Analysis of chemotactic bacterial distributions in population migration assays using a mathematical model applicable to steep or shallow attractant gradients

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.     

The complete classification for dynamics in a homosexually-transmitted disease model

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population was proposed by Li et al. in (J Math Biol 10:1037–1052, 1986). The sufficient and necessary conditions for coexistence and the sufficient conditions for stability of the boundary equilibria were provided. This paper will present a thorough classification of dynamics for this model in terms of the first and second so called reproductive numbers of infection in strains I and J. This classification not only solves a conjecture proposed in (Li et al., J Math Biol 10:1037–1052, 1986) but also gives the sufficient and necessary conditions for the competitive exclusion. Supported by the NSF of China grants 10531030 and 10671143.     

Memory capacity in large idiotypic networks

Many models of immune networks have been proposed since the original work of Jerne [1974,Ann. Immun. (Inst. Pasteur) 125C, 373–389]. Recently, a limited class of models (Weisbuchet al., 1990,J. theor. Biol. 146, 483–499) have been shown to maintain immunological memory by idiotypic network interactions. We examine generalizations of these models when the networks are both large and highly connected to study their memory capacity, i.e. their ability to account for immunization to a large number of random antigens. Our calculations show that in these minimal models, random connectivities with continuously distributed affinities reduce the memory capacity to essentially nil.     

Chaperone receptors: guiding proteins to intracellular compartments

Despite mitochondria and chloroplasts having their own genome, 99% of mitochondrial proteins (Rehling et al., Nat Rev Mol Cell Biol 5:519–530, 2004) and more than 95% of chloroplast proteins (Soll, Curr Opin Plant Biol 5:529–535, 2002) are encoded by nuclear DNA, synthesised in the cytosol and imported post-translationally. Protein targeting to these organelles depends on cytosolic targeting factors, which bind to the precursor, and then interact with membrane receptors to deliver the precursor into a translocase. The molecular chaperones Hsp70 and Hsp90 have been widely implicated in protein targeting to mitochondria and chloroplasts, and receptors capable of recognising these chaperones have been identified at the surface of both these organelles (Schlegel et al., Mol Biol Evol 24:2763–2774, 2007). The role of these chaperone receptors is not fully understood, but they have been shown to increase the efficiency of protein targeting (Young et al., Cell 112:41–50, 2003; Qbadou et al., EMBO J 25:1836–1847, 2006). Whether these receptors contribute to the specificity of targeting is less clear. A class of chaperone receptors bearing tetratricopeptide repeat domains is able to specifically bind the highly conserved C terminus of Hsp70 and/or Hsp90. Interestingly, at least of one these chaperone receptors can be found on each organelle (Schlegel et al., Mol Biol Evol 24:2763–2774, 2007), which suggests a universal role in protein targeting for these chaperone receptors. This review will investigate the role that chaperone receptors play in targeting efficiency and specificity, as well as examining recent in silico approaches to find novel chaperone receptors.     

Recent Advances in GFP Folding Reporter and Split-GFP Solubility Reporter Technologies. Application to Improving the Folding and Solubility of Recalcitrant Proteins from Mycobacterium tuberculosis

We have improved our green fluorescent protein (GFP) folding reporter technology [Waldo et al., (1999) Nat. Biotechnol. 17, 691–695] to evolve recalcitrant proteins from Mycobacterium tuberculosis. The target protein is inserted into the scaffolding of the GFP, eliminating false-positive artifacts caused by expression of truncated protein variants from internal cryptic ribosome binding sites in the target RNA. In parallel, we have developed a new quantitative fluorescent protein tagging and detection system based on micro-domains of GFP. This split-GFP system, which works both in vivo and in vitro, is amenable to high-throughput assays of protein expression and solubility [Cabantous et al., (2005) Nat. Biotechnol. 23, 102–107]. Together, the GFP folding reporter and split-GFP technologies offer a comprehensive system for manipulating and improving protein folding and solubility.     

