High temporal resolution gastric emptying breath tests in mice.

BACKGROUND: Gastric emptying is a complex physiological process regulating the division of a meal into smaller partitions for the small intestine. Disrupted gastric emptying contributes to digestive disease, yet current measures may not reflect different mechanisms by which the process can be altered. METHODS: We have developed high temporal resolution solid and liquid gastric emptying breath tests in mice using [13 C]-octanoic acid and off axis- integrated cavity output spectroscopy (OA-ICOS). Stretched gamma variate and 2-component stretched gamma variate models fit measured breath excretion data. KEY RESULTS: These assays detect acceleration and delay using pharmacological (7.5 mg/kg atropine) or physiological (nutrients, cold exposure stress, diabetes) manipulations and remain stable over time. High temporal resolution resolved complex excretion curves with 2 components, which was more prevalent in mice with delayed gastric emptying following streptozotocin-induced diabetes. There were differences in the gastric emptying of Balb/c vs C57Bl6 mice, with slower gastric emptying and a greater occurrence of two-phase gastric emptying curves in the latter strain. Gastric emptying of C57Bl6 could be accelerated by halving the meal size, but with no effect on the occurrence of two-phase gastric emptying curves. A greater proportion of two-phase gastric emptying was induced in Balb/c mice with the administration of PYY (8-80 nmol) 60 min following meal ingestion. CONCLUSIONS AND INFERENCES: Collectively, these results demonstrate the utility of high temporal resolution gastric emptying assays. Two-phase gastric emptying is more prevalent than previously reported, likely involves intestinal feedback, but contributes little to the overall rate of gastric emptying.

Dynamics of melanoma tumor therapy with vesicular stomatitis virus: explaining the variability in outcomes using mathematical modeling.

Tumor selective, replication competent viruses are being tested for cancer gene therapy. This approach introduces a new therapeutic paradigm due to potential replication of the therapeutic agent and induction of a tumor-specific immune response. However, the experimental outcomes are quite variable, even when studies utilize highly inbred strains of mice and the same cell line and virus. Recognizing that virotherapy is an exercise in population dynamics, we utilize mathematical modeling to understand the variable outcomes observed when B16ova malignant melanoma tumors are treated with vesicular stomatitis virus in syngeneic, fully immunocompetent mice. We show how variability in the initial tumor size and the actual amount of virus delivered to the tumor have critical roles on the outcome of therapy. Virotherapy works best when tumors are small, and a robust innate immune response can lead to superior tumor control. Strategies that reduce tumor burden without suppressing the immune response and methods that maximize the amount of virus delivered to the tumor should optimize tumor control in this model system.

Dynamics of multiple myeloma tumor therapy with a recombinant measles virus.

Replication-competent viruses are being tested as tumor therapy agents. The fundamental premise of this therapy is the selective infection of the tumor cell population with the amplification of the virus. Spread of the virus in the tumor ultimately should lead to eradication of the cancer. Tumor virotherapy is unlike any other form of cancer therapy as the outcome depends on the dynamics that emerge from the interaction between the virus and tumor cell populations both of which change in time. We explore these interactions using a model that captures the salient biological features of this system in combination with in vivo data. Our results show that various therapeutic outcomes are possible ranging from tumor eradication to oscillatory behavior. Data from in vivo studies support these conclusions and validate our modeling approach. Such realistic models can be used to understand experimental observations, explore alternative therapeutic scenarios and develop techniques to optimize therapy.

Noninvasive measurement of concurrent single-kidney perfusion, glomerular filtration, and tubular function.

