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1.
N. Rashevsky 《Bulletin of mathematical biology》1969,31(3):605-617
A previous study (Bull. Math. Biophysics,31, 417–427, 1969) on the definitions of stability of equilibria in organismic sets determined byQ relations is continued. An attempt is made to bring this definition into a form as similar as possible to that used in physical
systems determined byF-relations. With examples taken from physics, biology and sociology, it is shown that a definition of equilibria forQ-relational systems similar to the definitions used in physics can be obtained, provided the concept of stable or unstable
structures of a system determined byQ-relations is considered in a probabilistic manner. This offers an illustration of “fuzzy categories,” a notion introduced
by I. Bąianu and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968), in their paper on organismic supercategories, which is designed to provide a mathematical formalism for
Rashevsky's theory of Organismic Sets (Bull. Math. Biophysics,29, 389–393, 1967;30, 163–174, 1968;31, 159–198, 1969). A suggestion is made for a method of mapping the abstract discrete space ofQ-relations on a continuum of variables ofF-relations. Problems of polymorphism and metamorphosis, both in biological and social organisms, are discussed in the light
of the theory. 相似文献
2.
Robert I. Macey 《Bulletin of mathematical biology》1962,24(3):291-302
The diffusion of a binary salt through media containing uniformly dispersed immobile ions is formally equivalent to the diffusion
of a nonelectrolyte with a concentration-dependent diffusion coefficient. This permits the application of a quasi-steady-state
approximation, developed in a previous paper (Bull. Math. Biophysics,21, 19–32, 1959), to problems of transient diffusion. Free diffusion across an interface involving a discontinuity in immobile
ion concentration is considered and expressions for the salt concentration and electrical potential at any point are developed.
The dependence of electrical potential on the fixed charge density, ionic mobilities, as well as on the boundary concentrations
is illustrated by a numerical example. This particular example is suggested by experiments on connective tissue. 相似文献
3.
N. Rashevsky 《Bulletin of mathematical biology》1971,33(2):157-164
In classical physics the stability of an equilibrium requires that any, even infinitesimal, displacement from the configuration
of equilibrium results in forces which tend to restore the original equilibrium configuration. In case of several stable equilibrium
configurations, the height of the threshold, which must be exceeded by the deviarion from the stable equilibrium in order
to bring the configuration into another stable equilibrium is taken as a measure of stability of the first configuration.
In quantum mechanics, and in the recent work of I. Baianu, S. Comorosan and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968;31, 59–70, 1969;32, 539–561, 1970) on organismic supercategories, preference is given to take, as ameasure of the degree of stability of a configuration,
or of a “state”, the length of time during which the system remains in that configuration. It is shown that under rather general
conditions the two criteria are equivalent. 相似文献
4.
N. Rashevsky 《Bulletin of mathematical biology》1964,26(1):57-61
In connection with a series of previous papers by this author (Bulletin of Mathematical Biophysics,21, 299–308, 375–385;22, 257–262, 263–267;23, 19–29;24, 319–325) results obtained by A. Crawford (Economics
5, 417–428) on the effects of irrelevant lights on reaction times toward a given light stimulus are discussed. The conclusions
from a previous paper of this author (Bulletin of Mathematical Biophysics,23, 19–29) are elaborated. 相似文献
5.
Functional characterization of a LAHC sucrose transporter isolated from grape berries in yeast 总被引:2,自引:0,他引:2
Ya Li Zhang Qing Yong Meng Hong Liang Zhu Ying Guo Hong Yan Gao Yun Bo Luo Jiang Lu 《Plant Growth Regulation》2008,54(1):71-79
Large amounts of sugar are imported into grape berries from source leaves during ripening, and sucrose transporters play a
key role during this process. In this study, a putative grape sucrose transporter gene VvSUC27, primarily expressed in sink tissue, was transformed into a yeast strain to characterize its function as a sucrose transporter.
Sucrose was taken up by yeast transformed with VvSUC27 at an optimum pH of 4.0–5.0 and a K
m of 8.0–10.5 mM, indicating VvSUC27 is a LAHC (low-affinity/high-capacity) sucrose transporter. The ability of sucrose uptake
in transformed yeast was activated by monosaccharides and inhibited by maltose and DEPC.
Ya Li Zhang and Qing Yong Meng contributed equally to the paper. 相似文献
6.
