Lobular capillary hemangioma (pyogenic granuloma) with satellitosis

We describe a 43-year-old white man who rapidly developed multiple, extensive angiomatous lesions on the temple and scalp after excision of a solitary lobular capillary hemangioma. This is a well-recognized but rare event. Our case differs from previously reported examples in terms of the age of the patient, the location and extent of the lesions, the histologic features in the form of small foci of angiosarcoma-like infiltration, and possibly with respect to the response to therapeutic intervention. Because of the alarming clinical picture produced by multiple lobular capillary hemangiomas, in addition to the occurrence of disturbing histologic features, the benign and self-limited nature of this disease must be emphasized.

Convenient purification of tritylated and detritylated oligonucleotides up to 100-mer

Oligomers from crude phosphoramidite synthesis mixtures have been purified by reversed-phased high-performance liquid chromatography by exploiting the chromatographic variables of stationary phase pore size, chain length, and gradient shape. Chromatography was performed on oligomers up to 100-mer with mobile phases containing triethylammonium acetate/acetonitrile mixtures. Convenient guidelines are offered to enrich or purify synthetic oligomers. Tritylated oligomers up to 25 bases in length are best purified on C8 or C18, 80 A columns with moderate strength mobile phases using a combination of isocratic delays and shallow gradients. For oligomers longer than 25-mer, C3, 300 A columns provide adequate fast purification in as little as 5 min, while 300 A, C8 columns with long, slow gradients gave substantially increased purity. Chromatography of detritylated oligomers requires a modified approach. Up to 25-mer they are best purified on 80 A, C18 columns with much lower organic concentrations and shallower gradients than those used for tritylated oligomers. Detrytilated oligomers greater than 25-mer can be enriched on both C3 and C8, 300 A columns using the same conditions described for shorter detritylated oligomers.

Myxoma of the skin of a finger

A case of a true myxoma of the fingertip is presented. The lesion was removed by simple shave excision. Reports of myxoma of the skin are reviewed, and the differential diagnosis of this rare tumor is discussed.

An assessment of prolonged reactivity of seven monoclonal antibodies against CX-1 tumor xenografts using a hand-held gamma-detecting probe

The biodistribution and kinetics of 7 monoclonal antibodies (MAb) with known reactivity against CX-1 tumor were examined over 21 days using a hand-held gamma-detecting probe (Neoprobe system). Twenty-eight immuno-deprived (athymic) nude mice implanted with human colon adenocarcinoma CX-1 xenografts were injected intraperitoneally with 50 microCi of 125I-labeled antibodies (4 mice/antibody). Of the 7 monoclonal antibodies, 4 were anti-CEA (MA, MB, MC, and MD), 2 were anti-TAG 72 (B72.3 NCI and B72.3 fermented) and one was anti-colorectal cancer (17-1A). Daily probe counts were recorded in duplicate over the tumor site and the contralateral nontumor site (background), and tumor-to-background (Tu/Bkg) ratios were calculated. Animals were sacrificed on day 21, and blood, heart, liver, spleen, lungs, kidneys, intestine, muscle, and the tumor were removed for gamma well counting. All antibodies identified the tumor as early as 24 h postinjection and specific tumor localization improved over time. Patterns of prolonged tumor binding varied considerably from one antibody to another, although all but one (MB) showed continuously increasing Tu/Bkg ratios. These data indicate progressive clearance of the antibodies from the background tissue and a persistence of labeled MAb activity in tumor resulting in improved tumor localization with increasing postinjection time.

Discrete-time random walks on diagrams (graphs) with cycles

After a review of the diagram method for continuous-time random walks on graphs with cycles, the method is extended to discrete-time random walks. The basic theorems carry over formally from continuous time to discrete time. Three problems in tennis probabilities are used to illustrate random walks on discrete-time diagrams with cycles.

Number of visits to a state in a random walk, before absorption, and related topics

Equations are derived for the probability of n visits to a given state during the course of a random walk on a finite diagram that starts from a specified state and ends with absorption. By deriving the mean number of visits in two different ways, certain conjectures or theorems are encountered that connect properties of different but related diagrams in an interesting way. Other subjects included are (i) number of one-way transitions between two states before absorption; (ii) time dependence of the rate of cycle completions before absorption; and (iii) the relation of this work to the "return process" of Karlin and Taylor.