Development of a multiallelic SCAR marker for the scab resistance gene Vr1/Vh4/Vx from R12740-7A apple and its utility for molecular breeding

A major scab resistance gene initially called Vr1 was identified in the apple cultivar “Regia” derived from the Malus scab resistance source R12740-7A (Russian seedling, RS). A codominant, multiallelic sequence characterized amplified region (SCAR) marker was developed from a random amplified polymorphic DNA marker identified by bulked-segregant analysis. Additional alleles of the AD13 marker locus proved to be informative for the analysis of genetic relationships within Malus including putative relatives of RS. Separate linkage maps were created for the two families derived from crosses with “Regia”. Using phenotypic data from the greenhouse scab tests, the recombination frequency between Vr1 and AD13-SCAR was between 6 and 17%. The Vr1 locus appeared to be closely linked to the Vx [Hemmat et al. J Am Soc Hortic Sci, 127:365–370, 2002], Vr2 [Patocchi et al. Theor Appl Genet, 109:1087–1092, 2004], and the Vh4 gene [Bus et al. Mol Breed, 15:103–116, 2005a]. Our linkage analysis of the molecular markers identified by Hemmat et al. [J Am Soc Hortic Sci, 127:365–370, 2002] for two scab resistance factors from RS (Vr and Vx) indicate that both genes are separated by a large distance on apple linkage group 2 [Boudichevskaia et al. Acta Hortic, 663:171–175, 2004]. This is in agreement with the results of Bus et al., [Mol Breed, 15:103–116, 2005a] who concluded that (1) the RS-derived gene Vh2 is identical to Vr, (2) the RS-derived gene Vh4 is identical to Vx and Vr1, (3) Vh2/Vr and Vh4/Vr1/Vx map on opposite sides of LG 2. One of our main goals was the verification of the Vr1-SCAR within a practical apple-breeding program. The utility of the AD13-SCAR was evident after 2 years under natural scab infection conditions in both families investigated. This is the first report about the confirmation of a molecular marker for a RS resistance factor in a 2-year field experiment. A multiplex polymerase chain reaction assay based on two codominant SCARs for Vf and Vr1 was tested in an apple progeny segregating for both genes. The result of the two-marker approach is discussed with respect to scab races, which are able to overcome the Vf resistance gene.     

Window automata analysis of population dynamics in the immune system

A formalism based on window automata is proposed as a method to analyse complex population dynamics. The method is applied to a model of the immune network (Weisbuch, G.et al., 1990.J. theor. Biol. 146, 483–499), and used to predict which attractor the system reaches after antigenic stimulation, as a function of the parameters. The attractors of the dynamics are interpreted in terms of immune conditions such as vaccination or tolerance. Scaling laws that define the regimes in the parameter space corresponding to the specific attractor reached under antigenic stimulation are derived.     

Chemotaxis and chemokinesis in eukaryotic cells: The Keller-Segel equations as an approximation to a detailed model

More than 20 years after its proposal, Keller and Segel's model (1971,J. theor. Biol.,30, 235–248) remains by far the most popular model for chemical control of cell movement. However, before the Keller-Segel equations can be applied to a particular system, appropriate functional forms must be specified for the dependence on chemical concentration of the cell transport coefficients and the chemical degradation rate. In the vast majority of applications, these functional forms have been chosen using simple intuitive criteria. We focus on the particular case of eukaryotic cell movement, and derive an approximation to the detailed model of Sherrattet al. (1993,J. theor. Biol.,162, 23–40). The approximation consists of the Keller-Segel equations, with specific forms predicted for the cell transport coefficients and chemical degradation rate. Moreover, the parameter values in these functional forms can be directly measured experimentally. In the case of the much studied neutrophil-peptide system, we test our approximation using both the Boyden chamber and under-agarose assays. Finally, we show that for other cell-chemical interactions, a simple comparison of time scales provides a rapid check on the validity of our Keller-Segel approximation.     

Induction of a non-specific permeability transition in mitochondria from Yarrowia lipolytica and Dipodascus (Endomyces) magnusii yeasts