The purpose of this paper is to present a mathematical model for the tumor vascularization theory of tumor growth proposed
by Judah Folkman in the early 1970s and subsequently established experimentally by him and his coworkers [Ausprunk, D. H.
and J. Folkman (1977) Migration and proliferation of endothelial cells in performed and newly formed blood vessels during
tumor angiogenesis, Microvasc Res., 14, 53–65; Brem, S., B. A. Preis, ScD. Langer, B. A. Brem and J. Folkman (1997) Inhibition of neovascularization by an extract
derived from vitreous Am. J. Opthalmol., 84, 323–328; Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64; Gimbrone, M. A. Jr, R. S. Cotran, S. B. Leapman and J. Folkman (1974) Tumor growth and neovascularization: an experimental
model using the rabbit cornea, J. Nat. Cancer Inst., 52, 413–419]. In the simplest version of this model, an avascular tumor secretes a tumor growth factor (TGF) which is transported
across an extracellular matrix (ECM) to a neighboring vasculature where it stimulates endothelial cells to produce a protease
that acts as a catalyst to degrade the fibronectin of the capillary wall and the ECM. The endothelial cells then move up the
TGF gradient back to the tumor, proliferating and forming a new capillary network. In the model presented here, we include
two mechanisms for the action of angiostatin. In the first mechanism, substantiated experimentally, the angiostatin acts as
a protease inhibitor. A second mechanism for the production of protease inhibitor from angiostatin by endothelial cells is
proposed to be of Michaelis-Menten type. Mathematically, this mechanism includes the former as a subcase.
Our model is different from other attempts to model the process of tumor angiogenesis in that it focuses (1) on the biochemistry
of the process at the level of the cell; (2) the movement of the cells is based on the theory of reinforced random walks;
(3) standard transport equations for the diffusion of molecular species in porous media.
One consequence of our numerical simulations is that we obtain very good computational agreement with the time of the onset
of vascularization and the rate of capillary tip growth observed in rabbit cornea experiments [Ausprunk, D. H. and J. Folkman
(1977) Migration and proliferation of endothelial cells in performed and newly formed blood vessels during tumor angiogenesis,
Microvasc Res., 14, 73–65; Brem, S., B. A. Preis, ScD. Langer, B. A. Brem and J. Folkman (1997) Inhibition of neovascularization by an extract
derived from vitreous Am. J. Opthalmol., 84, 323–328; Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64; Gimbrone, M. A. Jr, R. S. Cotran, S. B. Leapman and J. Folkman (1974) Tumor growth and neovascularization: An experimental
model using the rabbit cornea, J. Nat. Cancer Inst., 52, 413–419]. Furthermore, our numerical experiments agree with the observation that the tip of a growing capillary accelerates
as it approaches the tumor [Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64].
An erratum to this article is available at . 相似文献
7.
N. Rashevsky 《Bulletin of mathematical biology》1969,31(3):591-603
A previous study (Bull. Math. Biophysics,30, 735–749) is generalized to the case of active transport, which acts together in general with ordinary diffusion. The basic
results obtained are the same except for an additional important conclusion. In principle it is possible to obtain sustained
oscillations even when the secretions of the different glands do not affect the rates of formation or decay of each other
at all, but affect the “molecular pumps,” which are responsible for the active transports in various parts of the system.
Thus no biochemical interactions need necessarily take place between then-metabolites to make sustained oscillations possible in principle. This is an addition to a previous finding (Bull. Math. Biophysics,30, 751–760) that due to effects of the secreted hormones on target organs, non-linearity of biochemical interactions is not
needed for production of sustained oscillations. 相似文献
8.
We consider the spatio-temporal dynamics of a spatially-structured generalization of the phytoplankton-zooplankton-fish larvae
model system proposed earlier (Biktashev et al., 2003, J. Plankton Res. 5, 21–33; James et al., 2003, Ecol. Model. 160, 77–90). In contrast to Pitchford and Brindley (2001, Bull. Math. Biol. 63, 527–546), who were concerned with small scale patchiness (i.e., 1–10m), on which the (stochastic) raptorial behaviour of
individual larvae is important, we address here the much larger scale ‘patchy’ problems (i.e., 10–100 km), on which both larvae
and plankton may be regarded as passive tracers of the fluid motion, dispersed and mixed by the turbulent diffusion processes.
In particular, we study the dependence of the fish recruitment on carrying capacities of the plankton subsystem and on spatio-temporal
evolution of that subsystem with respect to the larvae hatching site(s). It is shown that the main features found both in
the nonstructured and age-structured spatially uniform models are observed in the spatially structured case, but that spatial
effects can significantly modify the overall quantitative outcome.
