Multiscale Asymptotic Analysis Reveals How Cell Growth and Subcellular Compartments Affect Tissue-Scale Hormone Transport.

Determining how cell-scale processes lead to tissue-scale patterns is key to understanding how hormones and morphogens are distributed within biological tissues and control developmental processes. In this article, we use multiscale asymptotic analysis to derive a continuum approximation for hormone transport in a long file of cells to determine how subcellular compartments and cell growth and division affect tissue-scale hormone transport. Focusing our study on plant tissues, we begin by presenting a discrete multicellular ODE model tracking the hormone concentration in each cell's cytoplasm, subcellular vacuole, and surrounding apoplast, represented by separate compartments in the cell-file geometry. We allow the cells to grow at a rate that can depend both on space and time, accounting for both cytoplasmic and vacuolar expansion. Multiscale asymptotic analysis enables us to systematically derive the corresponding continuum model, obtaining an effective reaction-advection-diffusion equation and revealing how the effective diffusivity, effective advective velocity, and the effective sink term depend on the parameters in the cell-scale model. The continuum approximation reveals how subcellular compartments, such as vacuoles, can act as storage vessels, that significantly alter the effective properties of hormone transport, such as the effective diffusivity and the induced effective velocity. Furthermore, we show how cell growth and spatial variance across cell lengths affect the effective diffusivity and the induced effective velocity, and how these affect the tissue-scale hormone distribution. In particular, we find that cell growth naturally induces an effective velocity in the direction of growth, whereas spatial variance across cell lengths induces effective velocity due to the presence of an extra compartment, such as the apoplast and the vacuole, and variations in the relative sizes between the compartments across the file of cells. It is revealed that hormone transport is faster across cells of decreasing lengths than cells with increasing lengths. We also investigate the effect of cell division on transport dynamics, assuming that each cell divides as soon as it doubles in size, and find that increasing the time between successive cell divisions decreases the growth rate, which enhances the effect of cell division in slowing hormone transport. Motivated by recent experimental discoveries, we discuss particular applications for transport of gibberellic acid (GA), an important growth hormone, within the Arabidopsis root. The model reveals precisely how membrane proteins that mediate facilitated GA transport affect the effective tissue-scale transport. However, the results are general enough to be relevant to other plant hormones, or other substances that are transported in a similar way in any type of cells.

A biomechanical model of anther opening reveals the roles of dehydration and secondary thickening.

Understanding the processes that underlie pollen release is a prime target for controlling fertility to enable selective breeding and the efficient production of hybrid crops. Pollen release requires anther opening, which involves changes in the biomechanical properties of the anther wall. In this research, we develop and use a mathematical model to understand how these biomechanical processes lead to anther opening. Our mathematical model describing the biomechanics of anther opening incorporates the bilayer structure of the mature anther wall, which comprises the outer epidermal cell layer, whose turgor pressure is related to its hydration, and the endothecial layer, whose walls contain helical secondary thickening, which resists stretching and bending. The model describes how epidermal dehydration, in association with the thickened endothecial layer, creates forces within the anther wall causing it to bend outwards, resulting in anther opening and pollen release. The model demonstrates that epidermal dehydration can drive anther opening, and suggests why endothecial secondary thickening is essential for this process (explaining the phenotypes presented in the myb26 and nst1nst2 mutants). The research hypothesizes and demonstrates a biomechanical mechanism for anther opening, which appears to be conserved in many other biological situations where tissue movement occurs.

A model of crosslink kinetics in the expanding plant cell wall: yield stress and enzyme action.

The plant primary cell wall is a composite material containing stiff cellulose microfibrils that are embedded within a pectin matrix and crosslinked through a network of hemicellulose polymers. This microstructure endows the wall with nonlinear anisotropic mechanical properties and allows enzymatic regulation of expansive cell growth. We present a mathematical model of hemicellulose crosslink dynamics in an expanding cell wall incorporating strain-enhanced breakage and enzyme-mediated crosslink kinetics. The model predicts the characteristic yielding behaviour in the relationship between stress and strain-rate seen experimentally, and suggests how the effective yield and extensibility of the wall depend on microstructural parameters and on the action of enzymes of the XTH and expansin families. The model suggests that the yielding behaviour encapsulated in the classical Lockhart equation can be explained by the strongly nonlinear dependence of crosslink breakage rate on crosslink elongation. The model also demonstrates how enzymes that target crosslink binding can be effective in softening the wall in its pre-yield state, whereas its post-yield extensibility is determined primarily by the pectin matrix.

