Assessment of gastrointestinal health in racing Alaskan sled dogs using capsule endoscopy and inflammatory cytokines

OBJECTIVES

Exercise-induced gastrointestinal syndrome occurs in dogs and people and might compromise athlete performance by increasing intestinal permeability and causing gastrointestinal erosions. Racing sled dogs often receive acid suppressant prophylaxis which decreases the incidence of gastric erosions induced by exercise. The objectives were to quantify intestinal injury by measuring serum pro-inflammatory cytokine concentrations before and after exercise and to evaluate gastrointestinal mucosa using video capsule endoscopy after exercise.

MATERIALS AND METHODS

Prospective study of 12 racing Alaskan sled dogs receiving approximately 1 mg/kg omeprazole once daily from the day before the race until race completion. Blood was drawn before and 8 to 10 hours after an endurance race for the quantification of cytokines. Gastrointestinal tract mucosa was assessed with video capsule endoscopy immediately post-race.

RESULTS

Eight of nine dogs (89%; 95% confidence interval 52 to 100%) had gastric erosions; all dogs (100%, 95% confidence interval 63 to 100%) had small intestinal erosions. Most of the dogs (seven of nine) had straw or foreign material present. Cytokine levels were not different from before to after the race.

CLINICAL SIGNIFICANCE

Video capsule endoscopy identified gastrointestinal tract mucosal erosions after exercise in all dogs receiving once-daily omeprazole treatment, though other causes for the lesions besides exercise are possible.

Pyloric outflow obstruction secondary to sclerosing encapsulating peritonitis in a dog

A 6-year-old, male neutered mixed breed dog was presented emergently with a three-week history of hyporexia, vomiting, diarrhoea and weight loss. Upon examination, the patient was dull, had generalised muscle atrophy, moderate abdominal pain and a mild amount of peritoneal effusion. A fluid-filled, distended, corrugated small bowel with marked gastroparesis and moderate peritoneal effusion was noted on abdominal ultrasonography. Endoscopy revealed hyperaemic and friable mucosa and a subjectively narrowed pylorus. Emergency exploratory celiotomy was performed due to worsening patient condition and revealed thick, diffuse, fibrous adhesions of the abdominal cavity. Based on these findings, sclerosing encapsulating peritonitis (SEP) was suspected. A large mass of omentum adjacent to the greater curvature of the stomach had caused a pyloric outflow obstruction. Adhesiolysis was attempted but was unsuccessful due to the friability of the small intestines. The dog was humanely euthanased under anaesthesia. A diagnosis of SEP was confirmed via necropsy. No underlying cause was identified. This is the first known case of a pyloric outflow obstruction secondary to SEP in a dog. Although rare, this condition should be considered as a differential for dogs with signs of a pyloric outflow obstruction with concurrent ascites and abdominal pain, hyporexia, vomiting and diarrhoea.

Comparing the direct normal form and multiple scales methods through frequency detuning

Approximate analytical methods, such as the multiple scales (MS) and direct normal form (DNF) techniques, have been used extensively for investigating nonlinear mechanical structures, due to their ability to offer insight into the system dynamics. A comparison of their accuracy has not previously been undertaken, so is addressed in this paper. This is achieved by computing the backbone curves of two systems: the single-degree-of-freedom Duffing oscillator and a non-symmetric, two-degree-of-freedom oscillator. The DNF method includes an inherent detuning, which can be physically interpreted as a series expansion about the natural frequencies of the underlying linear system and has previously been shown to increase its accuracy. In contrast, there is no such inbuilt detuning for MS, although one may be, and usually is, included. This paper investigates the use of the DNF detuning as the chosen detuning in the MS method as a way of equating the two techniques, demonstrating that the two can be made to give identical results up to ε 2 order. For the examples considered here, the resulting predictions are more accurate than those provided by the standard MS technique. Wolfram Mathematica scripts implementing these methods have been provided to be used in conjunction with this paper to illustrate their practicality.

Force appropriation of nonlinear structures

Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the system response and the applied excitation. This paper demonstrates that this commonly used quadrature condition can give results that are significantly different from the true NNM, in particular, when the excitation applied to the system is limited to one input force, as is frequently used in practice. The system studied is a clamped-clamped cross-beam with two closely spaced modes. This paper shows that the regions where the quadrature condition is (in)accurate can be qualitatively captured by analysing transfer of energy between the modes of the system, leading to a discussion of the appropriate number of input forces and their locations across the structure.