Spatial patterns in the metamorphosed fish distribution are a consequence of quasi-local interaction of larvae with plankton,
in which the dispersion of larvae by large scale turbulent eddies plays little part due to the relatively short timescale
of the larvae development. As a result, in a strong phyto/zooplankton subsystem, with fast reproduction rate and large carrying
capacity of phytoplankton and high conversion ratio of zooplankton, recruitment success depends only on the localization and
timing of the hatching with respect to the plankton patches. In a weak phyto/zooplankton system, with slow reproduction rate
and small carrying capacity of phytoplankton and low conversion ratio of zooplankton, the larvae may significantly influence
the evolution of the plankton patches, which may lead to nontrivial cooperative effects between different patches of larvae.
However, in this case, recruitment is very low. 相似文献
9.
Calcium plays an essential role in excitation-contraction coupling in muscle, and derangements in calcium handling can produce
a variety of potentially harmful conditions, especially in cardiac muscle. In cardiac tissue specialized invaginations of
the sarcolemma, called T-tubules, penetrate deep into each sarcomere, and depolarization of the SL leads to an influx of calcium
through voltage-sensitive channels in the T-tubules that in turn triggers further calcium release from the sarcoplasmic reticulum
via ryanodine-sensitive calcium channels. Under certain conditions, such as elevated external Ca2+, cardiac cells can release calcium from the sarcoplasmic reticulum spontaneously, producing a calcium ’spark’ and propagating
traveling waves of elevated Ca2+ concentration, without depolarization of the SL (Wier and Blatter, 1991a, Cell Calcium
12, 241–254; Williams, 1993, Cell Calcium
14, 724–735; Cheng et al., 1993a, Science
262, 740–744). However, under normal resting conditions these potentially harmful waves seldom occur. In this paper we investigate
the role of the periodic distribution of ryanodine-sensitive channels in determining whether a spark can trigger a wave, using
a modification of the kinetic model proposed by Tang and Othmer, 1994b, Biophys. J.
67, 2223–2235, for calcium-induced calcium release. We show that the spatial localization of these channels near the T-tubules
has a significant effect on both wave propagation and the onset of oscillations in this system. Spatial localization provides
a possible explanation for the differing effects of various experimental protocols on the system’s ability to propagate a
traveling wave.
Supported in part by NIH Grant GM29123. 相似文献
10.
Chemical shift anisotropy (CSA) tensor parameters have been determined for the protonated carbons of the purine bases in an
RNA kissing complex in solution by extending the model-independent approach [Fushman, D., Cowburn, D. (1998) J. Am. Chem. Soc. 120, 7109–7110]. A strategy for determining CSA tensor parameters of heteronuclei in isolated X–H two-spin systems (X = 13C or 15N) in molecules undergoing anisotropic rotational diffusion is presented. The original method relies on the fact that the
ratio κ2=R2auto/R2cross of the transverse auto- and cross-correlated relaxation rates involving the X CSA and the X–H dipolar interaction is independent
of parameters related to molecular motion, provided rotational diffusion is isotropic. However, if the overall motion is anisotropic
κ2 depends on the anisotropy D||/D⊥ of rotational diffusion. In this paper, the field dependence of both κ2 and its longitudinal counterpart κ1=R1auto/R1cross are determined. For anisotropic rotational diffusion, our calculations show that the average κav = 1/2 (κ1+κ2), of the ratios is largely independent of the anisotropy parameter D||/D⊥. The field dependence of the average ratio κav may thus be utilized to determine CSA tensor parameters by a generalized model-independent approach in the case of molecules
with an overall motion described by an axially symmetric rotational diffusion tensor. 相似文献
11.
N. Rashevsky 《Bulletin of mathematical biology》1968,30(2):355-357
It is suggested that the development of organismic sets is governed not by the maximalization of the integral survival value,
as suggested previously (Bull. Math. Biophysics,28, 283–308, 1966;29, 139–152, 1967;30, 163–174, 1968), but by maximizing the number of new relations which appear as an organismic set develops. 相似文献
12.
Linearized oscillations in population dynamics 总被引:6,自引:0,他引:6
A linearized oscillation theorem due to Kulenović, Ladas and Meimaridou (1987,Quart. appl. Math.
XLV, 155–164) and an extension of it are applied to obtain the oscillation of solutions of several equations which have appeared
in population dynamics. They include the logistic equation with several delays, Nicholson's blowflies model as described by
Gurney, Blythe and Nisbet (1980,Nature, Lond.
