Network Development in Biological Gels: Role in Lymphatic Vessel Development

In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801–808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the Cahn–Hilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model. This work was supported by the Royal Society (London) by the award of a University Research Fellowship.     

Stable periodicity and negative circuits in differential systems

We provide a counter-example to a conjecture of René Thomas on the relationship between negative feedback circuits and stable periodicity in ordinary differential equation systems (Kaufman et al. in J Theor Biol 248:675–685, 2007). We also prove a weak version of this conjecture by using a theorem of Snoussi.     

Why Are Some Evolutionary Trees in Natural History Museums Prone to Being Misinterpreted?

Today, the picture of an evolutionary tree is a very well-known visual image. It is almost impossible to think of the ancestry and relationships of living beings without it. As natural history museums play a major role in the public understanding of evolution, they often present a wide variety of evolutionary trees. However, many studies have shown (Baum and Offner 2008; Baum et al. 2005; Catley and Novick 2008; Evans 2009; Gregory 2008; Matuk 2007; Meir et al. 2007b; Padian 2008) that even though evolutionary trees have the potential to engage visitors of natural history museums with the phenomena of evolution, many of them unwittingly might lead to misunderstandings about the process. As valuable research and educational institutions, one of the museum’s important missions should be the careful design of their exhibits on evolution considering, for example, common preconceptions visitors often bring, such as the notion that evolution is oriented from simple toward complex organisms (incarnating the idea of a single ladder of life amidst the extraordinary diversity of organisms) and that humans are at the pinnacle of the evolutionary story, as well as na?ve interpretations of phylogenies. Our aim in this article is to show from history where many of these misunderstandings come from and to determine whether five important Western natural history museums inadvertently present “problematic” evolutionary trees (which might lead to non-scientific notions).     

A PDE Model for Imatinib-Treated Chronic Myelogenous Leukemia

We derive a model for describing the dynamics of imatinib-treated chronic myelogenous leukemia (CML). This model is a continuous extension of the agent-based CML model of Roeder et al. (Nat. Med. 12(10), 1181–1184, 2006) and of its recent formulation as a system of difference equations (Kim et al. in Bull. Math. Biol. 70(3), 728–744, 2008). The new model is formulated as a system of partial differential equations that describe various stages of differentiation and maturation of normal hematopoietic cells and of leukemic cells. An imatinib treatment is also incorporated into the model. The simulations of the new PDE model are shown to qualitatively agree with the results that were obtained with the discrete-time (difference equation and agent-based) models. At the same time, for a quantitative agreement, it is necessary to adjust the values of certain parameters, such as the rates of imatinib-induced inhibition and degradation.     

Bioactive peptide design using the Resonant Recognition Model

With a large number of DNA and protein sequences already known, the crucial question is to find out how the biological function of these macromolecules is "written" in the sequence of nucleotides or amino acids. Biological processes in any living organism are based on selective interactions between particular bio-molecules, mostly proteins. The rules governing the coding of a protein's biological function, i.e. its ability to selectively interact with other molecules, are still not elucidated. In addition, with the rapid accumulation of databases of protein primary structures, there is an urgent need for theoretical approaches that are capable of analysing protein structure-function relationships. The Resonant Recognition Model (RRM) [1, 2] is one attempt to identify the selectivity of protein interactions within the amino acid sequence. The RRM [1, 2] is a physico-mathematical approach that interprets protein sequence linear information using digital signal processing methods. In the RRM the protein primary structure is represented as a numerical series by assigning to each amino acid in the sequence a physical parameter value relevant to the protein's biological activity. The RRM concept is based on the finding that there is a significant correlation between spectra of the numerical presentation of amino acids and their biological activity. Once the characteristic frequency for a particular protein function/interaction is identified, it is possible then to utilize the RRM approach to predict the amino acids in the protein sequence, which predominantly contribute to this frequency and thus, to the observed function, as well as to design de novo peptides having the desired periodicities. As was shown in our previous studies of fibroblast growth factor (FGF) peptidic antagonists [2, 3] and human immunodeficiency virus (HIV) envelope agonists [2, 4], such de novo designed peptides express desired biological function. This study utilises the RRM computational approach to the analysis of oncogene and proto-oncogene proteins. The results obtained have shown that the RRM is capable of identifying the differences between the oncogenic and proto-oncogenic proteins with the possibility of identifying the "cancer-causing" features within their protein primary structure. In addition, the rational design of bioactive peptide analogues displaying oncogenic or proto-oncogenic-like activity is presented here.     