Multiscale modelling of auxin transport in the plant-root elongation zone.

In the root elongation zone of a plant, the hormone auxin moves in a polar manner due to active transport facilitated by spatially distributed influx and efflux carriers present on the cell membranes. To understand how the cell-scale active transport and passive diffusion combine to produce the effective tissue-scale flux, we apply asymptotic methods to a cell-based model of auxin transport to derive systematically a continuum description from the spatially discrete one. Using biologically relevant parameter values, we show how the carriers drive the dominant tissue-scale auxin flux and we predict how the overall auxin dynamics are affected by perturbations to these carriers, for example, in knockout mutants. The analysis shows how the dominant behaviour depends on the cells' lengths, and enables us to assess the relative importance of the diffusive auxin flux through the cell wall. Other distinguished limits are also identified and their potential roles discussed. As well as providing insight into auxin transport, the study illustrates the use of multiscale (cell to tissue) methods in deriving simplified models that retain the essential biology and provide understanding of the underlying dynamics.

Modelling crystal aggregation and deposition in the catheterised lower urinary tract.

Urethral catheters often become encrusted with crystals of magnesium struvite and calcium phosphate. The encrustation can block the catheter, which can cause urine retention in the bladder and reflux into the kidneys. We develop a mathematical model to investigate crystal deposition on the catheter surface, modelling the bladder as a reservoir of fluid and the urethral catheter as a rigid channel. At a constant rate, fluid containing crystal particles of unit size enters the reservoir, and flows from the reservoir through the channel and out of the system. The crystal particles aggregate, which we model using Becker-Döring coagulation theory, and are advected through the channel, where they continue to aggregate and are deposited on the channel's walls. Inhibitor particles also enter the reservoir, and can bind to the crystals, preventing further aggregation and deposition. The crystal concentrations are spatially homogeneous in the reservoir, whereas the channel concentrations vary spatially as a result of advection, diffusion and deposition. We investigate the effect of inhibitor particles on the amount of deposition. For all parameter values, we find that crystals deposit along the full length of the channel, with maximum deposition close to the channel's entrance.

Exchanges across land-water-scape boundaries in urban systems: strategies for reducing nitrate pollution.

Conservation in urban areas typically focuses on biodiversity and large green spaces. However, opportunities exist throughout urban areas to enhance ecological functions. An important function of urban landscapes is retaining nitrogen thereby reducing nitrate pollution to streams and coastal waters. Control of nonpoint nitrate pollution in urban areas was originally based on the documented importance of riparian zones in agricultural and forested ecosystems. The watershed and boundary frameworks have been used to guide stream research and a riparian conservation strategy to reduce nitrate pollution in urban streams. But is stream restoration and riparian-zone conservation enough? Data from the Baltimore Ecosystem Study and other urban stream research indicate that urban riparian zones do not necessarily prevent nitrate from entering, nor remove nitrate from, streams. Based on this insight, policy makers in Baltimore extended the conservation strategy throughout larger watersheds, attempting to restore functions that no longer took place in riparian boundaries. Two urban revitalization projects are presented as examples aimed at reducing nitrate pollution to stormwater, streams, and the Chesapeake Bay. An adaptive cycle of ecological urban design synthesizes the insights from the watershed and boundary frameworks, from new data, and from the conservation concerns of agencies and local communities. This urban example of conservation based on ameliorating nitrate water pollution extends the initial watershed-boundary approach along three dimensions: 1) from riparian to urban land-water-scapes; 2) from discrete engineering solutions to ecological design approaches; and 3) from structural solutions to inclusion of individual, household, and institutional behavior.

Nucleotide sequence of the Bacillus subtilis tryptophan operon.

