The contribution of transplacental clearances and fetal clearance to drug disposition in the ovine maternal-fetal unit.

The total clearance of drugs from the fetus is the sum of clearance by the placenta from fetus to mother and clearance by nonplacental mechanisms such as renal excretion and biotransformation. Representing the maternal-fetal unit by a general two-compartment open model, we have derived equations for the calculation of placental and nonplacental drug clearances from the maternal compartment and fetal compartment under steady-state conditions. The equations suggest that fetal drug elimination to the exterior would result in a maternal-fetal concentration gradient at steady state after maternal drug administration. These equations have been applied to the study of methadone disposition in the ovine maternal-fetal unit.

The growth fraction of human myeloma cells.

Greater reductions of tumor load in patients with multiple myeloma may result from therapeutic strategies that are based on a better knowledge of growth kinetics. We have previously shown that the labeling index of myeloma cells remains unchanged when tumor mass is reduced and that the cells of relapsing patients have differnt biologic properties than the cells present before melphalan-prednisone therapy. This study investigated the growth fraction (GF) of myeloma cells at various disease stages using continuous i.v. infusions of tritiated thymidine. We studied 17 patients on 22 occasions (4 untreated, 2 unresponsive, 6 in remission, and 10 in relapse). All untreated an unresponsive patients and 5 of 6 patients in remission had a GF of less than 4%. GF was defined in these studies as the maximum percentage of labeled plasma cells exposed continuously to tritiated thymidine. Relapsing patients, with the most rapid tumor doubling times, had GF ranging from 14% to 83%. The plasma cell transit time through the proliferative compartment for all of the relapsing patients ranged from 6.6 to 11.9 days and the calculated intrinsic cell loss ranged from 50% to 86%. These findings support our model for the growth kinetics of multiple myeloma that assumes that the entire tumor mass issues from a small proportion of proliferating cells and that the growth kinetics of myeloma cells in relapsing patterns differ from those in untreated and unresponsive patients. Therapeutic trials with cycle-active agents need further investigation in selected relapsing patients who are likely to have a high growth fraction.

Investigation into the experimental kinetic support of the two-state model of the cell cycle.

Five previously published cell generation-time distribution functions have been examined in an effort to elucidate the parameters of the two-state model of the cell cycle. These parameters are the fractional number of cells that bypass the G0 state, the probability of exit from G0, and the distribution of traversal times through the active state. To explain observed beta-curve behavior of cell populations, it is necessary to define the parameters in terms of pairwise behavior of newborn sister cells. From the beta-curve, we demonstrate that at least 50% of the cells must pass through the G0 state. The alpha-curve is consistent with any positive fraction of newborn cells passing through the G0 state, and provides no further information. We explore a possible method for resolving the remaining indeterminacy regarding the number of cells bypassing the G0 state, namely, examination of the generation-time distribution functions of fast sister cells only. Such an approach, although theoretically attractive, presents formidable experimental difficulties, however. If it should turn out that indeed only 50% of the cells are apparently passing through a random-exiting phase of the cell cycle, then an alterative plausible biological mechanism for the observed variability in generation times is supplied by Prescott's hypothesis: variability is a consequence of the inequality in the metabolic content of sister cells at birth.

A theoretical approach to the analysis of axonal transport.

A theoretical model of intra-axonal transport is proposed that presupposes a carrier system moving down the axon in a distal direction. Protein and particle transport is achieved by their reversible association with the distally moving carriers. Mathematical equations representing the concentrations of moving carriers and proteins and/or particles within the axon at any position and time are proposed. Analysis of the equations demonstrates that a traveling wave solution for the particle concentration (an experimental fact) is possible provided the chemical interaction between particles and carriers exhibits positive cooperativity. The phase velocity of the wave solution is interpreted as the observed velocity of the intra-axonal transport, known to be independent of position of observation. In addition, the theory predicts a spectrum of transport velocities for different proteins, in agreement with observations. The velocity of a given protein is dependent on its affinity to the carrier.

A kinetic model of cooperativity in aspartate transcarbamylase.

A relatively simple kinetic model is proposed to account simultaneously for data on the binding of carbamyl phosphate and succinate to aspartate trans carbamylase (ATCase), and for the relaxation spectrum associated with this binding. The model also accounts for measurements of the initial velocity of the reaction of ATCase with respect to aspartate and carbamyl phosphate. The principal assumption made is that ATCase consists of three identical noninteracting cooperative dimers. Ordered binding and both sequential and concerted conformational changes in the dimers are needed to account for the properties of ATCase. The values of the parameters of this model can be determined by fitting to existing experimental evidence. Various new quantitative predictions are made that can serve as additional tests of the proposed theory.

The facilitated diffusion of oxygen by hemoglobin and myoglobin.