Low expression of Neu2 sialidase in the thymus of SM/J mice—existence of neuraminidase positive cells “Neu-medullocyte” in the murine thymus

We have already reported that the homogenate of the A/J mouse thymus shows a high sialidase activity at the neutral pH region and that in both soluble and membrane fractions optimal pH was 6.5–7 (Kijimoto-Ochiai et al., Glycoconj. J., 20:375–384, 2004). In the present study, we investigated the level of sialidase activities in the thymus of the SM/J mouse, a mouse strain that we know to have a Neu1^a allele that reveals a low level of sialidase activity in the liver. We found that while in the A/J thymus the soluble sialidase activity at pH 6.5 was high, the SM/J thymus lacked all such activity. A QTL analysis of SMXA recombinant inbred strains showed that soluble sialidase activity correlated well with the D1Mit8/9 marker on chromosome 1. The murine whole DNA-sequence data and the results of our FISH analysis (Kotani et al., Biochem. Biophys. Res. Comm., 286:250–258, 2001) showed that this location is consistent with the position of Neu2 gene. We confirmed that it is hard to detect the Neu2 enzyme of the SM/J mouse thymus by an anti-Neu2 antibody using a Western blot analysis. We also found that while the mRNA expression of Neu2 was quite normal in the SM/J mouse liver, it was very low in the SM/J mouse thymus. We therefore conclude that the lack of soluble sialidase activity in the SM/J mouse thymus is due to the thymus-specific low expression level of the Neu2 gene. We have previously shown that the sialidase positive cell which contains the Mac-1 and immunoglobulin, and which is located sparsely in the corticomedullar region or medullary region of the A/J mouse thymus (Kijimoto-Ochiai et al., Glycoconj. J., 20:375–384, 2004). We showed now in this paper that the detection of this cell in the SM/J mouse thymus at pH 7.0 was difficult. We propose, therefore, to name the cell “Neu-medullocyte”.     

Modeling the effects of a Staphylococcal Enterotoxin B (SEB) on the apoptosis pathway

Background  

The lack of detailed understanding of the mechanism of action of many biowarfare agents poses an immediate challenge to biodefense efforts. Many potential bioweapons have been shown to affect the cellular pathways controlling apoptosis [1–4]. For example, pathogen-produced exotoxins such as Staphylococcal Enterotoxin B (SEB) and Anthrax Lethal Factor (LF) have been shown to disrupt the Fas-mediated apoptotic pathway [2, 4]. To evaluate how these agents affect these pathways it is first necessary to understand the dynamics of a normally functioning apoptosis network. This can then serve as a baseline against which a pathogen perturbed system can be compared. Such comparisons can expose both the proteins most susceptible to alteration by the agent as well as the most critical reaction rates to better instill control on a biological network.     

Constraining prior probabilities of phylogenetic trees

Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means of the Principal Principle. In particular, I discuss a proposal due to Velasco (Biol Philos 23:455–473, 2008) of assigning prior probabilities to tree topologies based on the Yule process. By invoking the Principal Principle I argue that prior probabilities of tree topologies should rather be assigned a weighted mixture of probability distributions based on Pinelis’ (P Roy Soc Lond B Bio 270:1425–1431, 2003) multi-rate branching process including both the Yule distribution and the uniform distribution. However, I argue that this solves the problem of the priors of phylogenetic trees only in a weak form.     