In Bacillus subtilis, tryptophan biosynthesis is one of the most thoroughly characterized biosynthetic pathways. Recombinant DNA methodology has permitted a rapid characterization of the tryptophan (trp) gene cluster at the molecular level. In this report the nucleotide sequence of the six structural genes together with the intercistronic regions and flanking regulatory regions are presented.

Construction of a vector for cloning promoters in Bacillus subtilis.

A versatile vector for cloning DNA fragments containing promoter activity in Bacillus subtilis was derived from plasmids pBR322, pUB110 and pC194. Selection is based on chloramphenicol resistance which is dependent upon the introduction of DNA fragments allowing expression of a chloramphenicol acetyl transferase gene. The plasmid contains a second selectable marker, neomycin resistance, and contains functional origins of replication for both B. subtilis and Escherichia coli.

Nucleotide sequence of the Bacillus subtilis trpE and trpD genes.

Several overlapping portions of the tryptophan (trp) operon of Bacillus subtilis have been cloned into plasmid pBR322. The nucleotide sequence of the region comprising the trpE and trpD genes and a portion of the trpC gene has been determined. When the deduced amino acid sequences of these genes are compared with their counterparts in Escherichia coli, several regions of striking homology are seen. The probable initiation codons for the trpE, D and C genes are each preceded by a recognizable Shine-Dalgarno sequence. The coding sequences for the trpE and trpD genes and for the trpD and trpC genes overlap slightly, leaving no intercistronic regions between the genes.

The organization and nucleotide sequence of the Bacillus subtilis hisH, tyrA and aroE genes.

The nucleotide sequence of approximately 3 kb of Bacillus subtilis DNA distal to the trp operon was determined. Three open reading frames were found and these were shown to encode the hisH, tyrA and aroE genes. Integrative plasmids were constructed to interrupt transcription through this region. These data suggest that these three genes can be transcribed from both the trp promoter preceding the trp operon and from a promoter within the trpA structural gene.

Synthesis of an affinity ligand ('UPHIT') for in vivo acylation of the kappa-opioid receptor.

The isothiocyanate analog (1S,2S-trans-2-isothiocyanato-4,5-dichloro-N- methyl-N-[2-(1-pyrrolidinyl)cyclohexyl]benzeneacetamide, 3a) of the highly selective kappa-opioid receptor agonist, U50,488, was prepared as a potential site-directed affinity ligand for acylation of kappa-opioid receptors in vivo. The isothiocyanate (3a) which we have designated UPHIT and its enantiomer (3b) were synthesized in 3 steps starting from optically pure (1S,2S)-(+)-trans-2-pyrrolidinyl-N-methyl-cyclohexylamine (4a) and its enantiomer (4b), respectively, thus defining their absolute stereochemistry. Binding in vitro of the 1S,2S enantiomer 3a to kappa receptors labelled by [3H]U69,593 was shown to occur with an IC50 value of 25.92 +/- 0.36 nM, whereas 827.42 +/- 5.88 and 115.10 +/- 1.23 nM were obtained for the IC50 value of the 1R,2R enantiomer (3b) and (+/-)-3 respectively. Intracerebroventricular (ICV) injection of 100 micrograms of (+/-)-3 into guinea-pig brain followed by analysis of remaining kappa-binding sites 24 h later revealed that (+/-)-3 depleted 98% of the kappa receptors that bind [3H]U69,593 and 40% of those that bind [3H]bremazocine. These preliminary data suggest exciting uses for these compounds in furthering our knowledge of the kappa-opioid receptor.

Probes for narcotic receptor mediated phenomena. 17. Synthesis and evaluation of a series of trans-3,4-dichloro-N-methyl-N-[2-(1-pyrrolidinyl)cyclohexyl]benzeneacet amide (U50,488) related isothiocyanate derivatives as opioid receptor affinity ligands.