287, 17–21) and the Lasota-Wazewska model of the red blood cell supply in an animal. We also developed a linearized oscillation
result for difference equations and applied it to several equations taken from the biological literature. 相似文献
13.
The dynamics of the nucleobase and the ribose moieties in a 14-nt RNA cUUCGg hairpin-loop uniformly labeled with 13C and 15N were studied by 13C spin relaxation experiments. R1, R1ρ and the 13C-{1H} steady-state NOE of C6 and C1′ in pyrimidine and C8 and C1′ in purine residues were obtained at 298 K. The relaxation data were analyzed by the model-free formalism to yield dynamic
information on timescales of pico-, nano- and milli-seconds. An axially symmetric diffusion tensor with an overall rotational
correlation time τc of 2.31±0.13 ns and an axial ratio of 1.35±0.02 were determined. Both findings are in agreement with hydrodynamic calculations.
For the nucleobase carbons, the validity of different reported 13C chemical shift anisotropy values (Stueber, D. and Grant, D. M., 2002 J. Am. Chem. Soc. 124, 10539–10551; Fiala et al., 2000 J. Biomol. NMR 16, 291–302; Sitkoff, D. and Case, D. A., 1998 Prog. NMR Spectroscopy 32, 165–190) is discussed. The resulting dynamics are in agreement with the structural features of the cUUCGg motif in that
all residues are mostly rigid (0.82 < S2 < 0.96) in both the nucleobase and the ribose moiety except for the nucleobase of U7, which is protruding into solution (S2 = 0.76). In general, ribose mobility follows nucleobase dynamics, but is less pronounced. Nucleobase dynamics resulting from
the analysis of 13C relaxation rates were found to be in agreement with 15N relaxation data derived dynamic information (Akke et al., 1997 RNA 3, 702–709).
Electronic supplementary material Electronic supplementary material is available for this article at
and accessible for authorised users. 相似文献
14.
The mathematical model developed by Riveroet al. (1989,Chem. Engng Sci.
44, 2881–2897) is applied to literature data measuring chemotactic bacterial population distributions in response to steep as
well as shallow attractant gradients. This model is based on a fundamental picture of the sensing and response mechanisms
of individual bacterial cells, and thus relates individual cell properties such as swimming speed and tumbling frequency to
population parameters such as the random motility coefficient and the chemotactic sensitivity coefficient. Numerical solution
of the model equations generates predicted bacterial density and attractant concentration profiles for any given experimental
assay. We have previously validated the mathematical model from experimental work involving a step-change in the attractant
gradient (Fordet al., 1991Biotechnol. Bioengng.37, 647–660; For and Lauffenburger, 1991,Biotechnol. Bioengng,37, 661–672). Within the context of this experimental assay, effects of attractant diffusion and consumption, random motility,
and chemotactic sensitivity on the shape of the profiles are explored to enhance our understanding of this complex phenomenon.
We have applied this model to various other types of gradients with successful intepretation of data reported by Dalquistet al. (1972,Nature New Biol.
236, 120–123) forSalmonella typhimurum validating the mathematical model and supportin the involvement of high and low affinity receptors for serine chemotaxis
by these cells. 相似文献
15.
16.
N. Rashevsky 《Bulletin of mathematical biology》1968,30(4):735-749
In a series of papers, L. Danziger and G. Elmergreen (Bull. Math. Biophysics,16, 15–21, 1954;18, 1–13, 1956;19, 9–18, 1957) showed that a non-linear biochemical interaction between the anterior pituary gland and the thyroid gland may
result under certain conditions in sustained periodical oscillations of the rates of production and of the blood level of
the thyrotropic and of the thyroid hormone. They treated the systems, however, as a homogeneous one. N. Rashevsky (Some Medical Aspects of Mathematical Biology, Springfield, Illinois: Charles C. Thomas, Publisher, 1965;Bull. Math. Biophysics,29, 395–401, 1967) generalized the above results by taking into account the histological structures of the two glands as well
as the diffusion coefficients and permeabilities of cells involved. The present paper is the first step toward the theory
of interaction of any numbern of glands or, more generally,n components. The differential equations which govern the behavior of such a system represent a system of2n
2+n
non-linear first order ordinary equations and involve a total of 7 n
2+3n parameters of partly histological, partly biochemical nature. The requirements of the existence of sustained oscillations
demand 4n
2+2n+2 inequalities between those 7n
2+3n parameters. 相似文献
17.