A history of research on arbuscular mycorrhiza

This is not a review paper in the traditional sense, of which there are many. Three of the most influential reviews that summarized well some of the older literature include those by Nicolson (1967), Gerdemann (1968) and Mosse (1973). Instead, in this brief and incomplete work, we attempt to show the historical development of research on arbuscular mycorrhizas. We owe much to those who have written other historical accounts, including Rayner (1926–1927), Trappe and Berch (1985), Mosse (1985), Schenck (1985), Harley (1991) and Allen (1996), but the contents of this work naturally reflect our own ignorance, interests and biases. It was often difficult to distinguish between the historical and the contemporary, and we did not use any specific cutoff date in making this distinction. The degree to which we include contemporary literature was determined by our own assessment of its connectedness to older literature. In any case, we hope this will be of some interest to those of you who study the arbuscular mycorrhiza, and that it will serve the purpose of providing what we consider to be an important historical context for current researchers. We wish you good fortune in your research.Taken from a paper presented at the COST 8.38 meeting AM Research in Europe (Pisa, Italy): The Dawning of a New Millenium     

Periodic orbits near heteroclinic cycles in a cyclic replicator system

A species is semelparous if every individual reproduces only once in its life and dies immediately after the reproduction. While the reproduction opportunity is unique per year and the individual’s period from birth to reproduction is just n years, the individuals that reproduce in the ith year (modulo n) are called the ith year class, i = 1, 2, . . . , n. The dynamics of the n year-class system can be described by a differential equation system of Lotka–Volterra type. For the case n = 4, there is a heteroclinic cycle on the boundary as shown in previous works. In this paper, we focus on the case n = 4 and show the existence, growth and disappearance of periodic orbits near the heteroclinic cycle, which is a part of the conjecture by Diekmann and van Gils (SIAM J Appl Dyn Syst 8:1160–1189, 2009). By analyzing the Poincaré map near the heteroclinic cycle and introducing a metric to measure the size of the periodic orbit, we show that (i) when the average competitive degree among subpopulations (year classes) in the system is weak, there exists an asymptotically stable periodic orbit near the heteroclinic cycle which is repelling; (ii) the periodic orbit grows in size when some competitive degree increases, and converges to the heteroclinic cycle when the average competitive degree tends to be strong; (iii) when the average competitive degree is strong, there is no periodic orbit near the heteroclinic cycle which becomes asymptotically stable. Our results provide explanations why periodic solutions expand and disappear and why all but one subpopulation go extinct.     

Multilevel selection: the evolution of cooperation in non-kin groups

Hamiltons (1964a, 1964b) landmark papers are rightly recognized as the formal basis for our understanding of the evolution of altruistic traits. However, Hamiltons equation as he originally expressed it is simplistic. A genetically oriented approach to studying multilevel selection can provide insights into how the terminology and assumptions used by Hamilton can be generalized. Using contextual analysis I demonstrated that Hamiltons rule actually embodies three distinct processes, group selection, individual selection, and transmission genetics or heritability. Whether an altruistic trait will evolve depends the balance of all of these factors. The genetical approach, and particularly, contextual analysis provides a means of separating these factors and examining them one at a time. Perhaps the greatest issue with Hamiltons equation is the interpretation of r. Hamilton (1964a) interpreted this as relatedness. In this paper I show that what Hamilton called relatedness is more generally interpreted as the proportion for variance among groups, and that many processes in addition to relatedness can increase the variance among groups. I also show that the evolution of an altruistic trait is driven by the ratio of the heritability at the group level to the heritability at the individual level. Under some circumstances this ratio can be greater than 1. In this situation altruism can evolve even if selection favoring selfish behavior is stronger than selection favoring altruism.     

Stability Analysis of a Simplified Yet Complete Model for Chronic Myelogenous Leukemia

We analyze the asymptotic behavior of a partial differential equation (PDE) model for hematopoiesis. This PDE model is derived from the original agent-based model formulated by Roeder (Nat. Med. 12(10):1181–1184, 2006), and it describes the progression of blood cell development from the stem cell to the terminally differentiated state.     

