Contribution of vasomotion to vascular resistance: a comparison of arteries from virgin and pregnant rats

Intrinsic oscillatory activity, or vasomotion,within the microcirculation has many potential functions, includingmodulation of vascular resistance. Alterations in oscillatory activityduring pregnancy may contribute to the marked reduction in vascularresistance. The purpose of this study was1) to mathematically model theoscillatory changes in vessel diameter and determine the effect onvascular resistance and 2) tocharacterize the vasomotion in resistance arteries of pregnant andnonpregnant (virgin) rats. Mesenteric arteries were isolated fromSprague-Dawley rats and studied in a pressurized arteriograph.Mathematical modeling demonstrated that the resistance in a vessel withvasomotion was greater than that in a static vessel with the same meanradius. During constriction with the₁-adrenergic agonistphenylephrine, the amplitude of oscillation was less in the arteriesfrom pregnant rats. We conclude that vasomotor activity may provide amechanism to regulate vascular resistance and blood flow independent ofstatic changes in arterial diameter. During pregnancy the decrease invasomotor activity in resistance arteries may contribute to thereduction in peripheral vascular resistance.

     

A contribution to the mathematical biophysics of visual aesthetics

In continuation of previous studies, inequalities between different parameters of the brain are derived which determine whether an individual prefers in general visual patterns consisting of a relatively small number of relatively strongly excited elements, or such patterns which consist of a very large number of relatively weakly excited elements. As has been discussed in a previous publication, the first type of pattern is usually represented by artificial human-made designs, whereas the second type of pattern is formed predominantly in natural landscapes and sceneries. Thus the inequalities established in this paper give us the biophysical conditions which determine an individual's preference for either artificial designs or for landscapes and other natural objects.     

A mathematical contribution to the study of orientation of organisms

Organisms orient themselves to a stimulus by two general methods. One method is by directed orientation (taxis); the other is by undirected locomotory reaction (kinesis). An equation, and the methods for finding the necessary parameters of this equation, is derived for the distribution of organisms within a container, with the following limitations: (1) the organisms have no accommodation, (2) they are always active, and (3) the stimulus changes slowly with position. Necessary modifications of the equation are then derived, so that the last two limitations may be eliminated. The equation cannot be solved excatly because of its complexity; hence an approximation method must be used. This method is discussed, an approximate solution is found, and a time constant for equilibrium to be established is derived. Applications tovarious experiments in the literature are then made with fairly satisfactory results. A new interpretation of the theory of klino-kinesis with accommodation is found upon application of the equations developed to experimental work. Further limitations and uses of these equations are then discussed. This work was done while the author was Public Health Service Research Fellow of The National Institute of Mental Halth, Federal Security Agency.     

A contribution to the mathematical biophysics of psychophysical discrimination II

The properties of a neural mechanism previously discussed are given in more general form. It is shown that, under certain conditions, a psychophysical scale value is proportional to a difference between excitation factors at a synapse. More general relations are derived which hold among different variables in the two and three categories of judgment. An attempt is made to apply the results to the method of choices. Certain relations derived are compared with available experimental data.     

A contribution to the mathematical biophysics of psychophysical discrimination III

The neural mechanism previously discussed is further generalized. The case is considered in which a random variation is associated with each stimulus. The mechanism is generalized and equations are derived for discriminations between stimuli differing in several modalities. The latter indicates an analysis by the factor method. Suggestions are made in connection with the use of triads and with the problem of a multidimensional psychophysics.     

A contribution to the search of general mathematical principles in biology

A somewhat different approach to the principle of biotopological mapping, discussed in previous publications, is given. The organism is considered as a set of properties, each of which is in its turn a set of numerous subproperties which are logically included in the corresponding properties. Topology is introduced by an appropriate definition of neighborhoods, and four postulates are stated which concern the mapping of the spaces corresponding to higher organisms on those of lower ones. A number of conclusions are drawn from the postulates. Some of them correspond to well-known facts. For example, in man and some higher organisms appropriate emotional stimuli should produce gastrointestinal or cardiovascular disturbances; or some microorganisms should produce substances harmful to other microorganisms (antibiotics). Some other conclusions are still awaiting verification. One of them is, for example, that there must exist unicellular organisms which produce antibodies to appropriate antigens.     

A contribution to the mathematical biophycics of visual perception and aesthetics

In continuation of previous studies of the mathematical biophysics of visual perception in relation to the aesthetic evaluation of visual patterns, an expression for the total intensity of excitation in a discriminating center as a function of the intensity of the peripheral stimulus is derived. This expression is applied to the case of aesthetic judgments of similar polygons of different sizes. The theoretical conclusions are tested experimentally by use of standard psychological scaling methods. The theoretical predictions are found to be in agreement with the experimental results.     