To assess the reliability of electron beam computed tomography (EBCT), measurements of single-kidney renal blood flow (RBF), glomerular filtration rate (GFR), and intratubular contrast medium concentration (ITC) of radiographic contrast media were quantified in anesthetized pigs before and after acetylcholine-induced vasodilation and diuresis. EBCT measurements were compared with those obtained with intravascular Doppler and inulin clearance. The capability of EBCT to detect chronic changes in single-kidney function was evaluated in pigs with unilateral renal artery stenosis, and their long-term reproducibility in normal pigs was studied repeatedly at 1-mo intervals. EBCT-RBF (ml/min) correlated with Doppler-RBF as RBF(EBCT) = 45 + 1.07 * RBF(Doppler), r = 0.81. EBCT-GFR (ml/min) correlated with inulin clearance as GFR(EBCT) = 11.7 + 1.02 * GFR(inulin), r = 0.80. During vasodilation, RBF and GFR increased, whereas ITC decreased along the nephron. In renal artery stenosis, single-kidney GFR decreased linearly with the degree of stenosis, and ITC increased along the nephron, indicating increased fluid reabsorption. EBCT-RBF, GFR, and ITC were similar among repeated measurements. This approach might be invaluable for simultaneous quantification of regional hemodynamics and function in the intact kidneys, in a manner potentially applicable to humans.

The plasma membrane calcium pump displays memory of past calcium spikes. Differences between isoforms 2b and 4b.

To understand how the plasma membrane Ca(2+) pump (PMCA) behaves under changing Ca(2+) concentrations, it is necessary to obtain information about the Ca(2+) dependence of the rate constants for calmodulin activation (k(act)) and for inactivation by calmodulin removal (k(inact)). Here we studied these constants for isoforms 2b and 4b. We measured the ATPase activity of these isoforms expressed in Sf9 cells. For both PMCA4b and 2b, k(act) increased with Ca(2+) along a sigmoidal curve. At all Ca(2+) concentrations, 2b showed a faster reaction with calmodulin than 4b but a slower off rate. On the basis of the measured rate constants, we simulated mathematically the behavior of these pumps upon repetitive changes in Ca(2+) concentration and also tested these simulations experimentally; PMCA was activated by 500 nm Ca(2+) and then exposed to 50 nm Ca(2+) for 10 to 150 s, and then Ca(2+) was increased again to 500 nm. During the second exposure to 500 nm Ca(2+), the activity reached steady state faster than during the first exposure at 500 nm Ca(2+). This memory effect is longer for PMCA2b than for 4b. In a separate experiment, a calmodulin-binding peptide from myosin light chain kinase, which has no direct interaction with the pump, was added during the second exposure to 500 nm Ca(2+). The peptide inhibited the activity of PMCA2b when the exposure to 50 nm Ca(2+) was 150 s but had little or no effect when this exposure was only 15 s. This suggests that the memory effect is due to calmodulin remaining bound to the enzyme during the period at low Ca(2+). The memory effect observed in PMCA2b and 4b will allow cells expressing either of them to remove Ca(2+) more quickly in subsequent spikes after an initial activating spike.

Complex homogeneous and heterogeneous fluorescence anisotropy decays: enhancing analysis accuracy.

In biological macromolecules, fluorophores often exhibit multiple depolarizing motions that require multiple lifetimes and rotational relaxation times to define fluorescence intensity and anisotropy decays. The related analysis of time-correlated single-photon counting data becomes uncertain due to the multitude of decay parameters and numerical sensitivity to deconvolution of the instrument response function (IRF) via discretization of integrals. By using simulations we show that improved discretizations based on quadratic and cubic local approximations of the IRF yield more accurate estimation of short rotational relaxation times and lifetimes than the commonly used Grinvald-Steinberg discretization, which in turn appears more reliable than two discretizations based on linear local approximations of the IRF. In addition, our simulation suggests that cubic approximation is the most advantageous in discriminating complex heterogeneous and homogeneous anisotropy decay. We show that among three different information criteria, the Akaike information criterion is best suited for detection of heterogeneity in rotational relaxation times. It is capable of detecting heterogeneity even when anisotropy decay appears homogeneous within statistical errors of estimation.

Choline acetyltransferase mutations cause myasthenic syndrome associated with episodic apnea in humans.