We have clarified the use of Wyman's differential equation for the facilitated oxygen flux through a slab of solution of myoglobin or hemoglobin by showing that there is a unique choice of boundary condition on the carrier concentration to be employed in conjunction with it. The singular perturbation solution of Wyman's equation, due to Murrayand Mitchell and Murray, has been extended. By means of it, the paradox of Wittenberg, that the facilitated oxygen flux per mole of heme is apparently independent of the protein carrier, has been resolved.

A mathematical model of the chemotherapeutic treatment of acute myeloblastic leukemia.

Based on our previous mathematical model of the acute myeloblastic leukemic (AML) state in man, we superimpose a chemotherapeutic drug treatment regimen. Our calculations suggest that small changes in the protocol can have significant effects on the result of treatment. Thus, the optimal period between drug doses is the S-phase interval of the leukemic cells--about 20h--and the greater the number of doses administered in a given course treatment, the longer the rest interval should be before the next course is administered. For a patient with a "slow" growing AML cell population, remission can be achieved with one or two courses of treatment, and further suppression of the leukemic population can be achieved with continued courses of treatment. However, for patients with a "fast" growing AML cell population, a similar aggressive treatment regimen succeeds in achieving remission status only at the cost of very great toxic effects on the normal neutrophil population and its precursors.

A mathematical model of the acute myeloblastic leukemic state in man.

A dynamical mathematical model of the acute myeloblastic leukemic state is proposed in which normal neutrophils and their precursors, and leukemic myeloblasts, proliferate as distinct but interacting cell populations. Each population has a Go compartment, consisting of resting cells, that acts as a control center to determine the rate of proliferation. These rates are assumed to depend on the total number of cells in the combined populations. The presence of the leukemic population destabilizes the homeostatic state of the normal population, which is stable in the absence of leukemic cells, and drives the system to a new stable state consisting entirely of leukemic cells and no normal cells. Calculations based on the theory suggest that it is able to simulate the kinetic features of this disease state, at least in its typical manifestations.

Swimming of flagellated microorganisms.

The swimming motion of a microorganism with a single flagellum is investigated for both helical and planar flagellar motion. First the force and torque exerted on the organism by the surrounding fluid are calculated in terms of the specified flagellar motion and the unknown linear and angular velocity of the whole organism. Then these unknown velocities are determined by the condition that the net force and torque on the organism are zero. Using these velocities, the trajectory of the organism is found. In the case of helical flagellar motion, the path of the entire organism is found to be a helix of small radius. The axis of the flagellum is not parallel to the axis of the helical path, but makes a small angle with it and precesses around it. If the flagellar motion is planar and sinusoidal, then the trajectory of the organism is found to be a straight line with small oscillations about it. Each point of the flagellum also oscillates longitudinally with double the frequency of the transverse oscillation, producing a figure eight motion. However if the flagellar motion is planar and asymmetric, then the trajectory is found to be a circle with small superposed oscillations. These conclusions account for the observed helical and circular trajectories of sperm, and for the figure eight motion of the tip of the flagellum in the planar case.

A mathematical model of neutrophil production and control in normal man.

A comprehensive mathematical model of neutrophil production in normal man is presented. The model incorporates three control elements which regulate homeostatically the rates of release of marrow cells to proliferation, maturation, and to the blood. The steady state properties of the model are demonstrated analytically. The basic equations of the model, which are nonlinear, have been integrated numerically. The solutions so obtained display graphically the dynamical response of the system to various perturbations, which simulate experimental investigations that have been made in the past of granulocytopoiesis. By an appropriate choice of values of the parameters characterizing the system, it is shown how most of the principal kinetic properties of the neutrophil production and control system are represented in a quantitative manner.

Parameterization of in vivo leukemic cell populations.

A quantitative mathematical formalism which was previously introduced has been utilized to obtain the cell kinetic parameters which characterize the in vivo leukemic myeloblast cell populations in two patients studied by Clarkson and his coworkers. The principal tentative conclusions are: (a) all cells which are actively proliferating must enter the resting state following cell division; (b) about 90% of the cells are in the resting state; (c) the generation time of the cells in the active state is about 25 hr and is essentially the same as the generation time of normal myeloblast cells.

A simple model of a steady state differentiating cell system.

A simple theoretical model is hypothesized to describe the steady state behavior of a differentiating cell system as exemplified by blood cells. The cell system consists of several morphologically distinguishable cell classes which develop sequentially. Each cell class except the last one is mitotically capable. Mitosis is assumed to be either heteromorphogenic, homomorphogenic, or asymmetric. Some algebraic equations are derived which are conservation equations describing the flux of cells from one class to another. The theoretical considerations have been applied to some experimental observations in humans concerning neutrophil production, particularly in reference to relative cell numbers and mitotic fractions of the myeloblast, promyelocyte, and myelocyte cell classes. These observations are utilized to help determine the values of the parameters which characterize the model. Among these parameters are the generation times of the various cell classes, and the predicted values of the generation times are found to be in excellent agreement with observed grain-count halving times. However, the predicted mitotic times are in disagreement with their observed values.