Transmembrane threonine fluxes (i.e., uptake, diffusion, and carrier-mediated excretion) all contribut-ing to threonine production
by a recombinant strain of Corynebacterium glutamicum, were analyzed and quantitated. A threonine-uptake carrier that transports threonine in symport with sodium ions was identified.
Under production conditions (i.e., when internal threonine is high), this uptake system catalyzed predominantly threonine/threonine
exchange. Threonine export via the uptake system was excluded. Threonine efflux from the cells was shown to comprise both
carrier-mediated excretion and passive diffusion. The latter process was analyzed after inhibition of all carrier-mediated
fluxes. Threonine diffusion was found to proceed with a first-order rate constant of 0.003 min–1 or 0.004 μl min–1 (mg dry wt.)–1, which corresponds to a permeability of 8 × 10–10 cm s–1. According to this permeability, less than 10% of the efflux observed under optimal conditions takes place via diffusion,
and more than 90% must result from the activity of the excretion carrier. In addition, the excretion carrier was identified
by (1) inhibition of its activity by amino acid modifying reagents and (2) its dependence on metabolic energy in the form
of the membrane potential. Activity of the excretion system depended on the membrane potential, but not on the presence of
sodium ions. Threonine export in antiport against protons is proposed.
Received: 25 August 1995 / Accepted: 18 October 1995 相似文献
18.
The present-day practices of electrocardiography and vectorardiography are based upon the theory that the surface potential
differences can be assumed to be due to a single dipole inside the body. It is shown in this paper that a dipole cannot account
for all the surface potentials due to realistic current generators, and hence the determination of the current generator from
surface potential measurements based upon such a theory will lead to inconsistent representations of the heart for one and
the same subject.
To demonstrate this point two eccentric dipoles of different strengths and locations representing two muscle fibers are taken
to be the current generator in a homogeneous spherical conductor. The exact surface potentials are then expressed by means
of the “interior sphere theorem” of the authors. With these expressions the magnitude, direction, and location of the resultant
dipole are determined by the method of D. Gabor and C. V. Nelson (J. App. Physics,25, 413–16, 1954). The surface potentials due to this resultant dipole are again exactly expressed by means of the “interior
sphere theorem” and compared with those due to the eccentric dipoles assumed. It can be seen that the differences can be considerable.
It is suggested that the multipole model of the authors (Bull. Math. Biophysics,20, 203–16, 1958) be used as a more accurate and the only unique representation of the heart.
This investigation was supported by the National Heart Institute under a research grant H-2263(c). 相似文献
19.
Ruth M. Siewe Brita Weil Andreas Burkovski Lothar Eggeling R. Krämer Thomas Jahns 《Archives of microbiology》1998,169(5):411-416
When Corynebacterium glutamicum is grown with a sufficient nitrogen supply, urea crosses the cytoplasmic membrane by passive diffusion. A permeability coefficient
for urea diffusion of 9 × 10–7 cm s–1 was determined. Under conditions of nitrogen starvation, an energy-dependent urea uptake system was synthesized. Carrier-mediated
urea transport was catalyzed by a secondary transport system linked with proton motive force. With a K
m for urea of 9 μM, the affinity of this uptake system was much higher than the affinity of urease towards its substrate (K
m approximately 55 mM urea). The maximum uptake velocity depended on the expression level and was relatively low [2–3.5 nmol
min–1 (mg dry wt.)–1].
Received: 11 August 1997 / Accepted: 2 December 1997 相似文献
20.
N. Rashevsky 《Bulletin of mathematical biology》1960,22(1):73-84
The principle of biotopological mapping (Rashevsky, 1954,Bull. Math. Biophysics,16, 317–48) is given a generalized formulation, as the principle of relational epimorphism in biology. The connection between
this principle and Robert Rosen’s representation of organisms by means of categories (1958,Bull. Math. Biophysics,20, 317–41) is studied. Rosen’s theory of (M,R)-systems, (1958,Bull. Math. Biophysics,20, 245–60) is generalized by dropping the assumption that only terminalM
i
components are sending inputs into theR
i
components. It is shown that, if the primordial organism is an (M,R)-system, then the higher organisms, obtained by a construction well discussed previously (1958,Bull. Math. Biophysics,20, 71–93), are also (M,R)-systems. Several theorems about such derived (M,R)-systems are demonstrated.
It is shown that Rosen’s concept of an organism as a set of mappings throws light on phenomena of synesthesia and also leads
to the conclusion that Gestalt phenomena must occur not only in the fields of visual and auditory perception but in perceptions
of any modality. 相似文献