Choline acetyltransferase (ChAT; EC ) catalyzes the reversible synthesis of acetylcholine (ACh) from acetyl CoA and choline at cholinergic synapses. Mutations in genes encoding ChAT affecting motility exist in Caenorhabditis elegans and Drosophila, but no CHAT mutations have been observed in humans to date. Here we report that mutations in CHAT cause a congenital myasthenic syndrome associated with frequently fatal episodes of apnea (CMS-EA). Studies of the neuromuscular junction in this disease show a stimulation-dependent decrease of the amplitude of the miniature endplate potential and no deficiency of the ACh receptor. These findings point to a defect in ACh resynthesis or vesicular filling and to CHAT as one of the candidate genes. Direct sequencing of CHAT reveals 10 recessive mutations in five patients with CMS-EA. One mutation (523insCC) is a frameshifting null mutation. Three mutations (I305T, R420C, and E441K) markedly reduce ChAT expression in COS cells. Kinetic studies of nine bacterially expressed ChAT mutants demonstrate that one mutant (E441K) lacks catalytic activity, and eight mutants (L210P, P211A, I305T, R420C, R482G, S498L, V506L, and R560H) have significantly impaired catalytic efficiencies.

The rate of activation by calmodulin of isoform 4 of the plasma membrane Ca(2+) pump is slow and is changed by alternative splicing.

A reconstitution system allowed us to measure the ATPase activity of specific isoforms of the plasma membrane Ca(2+) pump continuously, and to measure the effects of adding or removing calmodulin. The rate of activation by calmodulin of isoform 4b was found to be very slow, with a half-time (at 235 nM calmodulin and 0.5 microM free Ca(2+)) of about 1 min. The rate of inactivation of isoform 4b when calmodulin was removed was even slower, with a half-time of about 20 min. Isoform 4a has a lower apparent affinity for calmodulin than 4b, but its activation rate was surprisingly faster (half time about 20 s). This was coupled with a much faster inactivation rate, consistent with its low affinity. A truncated mutant of isoform 4b also had a more rapid activation rate, indicating that the downstream inhibitory region of full-length 4b contributed to its slow activation. The results indicate that the slow activation is due to occlusion of the calmodulin-binding domain of 4b, caused by its strong interaction with the catalytic core. Since the activation of 4b occurs on a time scale comparable to that of many Ca(2+) spikes, this phenomenon is important to the function of the pump in living cells. The slow response of 4b indicates that this isoform may be the appropriate one for cells which respond slowly to Ca(2+) signals.

Differences in metabolism of 5-fluorouracil and 5-fluorouridine and regulation by glucosamine in human colon cancer multicell tumor spheroids.

Glucosamine (GlcN) modulates fluoropyrimidine metabolism and enhances cytotoxicity of 5-fluorouridine (FUrd), but not of 5-fluorouracil (FUra), in human tumor models. To elucidate the underlying metabolic differences between FUra and FUrd, by the use of 19F and 31P NMR spectroscopy we studied these drugs in multicell tumor spheroids (MTS) formed by human colon carcinoma cells HT-29. This experimental system allowed detailed kinetic measurements of anabolic intracellular phosphates and fluorophosphates over periods of up to 2 days. Time-dependent NMR data were reduced and interpreted by the use of nonlinear compartmental models which yielded numerical values for the empirical rate constants characterizing mass transfer among the compartments. An analysis of these rate constants indicated qualitative and quantitative differences in the metabolism of FUra and FUrd and in the effects of GlcN on these drugs. The enhanced generation of FUDP-hexoses was a predicted effect of GlcN, but inhibited formation of fluorouridine diphosphates and fluorouridine triphosphates in FUra-treated MTS, and the magnitude of stimulation of fluoropyrimidine incorporation into macromolecules in FUrd-treated MTS were not predicted.

Rotational and translational motion of troponin C.