Interrelations between random walks on diagrams (graphs) with and without cycles

Three topics are discussed. A discrete-state, continuous-time random walk with one or more absorption states can be studied by a presumably new method: some mean properties, including the mean time to absorption, can be found from a modified diagram (graph) in which each absorption state is replaced by a one-way cycle back to the starting state. The second problem is a random walk on a diagram (graph) with cycles. The walk terminates on completion of the first cycle. This walk can be replaced by an equivalent walk on a modified diagram with absorption. This absorption diagram can in turn be replaced by another modified diagram with one-way cycles back to the starting state, just as in the first problem. The third problem, important in biophysics, relates to a long-time continuous walk on a diagram with cycles. This diagram can be transformed (in two steps) to a modified, more-detailed, diagram with one-way cycles only. Thus, the one-way cycle fluxes of the original diagram can be found from the state probabilities of the modified diagram. These probabilities can themselves be obtained by simple matrix inversion (the probabilities are determined by linear algebraic steady-state equations). Thus, a simple method is now available to find one-way cycle fluxes exactly (previously Monte Carlo simulation was required to find these fluxes, with attendant fluctuations, for diagrams of any complexity). An incidental benefit of the above procedure is that it provides a simple proof of the one-way cycle flux relation Jn +/- = IIn +/- sigma n/sigma, where n is any cycle of the original diagram.

Further properties of random walks on diagrams (graphs) with and without cycles

Three problems are considered. The first is the relation between ensemble-averaged state probabilities in a random walk with absorption and time-averaged state probabilities in the corresponding closed diagram. The second problem is concerned with random walks on diagrams with cycles in which the cycle completion rates and probabilities may depend on the "remainder" after the previously completed cycle. The final topic is a study of cycle completions prior to absorption for diagrams that involve both cycles and absorption (e.g., a cycling enzyme that binds a dead-end inhibitor or poison in one of its states).

Theoretical calculation methods for kinesin in fast axonal transport

The method of making Monte Carlo calculations of the velocity of fast axonal transport is described and applied in a relatively simple case. These illustrative calculations are supplemented by a differential equation solution of the same problem, valid as an asymptotic limit. The latter treatment is closely related to the theory of muscle contraction.

Theoretical studies on oscillations in microtubule polymerization

Oscillations in the polymerization of microtubules have been studied theoretically, using differential equations and (more realistically) Monte Carlo simulations. There is gross qualitative agreement between theory and experiment but a really satisfactory model has not been found as yet.

Synchronous oscillations in microtubule polymerization

Under conditions where microtubule nucleation and growth are fast (i.e., high magnesium ion and tubulin concentrations and absence of glycerol), microtubule assembly in vitro exhibits an oscillatory regime preceding the establishment of steady state. The amplitude of the oscillations can represent greater than 50% of the maximum turbidity change and oscillations persist for up to 20 periods of 80 s each. Oscillations are accompanied by extensive length redistribution of microtubules. Preliminary work suggests that the oscillatory kinetics can be simulated using a model in which many microtubules undergo synchronous transitions between growing and rapidly depolymerizing phases, complicated by the kinetically limiting rate of nucleotide exchange on free tubulin.

Use of muscle contraction formalism for kinesin in fast axonal transport

The general procedure is discussed for calculating the velocity of a vesicle along a microtubule. The formalism used previously for isotonic contraction in muscle (with multiple actin sites for a given cross-bridge) can be employed. However, some modifications must be made: (i) the kinetic diagram must include a state in which kinesin is absent from a vesicle binding site, (ii) an average must be taken over the locations of the vesicle binding sites relative to microtubule sites, and (iii) a self-consistency condition must be imposed that equates the mean force exerted by kinesin molecules on the vesicle with the frictional resisting force of the medium.