A contribution to the mathematical biology of the rates of historical development

The paper is a second step toward a biomathematical theory of the rates of spread of new nonconformist ideas or behaviors in a society. It is intended as a preliminary and purely theoretical study of a very oversimplified case. An equation which determines the distribution function of the tendencies toward conformist and nonconformist behaviors is set up under a number of oversimplified assumptions, and a solution by successive approximations is indicated. The expression for the first approximation is given, and an estimate of the order of magnitude of the rates of changes is made. In conclusion an outline is given for further improvement of the theory.     

A contribution to the mathematical biology of social behavior: Comparison of non-violent resistance and of riots by oppressed groups

A previous paper (Bulletin of Mathematical Biophysics,30, 501–518, 1968) discussed the mathematical biosociology of riots by suppressed groups. In this paper the effect of non-violent disobedience as a method of prevention of oppression is discussed from a biosociological point of view. It is found that in general, other conditions being equal, a non-violent resistance is more effective than a violent riot. In a large number of cases however, depending on the choice of the biosociological parameter, the above conclusion may not hold. The actual outcome depends not only on the attitude of the oppressed group, but also on the attitude of the oppressor group. When the choice between several attitudes is allowed in both groups, the situation depends on 224 parameters. With certain choices of those, it is possible that only violent revolts will lead to abolition of oppression.     

A contribution to Rashevsky’s mathematical theory of development

The application of Rashevsky’s transformationT to a primordial graph yields a set of graphs corresponding to different stages in the development of the organism. However, sinceT is multiple-valued the graphs obtained are not ordered. To obtain an ordering, it is first shown that the set of graphs under consideration is equivalent to a well defined setO (for “organism”) ofn-tuples. A metric is then introduced which is based on a biological consideration discussed by Rashevsky (Bull. Math. Biophysics,16, 317–348, 1954). Since a metric implies an ordering of the setO, with a knowledge of the structure of the primordial, one can obtain the developmental sequence. Unfortunately, at present, the structure of the primordial graph is unknown which makes the direct application of the above principle impossible. Consequently, an indirect approach which makes use of more accessible biological phenomena is discussed as well. The hypothesis thatrate of development decreases exponentially and the implications this has with regard to the metric onO are discussed. It is shown that if the hypothesis is accepted the search for the developmental sequence is narrowed.     

Selected contribution: Gender differences in the endothelin-B receptor contribution to basal cutaneous vascular tone in humans.

To test whether the contribution of endothelin-B (ET-B) receptors to resting vascular tone differs between genders, we administered the ET-B receptor antagonist BQ-788 into the forearm skin of 11 male and 11 female subjects by intradermal microdialysis. Skin blood flow was measured using laser-Doppler flowmetry at the microdialysis site. The probe was perfused with Ringer solution alone, followed by BQ-788 (150 nM) and finally sodium nitroprusside (28 mM) to effect maximal cutaneous vasodilation. Cutaneous vascular conductance (CVC) was calculated (laser-Doppler flowmetry/mean arterial pressure) and normalized to maximal levels (%max). In male subjects, baseline CVC was (mean +/- SE) 19 +/- 3%max and increased to 26 +/- 5%max with BQ-788 (P < 0.05 vs. baseline). In female subjects, baseline CVC was 13 +/- 1%max and decreased to 10 +/- 1%max in response to BQ-788. CVC responses to BQ-788 differed with gender (P < 0.05); thus the contribution of ET-B receptors to resting cutaneous vascular tone differs between men and women. In men, ET-B receptors mediate tonic vasoconstriction, whereas, in women, ET-B receptors mediate tonic vasodilation.     

Modulation of vasomotion in resistance arteries of JCR:LA-cp rats: a model of insulin resistance.

Obesity and insulin resistance are strongly associated with an increased risk of vascular disease. Vasomotion is the cyclic variation in the diameter of arteries and is a general feature of the vasculature that may have important physiological consequences. We tested the hypothesis that obesity - insulin resistance is associated with abnormal vasomotion by comparing obese, insulin-resistant JCR:LA-cp rats, known to develop vasculopathy, atherosclerosis, and ischemic lesions of the heart, with lean insulin-sensitive animals from the same strain. Vasomotion was assessed using isolated mesenteric arteries on a myograph system after preconstriction to 50% of maximal constriction with norepinephrine. The amplitude of vasomotion was enhanced by the presence of meclofenamate, a prostaglandin H synthase inhibitor, and was diminished by N(G)-nitro-L-arginine methyl ester (L-NAME), a nitric oxide synthase inhibitor. Removal of the endothelium essentially abolished vasomotion, and meclofenamate had no effect on de-endothelialized arteries. Frequency was not altered by either L-NAME or meclofenamate. Although pharmacological inhibition of nitric oxide and eicosanoid production clearly altered vasomotion, there was no difference in the amplitude or frequency of vasomotion in arteries from obese rats compared with lean rats. These results indicate that the endothelium plays a central role in modulating vasomotion, involving both enhancing and inhibiting effects, and that vasomotion is similar between obese, insulin-resistant and lean, insulin-sensitive rats.     

