One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death II: transition state metastability

This is the second of two papers in which we study a mathematical model of cytoskeleton-induced neuron death. Recent evidence indicates that aggravated assembly or destruction of the cytoskeleton can trigger programmed death in neurons, by mechanisms as yet poorly understood. In our model, assembly control of the neuronal cytoskeleton interacts with both cellular stress levels and cytosolic free radical concentrations to trigger neurodegeneration. This trigger mechanism is further modulated by a diffusible toxic factor released from dying neurons. In the companion report we established that the model relates the observed general patterns of neuron decline to specific scales of cytoskeleton reorganization and cell-cell interaction strength. In this paper we study the transit of neurons through states intermediate between initial viability and cell death in our model. We find that the stochastic flow of neuron fate, from viability to cell death, self-organizes into two distinct temporal phases. There is a rapid relaxation of the initial neuron population to a more disordered phase that is long-lived, or metastable, with respect to the time scales of change in single cells. Strikingly, cellular egress from this metastable phase follows the one-hit kinetic pattern of exponential decline now established as a principal hallmark of cell death in neurodegenerative disorders. Intermediate state metastability may therefore be an important element in the systems biology of one-hit neurodegeneration.     

Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE)

One goal of this paper is to give an algorithm for computing a threshold condition for epidemiological systems arising from compartmental deterministic modeling. We calculate a threshold condition T(0) of the parameters of the system such that if T(0)<1 the disease-free equilibrium (DFE) is locally asymptotically stable (LAS), and if T(0)>1, the DFE is unstable. The second objective, by adding some reasonable assumptions, is to give, depending on the model, necessary and sufficient conditions for global asymptotic stability (GAS) of the DFE. In many cases, we can prove that a necessary and sufficient condition for the global asymptotic stability of the DFE is R(0)< or =1, where R(0) is the basic reproduction number [O. Diekmann, J.A. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York, 2000]. To illustrate our results, we apply our techniques to examples taken from the literature. In these examples we improve the results already obtained for the GAS of the DFE. We show that our algorithm is relevant for high dimensional epidemiological models.     

The shared reward dilemma

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma, namely the prisoner's dilemma (PD). Specifically, for a group of players that collect payoffs by playing a pairwise PD game with their partners, we consider an external entity that distributes a fixed reward equally among all cooperators. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared a vast variety of scenarios arises, including the traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the n-player game as well as of its evolutionary dynamics.     

Perturbation avalanches and criticality in gene regulatory networks

Boolean networks are simplified models of gene regulatory networks. We derive an approximation of the size distribution of perturbation avalanches in Boolean networks based on known results in the theory of branching processes. We show numerically that the approximation works well for different kinds of Boolean networks. It has been suggested that gene regulatory networks may be dynamically critical. To study this, as an application of the presented theory we present a novel method for estimating an order parameter from microarray data. According to the available data and our method, we find that gene regulatory networks appear to be stable and reside near the phase transition between order and chaos.     

Changes of enzyme activity in lipid signaling pathways related to substrate reordering

The static fluid mosaic model of biological membranes has been progressively complemented by a dynamic membrane model that includes phospholipid reordering in domains that are proposed to extend from nanometers to microns. Kinetic models for lipolytic enzymes have only been developed for homogeneous lipid phases. In this work, we develop a generalization of the well-known surface dilution kinetic theory to cases where, in a same lipid phase, both domain and nondomain phases coexist. Our model also allows understanding the changes in enzymatic activity due to a decrease of free substrate concentration when domains are induced by peptides. This lipid reordering and domain dynamics can affect the activity of lipolytic enzymes, and can provide a simple explanation for how basic peptides, with a strong direct interaction with acidic phospholipids (such as beta-amyloid peptide), may cause a complex modulation of the activities of many important enzymes in lipid signaling pathways.     

Three-person game facilitates indirect reciprocity under image scoring

Reputation building plays an important role in the evolution of reciprocal altruism when the same individuals do not interact repeatedly because, by referring to reputation, a reciprocator can know which partners are cooperative and can reciprocate with a cooperator. This reciprocity based on reputation is called indirect reciprocity. Previous studies of indirect reciprocity have focused only on two-person games in which only two individuals participate in a single interaction, and have claimed that indirectly reciprocal cooperation cannot be established under image scoring reputation criterion where the reputation of an individual who has cooperated (defected) becomes good (bad). In this study, we specifically examine three-person games, and reveal that indirectly reciprocal cooperation can be formed and maintained stably, even under image scoring, by a nucleus shield mechanism. In the nucleus shield, reciprocators are a shield that keeps out unconditional defectors, whereas unconditional cooperators are the backbone of cooperation that retains a good reputation among the population.     