A theoretical study of cooperative dual linear aggregation and the vernier effect

An introductory theoretical study is presented of cooperative dual linear aggregation, originating from a surface. That is, two kinds of molecules aggregate in side-by-side strands; lateral interactions cause the aggregation in the two strands to be cooperative. The vernier effect is a special case that is given particular attention: if the two kinds of molecules have different lengths, there will be certain combinations of numbers of molecules that will give the two strands the same length (a 'vernier structure'). Such a structure has extra thermodynamic and kinetic stability, literally because there are no loose ends. The increased lifetime of a vernier structure is, however, not very impressive unless some additional feature is incorporated into the model to enhance further such a structure. Aligned multi-stranded tubular aggregates are also discussed.

Effect of fluctuating surface structure and free energy on the growth of linear tubular aggregates

Simple linear tubular aggregates with up to eight strands are studied theoretically at equilibrium and under conditions of steady growth or shortening. The surface structure and free energy at an end of the polymer fluctuate as a consequence of the gain or loss of individual subunits. The surface free energy governs the probability distribution of surface structures at equilibrium. At steady state, on and off rate constants are crucial for this purpose; these depend on the gain or loss of neighbor interactions at the polymer end when a subunit is gained or lost. The observed on and off rate constants are averages of microscopic rate constants. A consequence of this is that the subunit flux onto the polymer end is, in general, not a linear function of the free subunit concentration, as is usually assumed. Monte Carlo calculations are needed at steady state for three or more strands. The general approach can be applied to microtubules, which have 13 strands. Actin is a special case, included here, with two strands.

Theoretical study of a model for the ATP cap at the end of an actin filament

The model used successfully by Pantaloni et al. to fit experimental data on steady-state actin polymerization is investigated theoretically. Many properties are deduced, as functions of the free subunit concentration. The model is simple enough so that one can examine analytically the question of whether actin shows the same dramatic phase changes associated with the GTP cap in microtubules. The answer is negative, judging from this model. However, it is possible to obtain such phase changes using the same model but with quite different, hypothetical choices of parameters. Thus, aside from its application to actin, this model is useful pedagogically to illustrate the nature of phase changes that may occur at the end of a steady-state polymer.

A model for actin polymerization and the kinetic effects of ATP hydrolysis

A model for actin polymerization is proposed in which the rate of elongation of actin filaments depends on whether adenosine 5'-triphosphate or adenosine 5'-diphosphate is bound to the two terminal subunits of the filament. This model accounts quantitatively for the experimental data on the kinetics of filament elongation and explains the effect of ATP hydrolysis on actin polymerization.

Theoretical problems related to the attachment of microtubules to kinetochores

A possible model is analyzed for the maintenance of attachment of a shortening microtubule (MT) to a kinetochore. In this model it is assumed that a MT is inserted and held in a sleeve or channel of the outer layer of a kinetochore while subunits are lost from the MT tip through the central layer of the kinetochore. A second problem considered is the elementary bioenergetics of MT growth and shortening, as associated with the presence or absence of a GTP cap on the MT ends. The free-energy source is the hydrolysis of GTP in solution. The third problem discussed is the kinetics of capture of a centrosomal MT by a target (e.g., a kinetochore).

Theoretical treatment of microtubules disappearing in solution

The origin of the two-phase (cap, no cap) macroscopic kinetic model of the end of a microtubule is reviewed. The model is then applied to a new theoretical problem, namely, the Mitchison-Kirschner [Mitchison, T. & Kirschner, M. W. (1984) Nature (London) 312, 237-242] experiment in which aggregated microtubules in solution spontaneously decrease in number (shorten to disappearance) while the surviving microtubules increase in length. The model fits the experiments without difficulty.

Muscle contraction and free energy transduction in biological systems

Muscle contraction occurs when the actin and myosin filaments in muscle are driven past each other by a cyclic interaction of adenosine triphosphate (ATP) and actin with cross-bridges that extend from myosin. Current biochemical studies suggest that, during each adenosine triphosphatase cycle, the myosin cross-bridge alternates between two main conformations, which differ markedly in their strength of binding to actin and in their overall structure. Binding of ATP to the cross-bridge induces the weak-binding conformation, whereas inorganic phosphate release returns the cross-bridge to the strong-binding conformation. This cross-bridge cycle is similar to the kinetic cycle that drives active transport and illustrates the general principles of free energy transduction by adenosine triphosphatase systems.