Allee threshold and extinction threshold for spatially explicit metapopulation dynamics with Allee effects

In this paper, we investigate a spatially explicit metapopulation model with Allee effects. We refer to the patch occupancy model introduced by Levins (Bull Entomol Soc Am 15:237–240, 1969) as a spatially implicit metapopulation model, i.e., each local patch is either occupied or vacant and a vacant patch can be recolonized by a randomly chosen occupied patch from anywhere in the metapopulation. When we transform the model into a spatially explicit one by using a lattice model, the obtained model becomes theoretically equivalent to a “lattice logistic model” or a “basic contact process”. One of the most popular or standard metapopulation models with Allee effects, developed by Amarasekare (Am Nat 152:298–302, 1998), supposes that those effects are introduced formally by means of a logistic equation. However, it is easier to understand the ecological meaning of associating Allee effects with this model if we suppose that only the logistic colonization term directly suffers from Allee effects. The resulting model is also well defined, and therefore we can naturally examine it by Monte Carlo simulation and by doublet and triplet decoupling approximation. We then obtain the following specific features of one-dimensional lattice space: (1) the metapopulation as a whole does not have an Allee threshold for initial population size even when each local population follows the Allee effects; and (2) a metapopulation goes extinct when the extinction rate of a local population is lower than that in the spatially implicit model. The real ecological metapopulation lies between two extremes: completely mixing interactions between patches on the one hand and, on the other, nearest neighboring interactions with only two nearest neighbors. Thus, it is important to identify the metapopulation structure when we consider the problems of invasion species such as establishment or the speed of expansion.     

The beaver (Mammalia,Castoridae) from the Miocene of Sandelzhausen (southern Germany)

The Early/Middle Miocene boundary locality Sandelzhausen (MN5, southern Germany) yielded three beaver teeth: one lower incisor fragment and two strongly worn upper premolars, a right and a left one. The latter are so similar in wear, height, size, and enamel pattern that they probably represent one individual. Although the teeth have been referred to Chalicomys jaegeri Kaup, 1832 (e.g., Hugueney 1999, Fahlbusch 2003), it seems more likely that they belong to Steneofiber depereti Mayet, 1908. However, the assignment of the present material to either one of these species is difficult, because in the advanced wear stage some diagnostic characteristics cannot be assessed. As to ecological implications for the locality Sandelzhausen the taxonomic identity of these two beaver species may not be important. Both are known from riverine, lacustrine or swamp sediments, and it can be assumed that they usually lived in close vicinity to water. Thus, the presence of beaver remains supports the presence of water at Sandelzhausen. However, the teeth might have an allochthonous origin from creeks of the rising Alps.      

The Miocene <Emphasis Type="Italic">Keramidomys</Emphasis> (Rodentia,Eomyidae) from the Sandelzhausen locality (Germany)

In this note the taxonomic position of the tiny eomyid genus Keramidomys (Hartenberger, 1967) from the Early/Middle Miocene boundary locality of Sandelzhausen in the Bavarian Upper Freshwater Molasse is reexamined. As the chronological dating of the Sandelzhausen fossil site has been modified in the past from formerly the Neogene mammal unit MN6 to now MN5 and thanks to new abundant material this rodent is compared with other European forms. It is shown that the Sandelzhausen eomyid must be called K. thaleri Hugueney & Mein, 1968 on the basis of several morphological dental differences from K. carpathicus Schaub & Zapfe, 1953. This rodent seems to be an immigrant from East Asia into Europe. Even if K. thaleri is known in many European localities, all correlated to MN5, it is always a rare element of European rodent faunas. Differentiation from K. carpathicus is not easy and requires a sufficiently large sample.      

Spatial clustering property and its self-similarity in membrane potentials of hippocampal CA1 pyramidal neurons for a spatio-temporal input sequence

To clarify how the information of spatiotemporal sequence of the hippocampal CA3 affects the postsynaptic membrane potentials of single pyramidal cells in the hippocampal CA1, the spatio-temporal stimuli was delivered to Schaffer collaterals of the CA3 through a pair of electrodes and the post-synaptic membrane potentials were recorded using the patch-clamp recording method. The input–output relations were sequentially analyzed by applying two measures; “spatial clustering” and its “self-similarity” index. The membrane potentials were hierarchically clustered in a self-similar manner to the input sequences. The property was significantly observed at two and three time-history steps. In addition, the properties were maintained under two different stimulus conditions, weak and strong current stimulation. The experimental results are discussed in relation to theoretical results of Cantor coding, reported by Tsuda (Behav Brain Sci 24(5):793–847, 2001) and Tsuda and Kuroda (Jpn J Indust Appl Math 18:249–258, 2001; Cortical dynamics, pp 129–139, Springer-Verlag, 2004).     