A series of U50,488 related isothiocyanates was synthesized from enantiomerically pure (S,S)-(+)-trans-2-pyrrolidinyl-N-methylcyclohexylamine [(+)-7] and (R,R)-(-)-trans-2-pyrrolidinyl-N-methylcyclohexylamine [(-)-7]. DCC coupling of (+)- and (-)-7 with nitrophenylacetic acids followed by catalytic hydrogenation and treatment with thiophosgene afforded a series of six isomeric aryl isothiocyanate analogues of U50,488. Similarly, DCC coupling of (+)- and (-)-7 with (+)- and (-)-N-t-Boc-protected phenylglycines afforded four isomeric alkyl isothiocyanates. Evaluation of the isothiocyanates for their capacity to produce wash-resistant inhibition of mu, delta, and kappa sites in vitro was performed using rat and guinea pig brain membranes. None of the compounds was able to irreversibly inhibit binding of [3H]bremazocine to guinea pig and rat brain membranes (depleted of functional mu and delta receptors by pretreatment with acylating agents BIT and FIT). However, (1S,2S)-trans-2-isothiocyanato-N-methyl-N-[2- (1-pyrrolidinyl)cyclohexyl]benzeneacetamide [(-)-1] was able to specifically and irreversibly inhibit kappa receptors labeled by [3H]-U69,593: Incubation of rat brain membranes for 60 min at 25 degrees C with 1 microM of (-)-1 resulted in a wash-resistant reduction of the binding to 11.2 +/- 2.5% of the control. Binding analysis revealed the wash-resistant reduction in [3H]-U69,593 binding by (-)-1 to be through an increase in the Kd without effect on the Bmax. (-)-1 failed to effect mu or delta binding in rat or guinea pig brain under the same conditions. The enantiomer of (-)-1, (1R,2R)-trans-2-isothiocyanato-N-methyl-N-[2- (1-pyrrolidinyl)cyclohexyl]benzeneacetamide [(+)-1], failed to affect kappa receptors labeled by [3H]-U69,593 under the same conditions as for (-)-1. (1S,2S)-trans-3-Isothiocyanato-N-methyl-N-[2- (1-pyrrolidinyl)cyclohexyl]benzeneacetamide [(-)-2] inhibited to 49.6 +/- 5.1% of the control, in a wash-resistant manner, kappa receptors labeled by [3H]-U69,593. However, (-)-2 was not as selective as (-)-1 since it also reduced [3H]DADLE (delta) binding to 82.4 +/- 8.0% of the control value. (1S,2S)-trans-4-Isothiocyanato-N-methyl-N-[2-(1-pyrrolidinyl)- cyclohexyl]benzeneacetamide [(-)-3] exhibited selective wash-resistant inhibition of delta receptors labeled by [3H]DADLE resulting in a reduction in binding to 42.9 +/- 4.2% of control.(ABSTRACT TRUNCATED AT 400 WORDS)

Synthesis and evaluation of N-substituted cis-N-methyl-2-(1-pyrrolidinyl)cyclohexylamines as high affinity sigma receptor ligands. Identification of a new class of highly potent and selective sigma receptor probes.