Bronchial vascular contribution to lung lymph flow

The lymphatic vessels of thelung provide an important route for clearance of interstitial edemafluid filtered from pulmonary blood vessels. However, the importance oflung lymphatics for the removal of airway liquid filtered from thesystemic circulation of the lung has not been demonstrated. We studiedthe contribution of the bronchial vasculature to lung lymph flow inanesthetized, ventilated sheep (n = 35). With the bronchial artery cannulated and perfused (control flow = 0.6 ml · min¹ · kg¹),lymph flow from the efferent duct of the caudal mediastinal lymph nodewas measured 1) during increasedbronchial vascular perfusion (300% of control flow);2) with a hydrated interstitium induced by a 1-h period of left atrial hypertension and subsequent recovery, both with and without bronchial perfusion; and3) during infusion (directly intothe bronchial artery) of bradykinin, an inflammatory mediator known tocause changes in bronchial vascular permeability. Increased bronchialperfusion for 90 min resulted in an average 35% increase in lung lymphflow. During left atrial hypertension, the increase in lung lymph flowwas significantly greater with bronchial perfusion (339% increase overbaseline) than without bronchial perfusion (138% increase).Furthermore, recovery after left atrial hypertension was more completeafter 90 min without bronchial perfusion (91%) than with bronchialperfusion (63%). Infusion of bradykinin into the bronchial arteryresulted in a prompt and prolonged 107% increase in lung lymph flow.This was not seen if the same dose was infused into the pulmonaryartery. Thus bronchial vascular transudate contributes significantly to lymph flow from the efferent duct of the caudal mediastinal lymph node.These results demonstrate that lymph vessels clear excess fluid fromthe airway wall and should be considered when evaluating the effect ofvascular leak in airway obstruction.

     

Determination of the mechanism of retrotransfer by mechanistic mathematical modeling.

Two mathematical models to elucidate the mechanism of retromobilization (or retrotransfer), that is, the ability of conjugative plasmids to mobilize genes into the cell containing the conjugative plasmid, were developed. This study deals with retromobilization of nonconjugative plasmids (Tra-Mob+). Plasmid transfer was modeled by two mass action models. The first is based on the hypothesis that retromobilization of the Tra-Mob+ vector occurs in one step, by means of the pilus formed by the Tra+ plasmid in the original host. In the second model, retromobilization is considered to be a two-step process involving two transfer events. The first step involves the transfer of the Tra+ plasmid from the recipient cell to the donor of the nonconjugative vector, and during the second encounter the nonconjugative vector is mobilized toward the recipient. Since the relationships between the number of transconjugants and the number of recipients for the two models are different, filter matings were performed for short time periods with different initial densities of the recipient population. Comparison of the numbers of transconjugants with the results of the mathematical equations confirmed the hypothesis that retromobilization is a one-step conjugation process.     

A contribution to the mathematical biophysics of cell growth and shapes: II

A theoretical study of the growing nerve cell filopodium is made using the assumptions of volume constancy, cylindrical shape, and substrate track of an earlier paper, but assuming additionally that a retarding force per unit area proportional to the rate of elongation is also acting. Equations of elongation for two different cases are derived.     

A contribution to the mathematical biophysics of cell growth and shapes: I

Under the assumption that the elongated shape assumed by a growing nerve cell is caused by surface tension forces between the cell, its fluid medium, and a fibrous substrate track along which the cell grows, equations of elongation and conditions insuring elongation are derived. One specific type of cell-substrate contact is considered. Equations of elongation and conditions for elongation are treated in both the nonfrictional and frictional types of motion of the cell-process.     

Experimental and mathematical approaches to modeling plant metabolic networks

To support their sessile and autotrophic lifestyle higher plants have evolved elaborate networks of metabolic pathways. Dynamic changes in these metabolic networks are among the developmental forces underlying the functional differentiation of organs, tissues and specialized cell types. They are also important in the various interactions of a plant with its environment. Further complexity is added by the extensive compartmentation of the various interconnected metabolic pathways in plants. Thus, although being used widely for assessing the control of metabolic flux in microbes, mathematical modeling approaches that require steady-state approximations are of limited utility for understanding complex plant metabolic networks. However, considerable progress has been made when manageable metabolic subsystems were studied. In this article, we will explain in general terms and using simple examples the concepts underlying stoichiometric modeling (metabolic flux analysis and metabolic pathway analysis) and kinetic approaches to modeling (including metabolic control analysis as a special case). Selected studies demonstrating the prospects of these approaches, or combinations of them, for understanding the control of flux through particular plant pathways are discussed. We argue that iterative cycles of (dry) mathematical modeling and (wet) laboratory testing will become increasingly important for simulating the distribution of flux in plant metabolic networks and deriving rational experimental designs for metabolic engineering efforts.