Finite element model of antibody penetration in a prevascular tumor nodule embedded in normal tissue.

We have developed a pharmacokinetic model for monoclonal antibodies (mAb) to aid in investigating protocols for targeting small primary tumors or sites of metastatic disease. The model describes the uptake of systemically-administered antibody by a prevascular spherical tumor nodule embedded in normal tissue. The model incorporates plasma kinetics, transcapillary transport, interstitial diffusion, binding reactions, and lymphatic clearance. Antigen internalization can easily be incorporated. Simulations obtained from a three-dimensional finite element analysis are used to assess errors in predictions from earlier models in which the influence of the normal tissue was collapsed into a boundary condition at the tumor surface. The model employing a Dirichlet boundary condition substantially overpredicted the mean total tumor mAb concentration at all times. Although the model with a concentration-dependent flux (composite) boundary condition underpredicted mAb concentration, the discrepancy with finite element results is only notable at early times. Sensitivity analyses were performed on mAb dose and on the coefficients for mAb diffusion in the tissue regions, since reported antibody diffusivity values have varied over 30-fold. The results of the study suggest that mAb diffusivity and mAb binding site density in tumors should have major influences on optimizing doses and scheduling of mAb administration in tumor targeting protocols.

Computational models of antibody-based tumor imaging and treatment protocols.

We present improved computational models for investigating monoclonal antibody-based protocols for diagnostic imaging and therapy of solid tumors. Our earlier models used a boundary condition (Dirichlet) that specified concentrations of diffusing molecular species at the interface between a prevascular tumor nodule and surrounding normal tissue. Here we introduce a concentration-dependent flux boundary condition with finite rates of diffusion in the normal tissue. We then study the effects of this new condition on the tumor's temporal uptake and spatial distribution of radiolabeled targeting agents. We compare these results to ones obtained with the Dirichlet boundary condition and also conduct parameter sensitivity analyses. Introducing finite diffusivity for any molecular species in normal tissue retards its delivery to and removal from the tumor nodule. Effects are protocol- and dose regimen-dependent: generally, however, mean radionuclide concentration and tumor-to-blood ratio declined, whereas relative exposure and mean residence time increased. Finite diffusivity exacerbates the negative effects of antigen internalization. Also, the sensitivity analyses show that mean concentration and tumor-to-blood ratio are quite sensitive to transcapillary permeability and lymphatic efflux values, yet relatively insensitive to precise values of diffusion coefficients. Our analysis underscores that knowledge of antigen internalization rates and doses required to saturate antigen in the tumor will be important for exploiting antibody-based imaging and treatment approaches.

An information-intensive approach to the molecular pharmacology of cancer.

Since 1990, the National Cancer Institute (NCI) has screened more than 60,000 compounds against a panel of 60 human cancer cell lines. The 50-percent growth-inhibitory concentration (GI50) for any single cell line is simply an index of cytotoxicity or cytostasis, but the patterns of 60 such GI50 values encode unexpectedly rich, detailed information on mechanisms of drug action and drug resistance. Each compound's pattern is like a fingerprint, essentially unique among the many billions of distinguishable possibilities. These activity patterns are being used in conjunction with molecular structural features of the tested agents to explore the NCI's database of more than 460,000 compounds, and they are providing insight into potential target molecules and modulators of activity in the 60 cell lines. For example, the information is being used to search for candidate anticancer drugs that are not dependent on intact p53 suppressor gene function for their activity. It remains to be seen how effective this information-intensive strategy will be at generating new clinically active agents.

Pharmacokinetic comparison of direct antibody targeting with pretargeting protocols based on streptavidin-biotin binding.

UNLABELLED: Several groups are currently investigating antibody pretargeting as a strategy for improving radionuclide delivery. Pharmacokinetic modeling of these protocols permits analysis of pretargeting protocols under a broad range of possible experimental conditions. METHODS: We used previously developed pharmacokinetic models to predict the temporal uptake and spatial distribution of directly radiolabeled MAb, radiolabeled biotin given after pretargeting with streptavidinylated MAb and radiolabeled streptavidin given after pretargeting with biotinylated MAb in a microscopic, prevascular tumor nodule. Two dose regimens were investigated, as were the effects of internalization and degradation of antibody-antigen complexes (24-hr time constant). RESULTS: Simulations indicate that the protocol involving streptavidinylated MAb and radiolabeled biotin yields higher tumor-to-blood and tumor-to-lung ratios and relative exposures than the other protocols. In the absence of antigen internalization, the peak average molar concentration and MRT of biotin in the tumor nodule is comparable to that of directly radiolabeled MAb, and the spatial distribution of radionuclide is more uniform. When antigen internalization occurs, the peak average concentration and the MRT in the tumor nodule are lower than the corresponding values for directly radiolabeled MAb. CONCLUSION: In the absence of antigen internalization, the protocol involving streptavidinylated MAb and radiolabeled biotin offers pharmacokinetic advantages over the other two protocols.