Certain benzeneacetamides [(-)- and (+)-cis-3,4-dichloro-N-methyl-N-[2-(1-pyrrolidinyl) cyclohexyl]benzeneacetamide] were recently reported to be potent sigma receptor ligands. In order to determine whether efficacy for the sigma receptor could be improved, a series of compounds related to the benzeneacetamides, N-substituted cis-2-(1-pyrrolidinyl)-N-methylcyclohexylamines, were synthesized and their structure-activity requirements were determined. The compounds were synthesized by starting with the previously reported (+/-)-, 1S,2R-(+)-, and 1R,2S-(-)-cis-2-(1-pyrrolidinyl)-N-methylcyclohexylamines. Analysis of sigma ([3H](+)-3-PPP), kappa ([3H]bremazocine and [3H]U69,593), dopamine-d2 ([3H](-)-sulpiride), and phencyclidine (PCP) ([3H]TCP) receptor binding in guinea pig brain revealed a number of highly potent and selective sigma receptor ligands. Notably, 1S,2R-cis-(-)-N-methyl-N-[2-(1-pyrrolidinyl)cyclohexyl]-(2-naphthyl) acetamide [(-)-29] (Ki = 8.66 +/- 0.35 nM), (+/-)-cis-2-amino-4,5-dichloro-N-methyl-N-[2-(1-pyrrolidinyl)cyclohexyl] benzeneacetamide [(+/-)-17] (Ki = 11 +/- 3 nM), 1S,2R-(-)-cis-N-methyl-N-[2-(3,4-dichlorophenyl)ethyl]-2-(1-pyrrolidinyl ) cyclohexylamine [(-)-44] (Ki = 1.3 +/- 0.3 nM), and 1R,2S-(+)-cis-N-methyl-N-[2-(3,4-dichlorophenyl)ethyl]-2-(1-pyrrolidinyl ) cyclohexylamine. [(+)-44] (Ki = 6 +/- 3 nM) exhibited very high affinity at sigma receptors, by displacement of [3H]-(+)-3-(3-hydroxyphenyl)-N-(1-propyl)piperidine [( 3H]-(+)-3-PPP). These compounds showed insignificant affinity for kappa, dopamine, or PCP receptors, making them valuable tools for the study of sigma receptors. Furthermore, these compounds also exhibited enantioselectivity ranging from 5-fold for (+)- and (-)-44 to 160-fold for (+)- and (-)-29. Several other compounds showed equivalent selectivity but displayed lower sigma receptor affinity.

Morphine and dynorphin(1-13) microinjected into the medial preoptic area and nucleus accumbens: effects on sexual behavior in male rats.

The effects on sexual behavior of opiate receptor stimulation within A10 and A14 terminal areas were examined in the following experiments. Morphine (0.01-6 nmol) and dynorphin(1-13) (0.01-3 pmol) were microinjected into the medial preoptic area (MPOA). Morphine (10-100 pmol) and dynorphin (10-100 fmol) injected into the MPOA reduced both the latency to ejaculate and the number of intromissions triggering ejaculation. Morphine (6 nmol) produced a failure to resume copulating following the second ejaculation. Morphine (1-10 nmol) injected into the nucleus accumbens (ACC) shortened the latency to the first intromission and lengthened the second postejaculatory interval. Naloxone (3 mg/kg i.p.) reversed the effects of morphine on intromission latency and attenuated the lowering of ejaculatory threshold.

Microinjection of cis-flupenthixol, a dopamine antagonist, into the medial preoptic area impairs sexual behavior of male rats.

Systemically administered dopamine agonists have been shown to facilitate copulation in male rats. Microinjection of the dopamine agonist apomorphine into the medial preoptic area has also been reported to facilitate sexual behavior. The present experiments investigated the effects of medial preoptic microinjections of the dopamine antagonist cis-flupenthixol on male rat copulatory behavior. Fewer males initiated copulation and fewer ejaculated following flupenthixol administration. Those males that did ejaculate following flupenthixol injections had fewer ejaculations and longer interintromission intervals. Flupenthixol also antagonized the facilitative effects of apomorphine injections into the medial preoptic area. Flupenthixol and apomorphine produced only minor alterations in noncopulatory behaviors. The results suggest that dopamine receptors within the medial preoptic area are important in the regulation of masculine sexual behavior in the rat.

Dopaminergic control of male sex behavior in rats: effects of an intracerebrally-infused agonist.

Systemically-administered dopaminergic drugs have been found to facilitate sexual behavior of men and male rats. The present experiments investigated the localization within the brain of dopaminergic effects on copulation of male rats. Apomorphine, a dopamine agonist, was microinfused into the medial preoptic area, caudate-putamen, nucleus accumbens, lateral septum and lateral ventricle. The lowest dose of apomorphine (0.2 microgram) infused into the ventricle reduced the number of ejaculations, slowed the rate of intromitting and decreased the percentage of mounts on which the male gained vaginal intromission. The higher two doses (0.5 and 2.0 micrograms) infused into the medial preoptic area and, in some cases, the ventricle, increased the number of ejaculations and the percentage of mounts with vaginal intromission, increased the rate of intromitting and decreased the latency to ejaculate and the postejaculatory interval before resuming copulation. Infusions into the caudate-putamen and lateral septum were without effect. Those into nucleus accumbens produced only a slight dose-related decrease in latency to begin copulating. The copulatory impairments associated with infusions of the lowest dose into the ventricle may have resulted from stimulation of autoreceptors, or from preferential stimulation by low doses of an undetermined area. The facilitative effects of the two higher doses into the medial preoptic area and lateral ventricle may have been due to stimulation of dopaminergic postsynaptic receptors.

