adjacent to the vacuole. In immuno-electron microscopy experiments these compartments labeled with antibodies directed against the rab5 homologue Ypt51p (Vps21p), the resident vacuolar protease carboxypeptidase Y, and the vacuolar H+-ATPase Vph1p. Using a new double-labeling technique we have colocalized antibodies against Ste2p and carboxypeptidase Y to this compartment, thereby identifying these compartments as prevacuolar late endosomes.

Polysomal ribonuclease 1 exists in a latent form on polysomes prior to estrogen activation of mRNA decay

Estrogen induces a global change in the translation profile of Xenopus hepatocytes, replacing serum protein synthesis with production of the yolk protein precursor vitellogenin. This is accomplished by the coordinate destabilization of serum protein mRNAs and the transcriptional induction and subsequent stabilization of vitellogenin mRNA. Previous work identified an endonuclease activity whose appearance on polysomes correlated with the disappearance of serum protein mRNAs. This enzyme, polysomal ribonuclease 1 (PMR1), is a novel member of the peroxidase gene family. The current study examined the association of PMR1 with its mRNA targets on polysomes and mRNPs. The highest amount of polysome-bound PMR1 was observed prior to estrogen induction of mRNA decay. Its distribution on sucrose density gradients matched the absorbance profile of polysome-bound mRNA, suggesting that PMR1 forms a latent complex with mRNA. Following dissociation with EDTA the 62 kDa PMR1 sedimented with a larger complex of >670 kDa. Estrogen induces a 22-fold increase in unit enzymatic activity of polysome-bound PMR1, and a time-dependent loss of PMR1 from polysomes in a manner that mirrors the disappearance of albumin mRNA. These data suggest that the key step in the extensive estrogen-induced change in mRNA decay in Xenopus liver is activation of a latent mRNA endonuclease associated with its target mRNA.

A Benzothiadiazole Primes Parsley Cells for Augmented Elicitation of Defense Responses

Systemic acquired resistance is an important component of the disease-resistance arsenal of plants, and is associated with an enhanced potency for activating local defense responses upon pathogen attack. Here we demonstrate that pretreatment with benzothiadiazole (BTH), a synthetic activator of acquired resistance in plants, augmented the sensitivity for low-dose elicitation of coumarin phytoalexin secretion by cultured parsley (Petroselinum crispum L.) cells. Enhanced coumarin secretion was associated with potentiated activation of genes encoding Phe ammonia-lyase (PAL). The augmentation of PAL gene induction was proportional to the length of pretreatment with BTH, indicating time-dependent priming of the cells. In contrast to the PAL genes, those for anionic peroxidase were directly induced by BTH in the absence of elicitor, thus confirming a dual role for BTH in the activation of plant defenses. Strikingly, the ability of various chemicals to enhance plant disease resistance correlated with their capability to potentiate parsley PAL gene elicitation, emphasizing an important role for defense response potentiation in acquired plant disease resistance.

Detection of Ca2+-Dependent Transglutaminase Activity in Root and Leaf Tissue of Monocotyledonous and Dicotyledonous Plants

Protein extracted from root and leaf tissue of the dicotyledonous plants pea (Pisum sativum) and broad bean (Vicia faba) and the monocotyledonous plants wheat (Triticum aestivum) and barley (Hordeum vulgare) were shown to catalyze the incorporation of biotin-labeled cadaverine into microtiter-plate-bound N′,N′-dimethylcasein and the cross-linking of biotin-labeled casein to microtiter-plate-bound casein in a Ca2+-dependent manner. The cross-linking of biotinylated casein and the incorporation of biotin-labeled cadaverine into N′,N′-dimethylcasein were time-dependent reactions with a pH optimum of 7.9. Transglutaminase activity was shown to increase over a 2-week growth period in both the roots and leaves of pea. The product of transglutaminase's protein-cross-linking activity, ε-(γ-glutamyl)-lysine isodipeptide, was detected in root and shoot protein from pea, broad bean, wheat, and barley by cation-exchange chromatography. The presence of the isodipeptide was confirmed by reversed-phase chromatography. Hydrolysis of the isodipeptide after cation-exchange chromatography confirmed the presence of glutamate and lysine.

Platelet-derived growth factor stimulates the secretion of hyaluronic acid by proliferating human vascular smooth muscle cells.

Total glycans from the cell layer and the culture medium of human vascular smooth muscle cells (VSMC) that had been cultivated in the presence of platelet-derived growth factor (PDGF) were isolated and purified by gel filtration after Pronase and DNase digestion and alkaliborohydride treatment. Measurements of the content of neutral hexoses and uronic acids revealed that PDGF stimulates total glycan synthesis by proliferating VSMC in a linear fashion from 24 h to 72 h of incubation. In contrast, total glycan synthesis by human fibroblasts, epithelial cells, or endothelial cells was not affected by PDGF, indicating cell-type specificity. Chemical, biochemical, and enzymological characterization of the total glycans synthesized by VSMC showed that PDGF stimulates the secretion of a 340-kDa glycan molecule in a time-dependent manner from 24 h to 72 h. This molecule is highly acidic, shares a common structure with hyaluronic acid, and exhibits a potent antiproliferative activity on VSMC. These results suggest that VSMC in response to PDGF are capable of controlling their own growth and migration by the synthesis of a specific form of hyaluronic acid with antiproliferative potency, which may be involved in the regulation of the local inflammatory responses associated with atherosclerosis.