Time resolved fluorescence anisotropy and sedimentation velocity has been used to study the rotational and translational hydrodynamic behavior of two mutants of chicken skeletal troponin C bearing a single tryptophan residue at position 78 or 154 in the metal-free-, metal-bound-, and troponin I peptide (residues 96-116 of troponin I)-ligated states. The fluorescence anisotropy data of both mutants were adequately described by two rotational correlation times, and these are compared with the theoretically expected values based on the rotational diffusion of an idealized dumbbell. These data imply that the motion of the N- and C-terminal domains of troponin C are independent. They also suggest that in the metal-free, calcium-saturated and calcium-saturated troponin I peptide-bound states, troponin C is elongated, having an axial ratio of 4-5. Calcium or magnesium binding to the high affinity sites alone reduces the axial ratio to approximately 3. However, with calcium bound to sites III and IV and in the presence of a 1:1 molar ratio of the troponin I peptide, troponin C is approximately spherical. The metal ion and troponin I peptide-induced length changes in troponin C may play a role in the mechanism by which the regulatory function of troponin C is effected.

Gompertzian growth as a self-similar and allometric process.

The Gompertz law of growth has puzzled scientists for decades: while it successfully described growth kinetics of various biological systems (e.g., tumor growth), its foundation has remained unclear. In this paper I recognize the Gompertzian growth as founded on self-similarity, which is so abundant in natural phenomena that it justifiably represents a fundamental natural paradigm. The self-similarity leads to an allometric principle: the sizes of a given biological system at different times are related by a simple power law. The stated relation can be also viewed as basic functional growth equation with unique nonconstant solutions being the Gompertz and the exponential functions. This equation also provides the description of growth and regression dynamics in terms of a difference equation which already has found practical application in characterizing tumor growth kinetics.

Analytical approach to the recovery of short fluorescence lifetimes from fluorescence decay curves.

Considerable effort in instrument development has made possible detection of picosecond fluorescence lifetimes by time-correlated single-photon counting. In particular, efforts have been made to narrow markedly the instrument response function (IRF). Less attention has been paid to analytical methods, especially to problem of discretization of the convolution integral, on which the detection and quantification of short lifetimes critically depends. We show that better discretization methods can yield acceptable results for short lifetimes even with an IRF several times wider than necessary for the standard discretization based on linear approximation (LA). A general approach to discretization, also suitable for nonexponential models, is developed. The zero-time shift is explicitly included. Using simulations, we compared LA, quadratic, and cubic approximations. The latter two proved much better for detection of short lifetimes and, in that respect, they do not differ except when the zero-time shift exceeds two channels, when one can benefit from using the cubic approximation. We showed that for LA in some cases narrowing the IRF beyond FWHM = 150 ps is actually counterproductive. This is not so for quadratic and cubic approximations, which we recommend for general use.

Tumor growth in vivo and as multicellular spheroids compared by mathematical models.

In vivo volume growth of two murine tumor cell lines was compared by mathematical modeling to their volume growth as multicellular spheroids. Fourteen deterministic mathematical models were studied. For one cell line, spheroid growth could be described by a model simpler than needed for description of growth in vivo. A model that explicitly included the stimulatory role for cell-cell interactions in regulation of growth was always superior to a model that did not include such a role. The von Bertalanffy model and the logistic model could not fit the data; this result contradicted some previous literature and was found to depend on the applied least squares fitting method. By the use of a particularly designed mathematical method, qualitative differences were discriminated from quantitative differences in growth dynamics of the same cells cultivated in two different three-dimensional systems.

Analysis of growth of multicellular tumour spheroids by mathematical models.