The potent opioid agonist, (+)-cis-3-methylfentanyl binds pseudoirreversibly to the opioid receptor complex in vitro and in vivo: evidence for a novel mechanism of action.

The present study demonstrates that pretreatment of rat brain membranes with (+)-cis-3-methylfentanyl [(+)-cis-MF], followed by extensive washing of the membranes, produces a wash-resistant decrease in the binding of [3H]-[D-ala2,D-leu5]enkephalin to the d binding site of the opioid receptor complex (delta cx binding site). Intravenous administration of (+)-cis-MF (50 micrograms/kg) to rats produced a pronounced catalepsy and also produced a wash-resistant masking of delta cx and mu binding sites in membranes prepared 120 min post-injection. Administration of 1 mg/kg i.v. of the opioid antagonist, 6-desoxy-6 beta-fluoronaltrexone (cycloFOXY), 100 min after the injection of (+)-cis-MF (20 min prior to the preparation of membranes) completely reversed the catatonia and restored masked delta cx binding sites to control levels. This was not observed with (+)-cycloFOXY. The implications of these and other findings for the mechanism of action of (+)-cis-MF and models of the opioid receptors are discussed.

Brain localization of cholinergic influence on male sex behavior in rats: agonists.

Cholinergic agonists were microinjected into either the lateral ventricle or the preoptic area of sexually experienced male rats. In Experiment 1 carbachol, injected into the lateral ventricles, delayed the initiation of sexual behavior. When injected into the preoptic area, carbachol again delayed the onset of copulation, but these delays were shorter than after ventricular injections. In addition, preoptic injections reduced the number of intromissions preceding ejaculation. In Experiment 2 ventricular injections of the muscarinic agonist oxotremorine again delayed initiation of sexual behavior and also slowed its rate. However, oxotremorine injections into the preoptic area, through cannulae angled to miss all ventricles, only decreased the number of intromissions preceding ejaculation. These data suggest that cholinergic synapses in proximity to the ventricles may decrease sexual arousal, while cholinergic mechanisms in or near the preoptic area may reduce ejaculatory threshold.

Brain localization of cholinergic influence on male sex behavior in rats: antagonists.

The muscarinic receptor antagonist scopolamine was microinjected into either the preoptic area or the lateral ventricle, preceding sexual behavior tests. In Experiment 1 unilateral ventricular injections of scopolamine delayed the initiation of copulation, while unilateral preoptic injections had no effect. In Experiment 2 bilateral injections into the preoptic area produced dose-related decreases in the percentages of animals intromitting and ejaculating. In Experiment 3 scopolamine, injected alone into the preoptic area, again decreased the percentages of animals mounting, intromitting, and ejaculating. The muscarinic agonist oxotremorine, injected alone into the preoptic area, decreased ejaculatory threshold (i.e., decreased the number of intromissions preceding ejaculation) as previously reported. Concurrent oxotremorine and scopolamine injections into the preoptic area were not different from vehicle; thus, scopolamine blocked oxotremorine's effect. These data suggest that some cholinergic activation of the preoptic area is critical for normal copulation, since bilateral blockade of muscarinic receptors there dramatically decreased the number of animals copulating. However, increased cholinergic activity there only reduced ejaculation threshold.

Bacillus subtilis requires a "stringent" Shine-Dalgarno region for gene expression.

A series of plasmids was constructed differing only in the sequence of the Shine-Dalgarno region preceding the leukocyte interferon-A gene. This series of plasmids was used to test the efficiency of interferon expression in both Bacillus subtilis and Escherichia coli. In B. subtilis, interferon expression was much more sensitive to changes in the sequence of the Shine-Dalgarno region than in E. coli and it appeared to require more homology to the 3' end of 16S ribosomal RNA.