In this study we used tightly-coupled mitochondria from Yarrowia lipolytica and Dipodascus (Endomyces) magnusii yeasts, possessing a respiratory chain with the usual three points of energy conservation. High-amplitude swelling and collapse of the membrane potential were used as parameters for demonstrating induction of the mitochondrial permeability transition due to opening of a pore (mPTP). Mitochondria from Y. lipolytica, lacking a natural mitochondrial Ca²⁺ uptake pathway, and from D. magnusii, harboring a high-capacitive, regulated mitochondrial Ca²⁺ transport system (Bazhenova et al. J Biol Chem 273:4372–4377, 1998a; Bazhenova et al. Biochim Biophys Acta 1371:96–100, 1998b; Deryabina and Zvyagilskaya Biochemistry (Moscow) 65:1352–1356, 2000; Deryabina et al. J Biol Chem 276:47801–47806, 2001) were very resistant to Ca²⁺ overload. However, exposure of yeast mitochondria to 50–100 μM Ca²⁺ in the presence of the Ca²⁺ ionophore ETH129 induced collapse of the membrane potential, possibly due to activation of the fatty acid-dependent Ca²⁺/nH⁺-antiporter, with no classical mPTP induction. The absence of response in yeast mitochondria was not simply due to structural limitations, since large-amplitude swelling occurred in the presence of alamethicin, a hydrophobic, helical peptide, forming voltage-sensitive ion channels in lipid membranes. Ca²⁺- ETH129-induced activation of the Ca²⁺/H⁺-antiport system was inhibited and prevented by bovine serum albumin, and partially by inorganic phosphate and ATP. We subjected yeast mitochondria to other conditions known to induce the permeability transition in animal mitochondria, i.e., Ca²⁺ overload (in the presence of ETH129) combined with palmitic acid (Mironova et al. J Bioenerg Biomembr 33:319–331, 2001; Sultan and Sokolove Arch Biochem Biophys 386:37–51, 2001), SH-reagents, carboxyatractyloside (an inhibitor of the ADP/ATP translocator), depletion of intramitochondrial adenine nucleotide pools, deenergization of mitochondria, and shifting to acidic pH values in the presence of high phosphate concentrations. None of the above-mentioned substances or conditions induced a mPTP-like pore. It is thus evident that the permeability transition in yeast mitochondria is not coupled with Ca²⁺ uptake and is differently regulated compared to the mPTP of animal mitochondria.     

1H, 13C and 15N NMR assignments of the C1A and C1B subdomains of PKC-delta

The Protein Kinase C family of enzymes is a group of serine/threonine kinases that play central roles in cell-cycle regulation, development and cancer. A key step in the activation of PKC is translocation to membranes and binding of membrane-associated activators including diacylglycerol (DAG). Interaction of novel and conventional isotypes of PKC with DAG and phorbol esters occurs through the two C1 regulatory domains (C1A and C1B), which exhibit distinct ligand binding selectivity that likely controls enzyme activation by different co-activators. PKC has also been implicated in physiological responses to alcohol consumption and it has been proposed that PKCα (Slater et al. J Biol Chem 272(10):6167–6173, 1997; Slater et al. Biochemistry 43(23):7601–7609, 2004), PKCε (Das et al. Biochem J 421(3):405–413, 2009) and PKCδ (Das et al. J Biol Chem 279(36):37964–37972, 2004; Das et al. Protein Sci 15(9):2107–2119, 2006) contain specific alcohol-binding sites in their C1 domains. We are interested in understanding how ethanol affects signal transduction processes through its affects on the structure and function of the C1 domains of PKC. Here we present the ¹H, ¹⁵N and ¹³C NMR chemical shift assignments for the Rattus norvegicus PKCδ C1A and C1B proteins.     

Synchronization of the behaviour within nests of the antLeptothorax acervorum (Fabricius)—II. Modelling the phenomenon and predictions from the model

Observations on activity of ants of the speciesLeptothorax acervorum show that ants within the nest are inactive for about 72% of their time (Frankset al., 1990.Bull. math. Biol.,52, 597–612). By examination of the activity of individual ants it is demonstrated that activity bouts of individuals are highly synchronized. The bursts of activity detected by Frankset al. occurred three to four times per hour. In this paper we develop a model to describe the phenomenon. As a result of the interdependence of the number of active ants within the nest and the high level of community activity some predictions are made, which are supported by experimental data in a quantitative way. In case of starvation the number of active ants will increase and no rhythms should occur. When proportionally more brood is present the rhythms should occur with a higher frequency. Eventually the rhythm breaks down and a stable equilibrium is reached.     

Phytoplankton blooms and fish recruitment rate: Effects of spatial distribution

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.     