Use of the Kohonen self-organizing map to study the mechanisms of action of chemotherapeutic agents.

BACKGROUND: Many natural and synthetic compounds might prove to be effective in cancer chemotherapy. To identify potentially useful agents, the National Cancer Institute screens over 10,000 compounds annually against a panel of 60 distinct human tumor cell lines in vitro. This screening program generates large amounts of data that are organized into relational databases. Important questions concern the information content of the data and ways to extract that information. Previously, statistical techniques have revealed that compounds with similar patterns of activity against the 60 cell lines are often similar in structure and mechanism of action. Feed-forward, back-propagation neural networks have been trained on this type of data to predict broadly defined mechanisms of action of chemotherapeutic agents. PURPOSE AND METHOD: In this report, we examine the information that can be extracted from the screening data by means of another type of neural network paradigm, the Kohonen self-organizing map. This is a topology-preserving function, obtained by unsupervised learning, that nonlinearly projects the high-dimensional activity patterns into two dimensions. Our dataset is almost identical to that used in the earlier neural network study. RESULTS: The self-organizing maps we constructed have several important characteristics. 1) They partition the two-dimensional array into distinct regions, each of which is principally occupied by agents having the same broadly defined mechanism of action. 2) These regions can be resolved into distinct subregions that conform to plausible submechanisms and chemically defined subgroups of submechanism. 3) These results (and exceptions to them) are consistent with those obtained with the use of such deterministic measures of similarity among activity patterns as the Euclidean distance or Pearson correlation coefficient. CONCLUSIONS: Our results indicate that the activity patterns obtained from the screen contain detailed information about mechanism of action and its basis in chemical structure. The self-organizing map can be used to suggest the mechanism of action of compounds identified by the screen as potentially useful chemotherapeutic agents and to probe the biology of the cell lines in the cancer screen. Kohonen self-organizing maps, unlike the previously applied neural networks, preserve and reveal the relationships among compounds acting by similar mechanisms and therefore have the potential to identify compounds that act by novel cytotoxic mechanisms.

Streptavidin distribution in metastatic tumors pretargeted with a biotinylated monoclonal antibody: theoretical and experimental pharmacokinetics.

We have developed a pharmacokinetic model for the analysis of a protocol that involves injection of a biotinylated monoclonal antibody followed at a later time by radiolabeled streptavidin. Three distinct physiological spaces are described: an avascular tumor nodule, the normal tissue surrounding the tumor, and the plasma. The model incorporates processes such as plasma kinetics, transcapillary transport, interstitial diffusion, binding reactions, and lymphatic clearances. We have modeled cases in which antigen turnover does not occur, in which antigen turnover does occur (24-h time constant), and in which circulating antibody is cleared from the plasma immediately prior to injection of streptavidin. We have calculated the spatial and temporal distributions of a tumor-specific antibody and of streptavidin in the tumor nodule using parameter values that simulate conditions of recent experiments on metastatic nodules in the guinea pig lung. The theoretical distribution of streptavidin in the tumor nodule shows an initial localization at the periphery that progresses to a fairly uniform distribution throughout the nodule, a temporal sequence that is very similar to experimental observation. This finding indicates that, in a tumor pretargeted with biotinylated antibody, streptavidin can encounter significant retardation in its penetration as a consequence of the high affinity interaction between these two species. Tumor:blood and tumor:lung ratios were calculated and compared to experimental results. In addition, the calculated tumor:blood ratios, tumor:lung ratios, and relative exposures were compared to values obtained from a model of one-step antibody delivery. The two-step protocol yielded an approximately 2- to 3-fold enhancement in these pharmacokinetic indices compared with the one-step method.

A distributed pharmacokinetic model of two-step imaging and treatment protocols: application to streptavidin-conjugated monoclonal antibodies and radiolabeled biotin.