Identifying the significance of nonlinear normal modes

Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system—highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared with simulated forced responses to verify these findings.

Evaluating Quality and Adequacy of Gastrointestinal Samples Collected using Reusable or Disposable Forceps

Background

Sample quality of gastrointestinal endoscopic biopsies is of paramount importance for accurate histological diagnosis. Many veterinary practices use reusable forceps as a result of perceived decreased cost. With reusable forceps, it remains unknown whether sample quality declines with repeated use and becomes inferior to single‐use forceps and is therefore more or less cost effective than single‐use forceps.

Hypothesis/Objectives

The study hypothesis was that reusable forceps sample quality would deteriorate after repeated use as compared to single‐use forceps.

Animals

Sixty‐five dogs undergoing gastrointestinal endoscopy for diagnostic investigations at the Hospital for Small Animals, Edinburgh University.

Method

A prospective, pathologist‐blinded study comparing single‐use and reusable alligator standard cup biopsy forceps (Olympus 2.0 mm 1550 mm) with 5 randomized reusable forceps. Sample quality (stomach, duodenum, ileum, and colon) was assessed by a single pathologist using the WSAVA guidelines.

Results

There was no difference in the adequacy, depth, villi number, or crush artifact in the 4 intestinal areas between forceps type with at least 10, and up to 15, repeated uses of the reusable forceps.

Conclusions and clinical importance

This study demonstrates that reusable cup biopsy forceps provide equivalent biopsy quality after repeated uses to single‐use forceps and are cost effective at 10‐case use.

Out-of-unison resonance in weakly nonlinear coupled oscillators

Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems.

Evaluation of urethral stent placement for benign urethral obstructions in dogs

Background

Benign urethral obstructions (BUO) in dogs result in substantial morbidity because of challenges with conventional therapies. Treatment of malignant urethral obstructions with intraluminal urethral stents is reported to successfully relieve obstructions.

Hypothesis/Objectives

To evaluate the efficacy and outcome of urethral stent placement for treatment of BUO in dogs.

Animals

Eleven client‐owned animals with urethral stents placed for treatment of BUO.

Methods

Retrospective study in which medical records were reviewed in dogs diagnosed with BUO and treated with a metallic urethral stent. Data collected included signalment, cause of benign obstruction, procedure time, size and type of stent, complications, and short‐ and long‐term outcome.

Results

Eleven dogs with 15 urethral stents were included. Intraluminal urethral stent(s) relieved the obstructions in all dogs. Four dogs had 2 stents placed in separate procedures because of incomplete patency after treatment (n = 1), inadvertent compression of the stent (n = 1), or tissue ingrowth through the stent (n = 2). The median continence score after stent placement was 10 of 10 (range 3–10) with 6 dogs being continent, 3 mildly incontinent, and 1 each moderately and severely incontinent. All owners considered their dog to have an excellent long‐term clinical outcome with long‐term urethral patency. The median follow‐up time was 24 months (range 4–48).

Conclusions and Clinical Importance

Urethral stents appear to be an effective treatment for benign urinary obstructions. Moderate to severe incontinence developed in a minority (12.5%) of dogs. Stents relieved obstructions in all dogs with an excellent long‐term outcome.

The effect of tramadol and indomethacin coadministration on gastric barrier function in dogs

Background

Tramadol is a centrally acting analgesic that is often used in conjunction with nonsteroidal anti‐inflammatory drugs (NSAIDs). The effect of coadministration of tramadol and indomethacin on gastric barrier function in dogs is unknown.

Hypothesis/Objectives

That coadministration of a nonselective NSAID (indomethacin) and tramadol would decrease recovery of barrier function as compared with acid‐injured, indomethacin‐treated, and tramadol‐treated mucosa.

Animals

Gastric mucosa of 10 humanely euthanized shelter dogs.

Methods

Ex vivo study. Mounted gastric mucosa was treated with indomethacin, tramadol, or both. Gastric barrier function, prostanoid production, and cyclooxygenase expression were quantified.