Dynamic formation of oriented patches in chondrocyte cell cultures

Growth factors have a significant impact not only on the growth dynamics but also on the phenotype of chondrocytes (Barbero et al. in J. Cell. Phys. 204:830–838, 2005). In particular, as chondrocytes approach confluence, the cells tend to align and form coherent patches. Starting from a mathematical model for fibroblast populations at equilibrium (Mogilner et al. in Physica D 89:346–367, 1996), a dynamic continuum model with logistic growth is developed. Both linear stability analysis and numerical solutions of the time-dependent nonlinear integro-partial differential equation are used to identify the key parameters that lead to pattern formation in the model. The numerical results are compared quantitatively to experimental data by extracting statistical information on orientation, density and patch size through Gabor filters.     

Aorta in vivo parameter identification using an axial force constraint

It was shown in a previous study by Stålhand et al. (2004) that both material and residual strain parameters for an artery can be identified noninvasively from an in vivo clinical pressure–diameter measurement. The only constraints placed on the model parameters in this previous study was a set of simple box constraints. More advanced constraints can also be utilized, however. These constraints restrict the model parameters implicitly by demanding the state of the artery to behave in a specified way. It has been observed in vitro that the axial force is nearly invariant to the pressure at the physiological operation point. In this paper, we study the possibility to include this behaviour as a constraint in the parameter optimization. The method is tested on an in vivo obtained pressure–diameter cycle for a 24-year-old human. Presented results show that the constrained parameter identification procedure proposed here can be used to obtain good results, and we believe that it may be applied to account for other observed behaviours as well.     

A role for anions in ATP synthesis and its molecular mechanistic interpretation

ATP, the ‘universal biological energy currency’, is synthesized by utilizing energy either from oxidation of fuels or from light, via the process of oxidative and photo-phosphorylation respectively. The process is mediated by the enzyme F₁F₀-ATP synthase, using the free energy of ion gradients in the final energy catalyzing step, i.e., the synthesis of ATP from ADP and inorganic phosphate (P_i). The details of the molecular mechanism of ATP synthesis are among the most important fundamental issues in biology and hence need to be properly understood. In this work, a role for anions in making ATP has been found. New experimental data has been reported on the inhibition of ATP synthesis at nanomolar concentrations by the potent, specific anion channel blockers 4,4′-diisothiocyanostilbene-2, 2′-disulphonic acid (DIDS) and tributyltin chloride (TBTCl). Based on these inhibition studies, attention has been drawn to anion translocation (in addition to proton translocation) as a requirement for ATP synthesis. The type of inhibition has been quantified and an overall kinetic scheme for mixed inhibition that explains the data has been evolved. The experimental data and the type of inhibition found have been interpreted in the light of the torsional mechanism of energy transduction and ATP synthesis (Nath J Bioenerg Biomembr 42:293–300, 2010a; J Bioenerg Biomembr 42:301–309, 2010b). This detailed and unified mechanism resolves long-standing problems and inconsistencies in the first theories (Slater Nature 172:975–978, 1953; Williams J Theor Biol 1:1–17, 1961; Mitchell Nature 191:144–148, 1961; Mitchell Biol Rev 41:445–502, 1966), makes several novel predictions that are experimentally verifiable (Nath Biophys J 90:8–21, 2006a; Process Biochem 41:2218–2235, 2006b), and provides us with a new and fruitful paradigm in bioenergetics. The interpretation presented here provides intelligent answers to the unexplained existing results in the literature. It is shown that mechanistic interpretation of the experimental data requires substantial addition to available conceptual foundations such that present concepts, theories, and mechanisms must be revised.