Two-step imaging and treatment protocols involve injecting a suitably prepared monoclonal antibody that can bind both to a specific tumor antigen and to a second reagent which carries a drug or radionuclide. The second component is injected later, after the antibody has distributed throughout the target tumors and been largely cleared from the plasma and normal tissues. We introduce a mathematical model for the analysis of such protocols and apply it to the case of a streptavidinylated monoclonal antibody and radiolabeled biotin diffusing into small, prevascular, densely cellular nodules that represent either primary or metastatic tumors. We examine the distribution of streptavidinylated antibody and radiolabeled biotin within a tumor nodule and compare the two-step protocol to a one-step protocol using radiolabeled antibody. Our analysis predicts that (1) streptavidinylation reduces both the amount of antibody that distributes into the tumor nodule and the homogeneity of that distribution; (2) streptavidinylated antibody in the nodule can be saturated by initial plasma concentrations of free radiolabeled biotin substantially lower than the initial plasma concentration of free streptavidinylated antibody; (3) radiolabeled biotin diffuses rapidly, but binds so quickly that it will not penetrate deeply into the nodule if too low a dose is given. Hence, nonuniform localization of radiolabel may result from a "binding site barrier" to diffusion of either or both components; and (4) the two-step protocol permits imaging sooner after injection of radiolabeled material than the one-step protocol and produces a higher exposure in tumor relative to plasma, even in the presence of antigen turnover.

Effects of the anesthetic dibucaine on the kinetics of the gel-liquid crystalline transition of dipalmitoylphosphatidylcholine multilamellar vesicles.

The effects of the anesthetic dibucaine on the relaxation kinetics of the gel-liquid crystalline transition of dipalmitoylphosphatidylcholine (DC16PC) multilamellar vesicles have been investigated using volume-perturbation calorimetry. The temperature and pressure responses to a periodic volume perturbation were measured in real time. Data collected in the time domain were subsequently converted into and analyzed in the frequency domain using Fourier series representations of the perturbation and response functions. The Laplace transform of the classical Kolmogorov-Avrami kinetic relation was employed to describe the relaxation dynamics in the frequency domain. The relaxation time of anesthetic-lipid mixtures, as a function of the fractional degree of melting, appears to be qualitatively similar to that of pure lipid systems, with a pronounced maximum, tau max, observed at a temperature corresponding to greater than 75% melting. The tau max decreases by a factor of approximately 2 as the nominal anesthetic/lipid mole ratio increases from 0 to 0.013 and exhibits no further change as the nominal anesthetic/lipid mole ratio is increased. However, the fractional dimensionality of the relaxation process decreases monotonically from slightly less than two to approximately one as the anesthetic/lipid mole ratio increases from 0 to 0.027. At higher ratios, the dimensionality appears to be less than one. These results are interpreted in terms of the classical kinetic theory and related to those obtained from Monte Carlo simulations. Specifically, low concentrations of dibucaine appear to reduce the average cluster size and cause the fluctuating lipid clusters to become more ramified. At the highest concentration of dibucaine, where n < 1, the system must be kinetically heterogeneous.

Gel-liquid crystalline transition of some multilamellar lipid bilayers follows classical kinetics with a fractional dimensionality of approximately two.

The relaxation kinetics of the gel-liquid crystalline transition of phosphatidylcholine (DC14PC, DC16PC, and DC18PC) multilamellar vesicles have been examined using volume-perturbation calorimetry. The time-dependent temperature and pressure changes associated with a periodic volume perturbation are monitored in real time. Data collected in the time domain are transformed to the frequency domain using Fourier series representations of the perturbation and response functions. Because a very small perturbation is imposed during the experiment, linear response theory is suitable for analysis of the relaxation process. The Laplace transform of the classical Kolmogorov-Avrami relation of transition kinetics is used to describe the dynamic response in the frequency domain. For DC14PC and DC16PC, the relaxation process is better fit with an effective dimensionality of n = 2 rather than n = 1. For DC18PC, we estimate that an effective dimensionality of approximately 1.5 will best fit the data. These results indicate that the gel-liquid crystalline transition of these lipid bilayers follows the classical Kolmogorov-Avrami kinetic model with an effective dimensionality greater than 1 and the assumption of simple exponential decay (n = 1) commonly used in data analysis may not always be valid for lipid transitions. Insofar as the dimensionality of the relaxation reflects the geometry of fluctuating lipid clusters, this parameter may be useful in connecting experimental thermodynamic and kinetic results with those obtained from Monte Carlo simulations.

Relaxation dynamics of the gel to liquid-crystalline transition of phosphatidylcholine bilayers. Effects of chainlength and vesicle size.