Analysis of the role of detergent mixtures on the crystallization of the reaction center of Photosystem II

We have recently reported the crystallization of the reaction center of Photosystem II in the presence of detergent mixtures [Adir N (1999) Acta Crystallogr D Biol Crystallogr D55: 891–894]. We have used high performance liquid chromatography, dynamic light scattering, native gel electrophoresis and thermoluminescence measurements to characterize the interaction between these detergent mixtures and RC II, to try and understand their role in the crystallization process. Size exclusion HPLC and dynamic light scattering confirmed that the isolated RC II used for crystallization was exclusively monomeric. Dynamic light scattering measurements show that the detergent mixtures formed single micelles within a limited range of hydrodynamic radii. Both size exclusion HPLC and dynamic light scattering were used to follow the interaction between the detergent mixtures and monomeric RC II. These techniques revealed a decrease in the detergent mixture treated RC II particle size (with respect with the untreated RC II), and that RC II from solubilized crystals contained particles of the same size. Native gel electrophoresis showed that this change in apparent size is not due to the disintegration of the internal structure of the RC II complex. Thermoluminescence measurements of solubilized RC II crystals showed charge recombination from the S_2,3Q_A ⁻ state, indicating that RC II remains functionally viable following detergent mixture treatment and crystallization. The role of the detergent mixtures in the crystallization of RC II is discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the theory of the cardiovascular system

Most theoretical studies of the circulation have focussed on the transmission line properties of arteries. Only a small number of papers have dealt with the circulation as a closed (lumped) system with two pumps connected by the lesser and greater circulation (Beneken, inCirculatory Analog Computers, No. Holland Publ. Co., Amsterdam, 1963; Defares,et al., inCirculatory Analog Computers, No. Holland Publ. Co., Amsterdam, 1963; Grodins,Quart. Rev. of Biology,34, 93, 1959; Guyton,Cardiac Output and its Regulation, Saunders Publ. Co., New York, 1963). F. W. Cope's recent studies in this journal (Bull. Math. Biophysics,22, 19, 1960;23, 337, 1961;24, 137, 1962) deal with essentially the same questions, although here the circuit is not “closed”. We have attempted to extend the analysis of the areflex (closed) circulation. The complete study is reported elsewhere (Defares,et al., Acta Physiol, et Parmac. Neerl., 1963).     

The heme environment of mouse neuroglobin: histidine imidazole plane orientations obtained from solution NMR and EPR spectroscopy as compared with X-ray crystallography

The ¹H NMR chemical shifts of the heme methyl groups of the ferriheme complex of metneuroglobin (Du et al. in J. Am. Chem. Soc. 125:8080–8081, 2003) predict orientations of the axial histidine ligands (Shokhirev and Walker in J. Biol. Inorg. Chem. 3:581–594, 1998) that are not consistent with the X-ray data (Vallone et al. in Proteins Struct. Funct. Bioinf. 56:85–94, 2004), and the EPR spectrum (Vinck et al. in J. Am. Chem. Soc. 126:4516–4517, 2004) is only marginally consistent with these data. The reasons for these inconsistencies appear to be rooted in the high degree of aqueous solution exposure of the heme group and the fact that there are no strong hydrogen-bond acceptors for the histidine imidazole N–H protons provided by the protein. Similar inconsistencies may exist for other water-soluble heme proteins, and ¹H NMR spectroscopy provides a simple means to verify whether the solution structure of the heme center is the same as or different from that in the crystalline state.     

Evolutionary tradeoff and equilibrium in an aquatic predator-prey system

Due to the conventional distinction between ecological (rapid) and evolutionary (slow) timescales, ecological and population models have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has been recently established and may be critical to understanding how populations persist in changing environments. In this paper we examine the relationship between ecological and evolutionary dynamics, focusing on a well-studied experimental aquatic predator-prey system (Fussmann et al., 2000, Science, 290, 1358–1360; Shertzer et al., 2002, J. Anim. Ecol., 71, 802–815; Yoshida et al., 2003, Nature, 424, 303–306). Major properties of predator-prey cycles in this system are determined by ongoing evolutionary dynamics in the prey population. Under some conditions, however, the populations tend to apparently stable steady-state densities. These are the subject of the present paper. We examine a previously developed model for the system, to determine how evolution shapes properties of the equilibria, in particular the number and identity of coexisting prey genotypes. We then apply these results to explore how evolutionary dynamics can shape the responses of the system to ‘management’: externally imposed alterations in conditions. Specifically, we compare the behavior of the system including evolutionary dynamics, with predictions that would be made if the potential for rapid evolutionary change is neglected. Finally, we posit some simple experiments to verify our prediction that evolution can have significant qualitative effects on observed population-level responses to changing conditions.     

On the number of balanced signed graphs

The classical enumeration theorem of Pólya (Acta Math.,68, 145–254, 1937) is applied to a modified version of Harary’s (Pacific J. Math.,8, 743–755, 1958) generating functions for counting bicolored graphs to derive a counting function for the number of balanced signed graphs. Methods for computing these counting polynomial functions are discussed.