Monte Carlo study of the GTP cap in a five-start helix model of a microtubule

Earlier Monte Carlo studies on a single-helix model of the GTP cap at the end of a microtubule are extended here to a more realistic five-start helix model of the microtubule end. As in the earlier work, phase changes occur at the microtubule end: the end is either capped with GTP and growing slowly or uncapped and shortening rapidly, and these two regimes alternate (at a given tubulin concentration) at steady state. Macroscopic rate constants for the two-phase model are deduced from the Monte Carlo results. The macroscopic rate constants lead to properties that are in semiquantitative agreement with related experiments of Mitchison and Kirschner.

Phase-change kinetics for a microtubule with two free ends

The two-phase macroscopic kinetic model of the end of a microtubule is extended to microtubules in solution, with two free ends. The theoretical treatment of this system is complicated by the possibility of microtubules shortening all the way to disappearance. Another possibility, if a microtubule is shortening from one end only (and has a GTP cap on the other end), is that completed shortening will leave a residual cap from which growth can then take place at both ends. Two approximations are introduced.

Introductory analysis of the GTP-cap phase-change kinetics at the end of a microtubule

An introductory analysis is provided for the two-phase macroscopic kinetic model of the end of a microtubule. Some general relations are derived for one end of a very long microtubule in solution but the main results refer to the steady-state properties of microtubules grown on nucleated sites, as in the experiments of Mitchison and Kirschner [Mitchison, T. & Kirschner, M. W. (1984) Nature (London), in press]. The two-phase model makes it possible to understand qualitatively how long microtubules can grow well below the critical concentration and also how grown microtubules can rapidly disappear from a nucleated site by shortening following a phase change.

Phase changes at the end of a microtubule with a GTP cap

Examination of Monte Carlo kinetic simulations, based on a realistic set of microscopic rate constants that apply to the end of a microtubule with a GTP cap, suggests that the end of a microtubule alternates between two quasimacroscopic phases. In one phase, the microtubule end has a GTP cap that fluctuates in size; in the other phase, the GTP cap has been lost. These repeated phase changes take place at any given tubulin concentration in a wide range of concentrations. While in the first phase, the microtubule grows slowly; while in the second phase, it shortens rapidly and may disappear completely. These results are closely related to the recent experimental work of Mitchison and Kirschner [Mitchison, T. & Kirschner, M.W. (1984) Nature (London), in press].

Interference of GTP hydrolysis in the mechanism of microtubule assembly: an experimental study

This paper reports an experimental study of the interference of GTP hydrolysis in the mechanism of microtubule assembly, following the model and theory previously published [Hill, T. L. & Carlier, M.-F. (1983) Proc. Natl. Acad. Sci. USA 80, 7234-7238]. Results from dilution experiments show that microtubules depolymerize faster below the critical concentration than expected with a reversible polymerization model. The experimental plot of flux versus tubulin concentration exhibits a slope discontinuity at the critical concentration, in agreement with the theory. Theoretical points calculated by the Monte Carlo method can be fitted qualitatively to the data. A consequence of this peculiar dynamic behavior of microtubules is that the ratio of tubulin dissociation and association rate constants measured, respectively, below and above the critical concentration does not yield the true value of the critical concentration. It is emphasized that the presence of GTP at microtubule ends is necessary to maintain the stability of the polymer.

Use of Monte Carlo calculations in the study of microtubule subunit kinetics

GTP-tubulin forms a cap on microtubule ends during aggregation. The bulk of the microtubule is GDP-tubulin. This complicates the usual simple kinetic theory of subunit exchange at microtubule ends to such an extent that Monte Carlo calculations are needed to handle the complications, except in special cases. The Monte Carlo method is introduced here, for this problem, and illustrated with steady-state and transient examples. Monte Carlo transients are needed to simulate dilution experiments. Preliminary results (with M. F. Carlier) have been obtained applying these theoretical procedures to experimental data.