Results

Indomethacin decreased recovery of transepithelial electrical resistance after injury, although neither tramadol nor the coadministration of the two had an additional effect. Indomethacin inhibited production of gastroprotective prostanoids prostaglandin E₂ (acid‐injured PGE₂: 509.3 ± 158.3 pg/mL, indomethacin + acid injury PGE₂: 182.9 ± 93.8 pg/mL, P < .001) and thromboxane B₂ (acid‐injured TXB₂: 233.2 ± 90.7 pg/mL, indomethacin + acid injury TXB₂: 37.9 ± 16.8 pg/mL, P < .001), whereas tramadol had no significant effect (PGE₂P = .713, TXB₂P = .194). Neither drug had an effect on cyclooxygenase expression (COX‐1 P = .743, COX‐2 P = .705). Acid injury induced moderate to marked epithelial cell sloughing, which was unchanged by drug administration.

Conclusions and Clinical Importance

There was no apparent interaction of tramadol and a nonselective cyclooxygenase in this ex vivo model. These results suggest that if there is an adverse interaction of the 2 drugs in vivo, it is unlikely to be via prostanoid inhibition.

Properties of some three-state, steady-state Ising systems, according to the Bragg-Williams approximation

We consider the steady-state properties of a lattice of three-state, cycling enzyme molecules, with nearest-neighbor interactions treated by the Bragg-Williams (mean field) approximation. Only a few particular cases are examined, but these illustrate the rich phase-transition possibilities of this class of systems. "Bifurcation" cases were treated in a previous paper; the present examples are of the nonbifurcation type. However, a few new theoretical properties of bifurcation cases are included.

Derivation of the relation between the linear Onsager coefficients and the equilibrium one-way cycle fluxes of a biochemical kinetic diagram

The Onsager flux-force coefficients L(ij) for any biochemical system at a steady state near equilibrium have a simple interpretation: they are linear combinations of the equilibrium one-way cycle fluxes of the kinetic diagram for the system. An explicit and general expression for L(ij) is derived. This supplements the more pedagogical argument published elsewhere, which was based on a particular special case.

Anomalous properties of a simple small-volume membrane transport system at steady state

We investigate the transport of a single ligand L, between two macroscopic baths with different concentrations of L, by a simple membrane system. The center of this system is a very small volume V that might contain N = 0, 1, 2,... molecules of L. Access to V from either bath is by means of a single binding site for L. The steady-state properties of this simple system are studied exactly by a discrete-N master-equation approach. It is found that the mean concentration of L in V, c = N/V, is not a significant quantity either kinetically or thermodynamically. Further, the chemical potential of L in V is not defined and hence the overall thermodynamic force on L between the two baths cannot be subdivided at V. In fact, because V is small, the transport system must be treated as an indivisible system with interdependent parts. In the limit when V and N are very large, V becomes in effect a third macroscopic bath and two well-defined transport subsystems emerge (between V and either bath).

Three-state, steady-state Ising systems: Monte Carlo and Bragg-Williams treatments

In two earlier papers, the steady-state critical and phase-transition properties of a lattice of three-state enzyme molecules were studied by using the "closed" Bragg-Williams (BW), or mean field, approximation. The "open" BW and Monte Carlo methods are applied to the same problem in this paper by using finite lattices. The open BW treatment provides a way of locating the cut across a van der Waals type of loop encountered in a phase transition in the closed BW system. Thermodynamic-like methods cannot be used for this purpose as they can with two-state, steady-state systems.

Steady-state phase or cooperative transitions between biochemical cycles

In a steady-state lattice of interacting enzyme molecules that have a multicycle kinetic diagram, a cooperative or phase transition may involve not only the conventional sudden change in the relative importance of the different states of a molecule but also a sudden change in the dominant cycles of the diagram. The latter effect implies a sudden switch in the dominant biochemistry (e.g., a sudden onset of active transport). An explicit example is discussed.

Extension of the thermodynamics of small systems to open metastable states: an example

By using a simplified model of small open liquid-like clusters with surface effects, in the gas phase, it is shown how the statistical thermodynamics of small systems can be extended to include metastable supersaturated gaseous states not too far from the gas-liquid equilibrium transition point. To accomplish this, one has to distinguish between mathematical divergence and physical convergence of the open-system partition function.

Adsorption from a one-dimensional lattice gas and the Brunauer-Emmett-Teller equation

An exact treatment of adsorption from a one-dimensional lattice gas is used to eliminate and correct a well-known inconsistency in the Brunauer-Emmett-Teller (B.E.T.) equation-namely, Gibbs excess adsorption is not taken into account and the Gibbs integral diverges at the transition point. However, neither model should be considered realistic for experimental adsorption systems.

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.