The relaxation kinetics of the gel to liquid-crystalline transition of five phosphatidylcholine (DC14PC to DC18PC) bilayer dispersions have been investigated using volume perturbation calorimetry, a steady-state technique which subjects a sample to sinusoidal changes in volume. Temperature and pressure responses to the volume perturbation are measured to monitor the relaxation to a new equilibrium position. The amplitude demodulation and phase shift of these observables are analyzed with respect to the perturbation frequency to yield relaxation times and amplitudes. In the limit of low perturbation frequency, the temperature and pressure responses are proportional to the equilibrium excess heat capacity and bulk modulus, respectively. At all temperatures, the thermal response data are consistent with a single primary relaxation process of the lipid. The less accurate bulk modulus data exhibit two relaxation times, but it is not clear whether they reflect lipid processes or are characteristic of the instrument. The observed thermal relaxation behavior of all multilamellar vesicles are quantitatively similar. The relaxation times vary from approximately 50 ms to 4 s, with a pronounced maximum at a temperature just greater than Tm, the temperature of the excess heat capacity maximum. Large unilamellar vesicles also exhibit a single relaxation process, but without a pronounced maximum in the relaxation time. Their relaxation time is approximately 80 ms over most of the transition range.

Multifrequency calorimetry of the folding/unfolding transition of cytochrome c.

The folding-unfolding transition of Fe(III) cytochrome c has been studied with the new technique of multifrequency calorimetry. Multifrequency calorimetry is aimed at measuring directly the dynamics of the energetic events that take place during a thermally induced transition by measuring the frequency dispersion of the heat capacity. This is done by modulating the folding/unfolding equilibrium using a variable frequency, small oscillatory temperature perturbation (approximately 0.05-0.1 degrees C) centered at the equilibrium temperature of the system. Fe(III) cytochrome c at pH 4 undergoes a fully reversible folding/unfolding transition centered at 67.7 degrees C and characterized by an enthalpy change of 81 kcal/mol and heat capacity difference between unfolded and folded states of 0.9 kcal/K*mol. By measuring the temperature dependence of the frequency dispersion of the heat capacity in the frequency range of 0.1-1 Hz it has been possible to examine the time regime of the enthalpic events associated with the transition. The multifrequency calorimetry results indicate that approximately 85% of the excess heat capacity associated with the folding/unfolding transition relaxes with a single relaxation time of 326 +/- 68 ms at the midpoint of the transition region. This is the first time that the time regime in which heat is absorbed and released during protein folding/unfolding has been measured.

Measuring the kinetics of membrane phase transitions.

This article presents a brief review of literature on the physical chemistry of lipid phase transitions with emphasis on their kinetic properties. The theoretical foundations of perturbation techniques, and specifically the volume-perturbation technique are discussed in some detail. These are presented as a rationale for, and introduction to, a volume-perturbation kinetic calorimeter that we have constructed for measurement of the kinetics of lipid phase transitions. The instrument has been applied to study the gel-liquid crystalline phase transition in a variety of phospholipid bilayer systems. The design and implementation of the volume-perturbation calorimeter are presented along with a discussion of the techniques of data analysis. Finally, we present typical results obtained with this methodology for a multilamellar vesicle dispersion of dipalmitoylphosphatidylcholine.

Frequency spectrum of enthalpy fluctuations associated with macromolecular transitions.

A multifrequency calorimeter has been designed to measure the amplitude and time regime of the enthalpic fluctuations associated with structural or conformational transitions in biological macromolecular systems. The heat capacity function at constant pressure is directly proportional to the magnitude of the enthalpic fluctuations in a system. Biological macromolecules undergo thermally induced transitions of different kinds. Within the transition region, these systems exhibit relatively large enthalpy fluctuations that give rise to the characteristic peaks observed by conventional differential scanning calorimetry. The multifrequency calorimeter developed in this laboratory has been designed to measure the frequency spectrum of the enthalpy fluctuations, thus allowing us to estimate thermodynamic parameters as well as relaxation times. This information is obtained from the attenuation in the amplitude or phase-angle shift of the response of the system to a periodic temperature oscillation. This instrument has been used to study the gel-liquid crystalline transition of phosphatidylcholine bilayers. The frequency-temperature response surface for large dimyristoyl phosphatidylcholine vesicles has been measured in the frequency range 0.04-1 Hz. The data are consistent with two enthalpic relaxation processes with time constants on the order of 3.8 s and 80 ms at the midpoint of the main gel-liquid crystalline transition.