We wished to determine the applicability of previously proposed deterministic mathematical models to description of growth of multicellular tumour spheroids. The models were placed into three general classes: empirical, functional and structural. From these classes, 17 models were applied systematically to growth curves of multicellular tumour spheroids used as paradigms of prevascular and microregional tumour growth. The spheroid growth curves were determined with uniquely high density of measurements and high precision. The theoretical growth curves obtained from the models were fitted by the weighted least-squares method to the 15 measured growth curves, each corresponding to a different cell line. The classical growth models such as von Bertalanffy, logistic and Gompertz were considered as nested within more general models. Our results demonstrate that most models fitted the data fairly well and that criteria other than statistical had to be used for final selection. The Gompertz, the autostimulation and the simple spheroid models were the most appropriate for spheroid growth in the empirical, functional and structural classes of models, respectively. We also showed that some models (e.g. logistic, von Bertalanffy) were clearly inadequate. Thus, contrary to the widely held belief, the sigmoid character of a three or more parameter growth function is not sufficient for adequate fits.

A model for multiexponential tryptophan fluorescence intensity decay in proteins.

Tryptophan fluorescence intensity decay in proteins is modeled by multiexponential functions characterized by lifetimes and preexponential factors. Commonly, multiple conformations of the protein are invoked to explain the recovery of two or more lifetimes from the experimental data. However, in many proteins the structure seems to preclude the possibility of multiple conformers sufficiently different from one another to justify such an inference. We present here another plausible multiexponential model based on the assumption that an energetically excited donor surrounded by N acceptor molecules decays by specific radiative and radiationless relaxation processes, and by transferring its energy to acceptors present in or close to the protein matrix. If interactions between the acceptors themselves and back energy transfer are neglected, we show that the intensity decay function contain 2N exponential components characterized by the unperturbed donor lifetime, by energy transfer rates and a probability of occurrence for the corresponding process. We applied this model to the fluorescence decay of holo- and apoazurin, ribonuclease T1, and the reduced single tryptophan mutant (W28F) of thioredoxin. Use of a multiexponential model for the analysis of the fluorescence intensity decay can therefore be justified, without invoking multiple protein conformations.

EndoCyte 1.2: An improved algorithm for quantitative analysis of receptor-mediated endocytosis.

This paper reports the improvement of EndoCyte, the computer program for kinetic analysis of receptor-mediated endocytosis. A non-standard algorithm for parameter evaluation was developed and incorporated into the program. The comparison of the original program and the updated EndoCyte 1.2 revealed that the new algorithm was significantly more efficient.

EndoCyte, an interactive computer program for quantitative analysis of receptor-mediated endocytosis.

We present EndoCyte, a user friendly interactive program for quantitative analysis of receptor-mediated endocytosis. The data, comprised of time-dependent concentrations of the ligand at the cell surface and the ligand internalized by cells, are analyzed by the application of a set of nested mathematical models of endocytosis. EndoCyte reduces data to parameters conventional in description of receptor-mediated endocytosis and a parameter which describes the non-linear effects. The performance of EndoCyte is documented by the analysis of applications to synthetic data.

Rate transition and regulatory coupling in endocytosis of interferon-alpha and tumor necrosis factor-alpha in human epithelial tumor cells.

The time-dependent concentrations of interferon-alpha and tumor necrosis factor-alpha associated with the membrane and internalized by cells contain information on the kinetics of endocytosis and their cellular processing. This information can be reduced quantitatively by application of the respective compartmental models. In our studies of human epithelial tumor cells interacting with human interferon-alpha and human tumor necrosis factor-alpha, we accounted only for actual endocytosis and elimination of the tracer from cells by a novel method sensitive to changes in the rate of endocytosis, to the delay in tracer elimination, and to the nonlinear regulatory coupling between endocytosis and the internalized ligand. Data reduced by this method resulted in best-fit parameter values statistically superior to values obtained by previous methods (Bajzer et al., 1989). The results indicate a change with time in the rate of endocytosis of tumor necrosis factor-alpha and the inhibition of endocytosis by the endocytosed ligand-receptor complex. We conclude that sorting and processing of interferon-alpha and tumor necrosis factor-alpha are restricted by the type of both the receptor and the cell.