The evolution of n-player cooperation-threshold games and ESS bifurcations

An evolutionary game of individuals cooperating to obtain a collective benefit is here modelled as an n-player Prisoner's Dilemma game. With reference to biological situations, such as group foraging, we introduce a threshold condition in the number of cooperators required to obtain the collective benefit. In the simplest version, a three-player game, complex behaviour appears as the replicator dynamics exhibits a catastrophic event separating a parameter region allowing for coexistence of cooperators and defectors and a region of pure defection. Cooperation emerges through an ESS bifurcation, and cooperators only thrive beyond a critical point in cost-benefit space. Moreover, a repelling fixed point of the dynamics acts as a barrier to the introduction of cooperation in defecting populations. The results illustrate the qualitative difference between two-player games and multiple player games and thus the limitations to the generality of conclusions from two-player games. We present a procedure to find the evolutionarily stable strategies in any n-player game with cost and benefit depending on the number of cooperators. This was previously done by Motro [1991. Co-operation and defection: playing the field and the ESS. J. Theor. Biol. 151, 145-154] in the special cases of convex and concave benefit functions and constant cost.     

Metabolism of [6,7-3H, 35S] estradiol 17-sulfate in rats

To confirm whether or not the sulfo group of estradiol 17-sulfate (ES) is removed during in vivo metabolism in rats, the doubly labeled conjugate [6,7-3H, 35S] ES was injected into rats, and its biliary and urinary metabolites were determined by reverse isotope dilution method (RIDM). In male rats, the major radioactivity was detected in biliary disulfate fraction, which was composed of mainly ES and its two minor metabolites, 2-hydroxyestradiol 17-sulfate (2-OH-ES) and 2-methoxyestradiol 17-sulfate (2-MeO-ES). In female rats, in contrast, the radioactivity was dispersed into three fractions:biliary monosulfate, biliary disulfate, and urinary monosulfate fractions (Frs.) In both monosulfate Frs., 7beta-hydroxyestradiol 17-sulfate was detected as the major metabolite followed by 6alpha-, 6beta-, and 15beta-hydroxyestradiol 17-sulfates. Like male rats, 2-OH-ES and 2-Meo-ES as the minor products were detected in biliary disulfate fraction. The isotope ratios of ES and its metabolites in both sexes were essentially the same as that of the dose except that of 6alpha-hydroxylated metabolite, which may be derived from the loss of the tritium labeled at C6. These results confirm the occurrence of the direct metabolism of ES in rats.     

Extent of over-expression of hepatocyte growth factor receptor in colorectal tumours is dependent on the choice of normaliser

For reliable results from quantitative RT-PCR, the starting quantity of total RNA and other parameters need to be controlled. Most studies do this by normalising their results to a single reference gene. This study quantified the mRNA expression of three putative reference genes (ubiquitin C, cyclophilin E, and porphobilinogen deaminase) and the target gene hepatocyte growth factor receptor (HGFR) in matched colorectal tumour and normal mucosa samples. Each of the putative reference genes was found to be significantly over-expressed in the tumour samples compared to the normal samples. When HGFR expression was normalised to each of these reference genes using the 2 (-DeltaDeltaC(T)) method of relative quantification, the number of tumour samples in which HGFR was found to be over-expressed varied from 30% to 63% depending on the reference gene chosen for normalisation. This shows that normalising to a single reference gene without prior validation is inappropriate.     

A divergent synthesis of [1-14C]-mono-E isomers of fatty acids

A convenient synthesis of [1-14C]-mono-trans fatty acid using olefin inversion as a key-step is described. This methodology allows for a facile synthesis of [1-14C]-labelled mono-trans analogues of oleic, linoleic and linolenic acids. As an example, only eleven steps were necessary to obtain the [1-14C]-mono-E isomers of linolenic acid from its commercial all-Z form. In the first step, Barton's decarboxylation procedure yielded a bromo intermediate. Epoxidation of this compound resulted in the formation of three monoepoxides, which could be separated by HPLC. After identification by 1H NMR and MS, the pure monoepoxides were then subjected to inversion consisting of a stereospecific deoxygenation followed by a beta-elimination step. Finally, the labelling was introduced by substitution of the bromine by a [14C]-cyano group followed by hydrolysis.     

Transmission dynamics of Toxoplasma gondii along an urban-rural gradient

Recently, several authors have proposed that the availability of intermediate hosts (IHs) for definitive hosts (DHs) may contribute to determining the dynamics and evolutionary ecology of parasites with facultative complex life cycles. The protozoa Toxoplasma gondii may be transmitted to DHs either via predation of infected IHs through a complex life cycle (CLC) or directly from a contaminated environment through a simple life cycle (SLC). This parasite is also present in contrasting host density environments. We tested the hypothesis that the relative contributions of the CLC and SLC along an urban-rural gradient depend on the IH supply. We built and analysed a deterministic model of the T. gondii transmission cycle. The SLC relative contribution is important only in urban-type environments, i.e., with low predation rate on IHs. In contrast, the parasite is predominantly transmitted through a CLC in suburban and rural environments. The association of the two cycles enables the parasite to spread in situations of low IH availability and low DH population size for which each cycle alone is insufficient.     

Self-organization at the origin of life

The concept of an (M,R) system with organizational invariance allows one to understand how a system may be able to maintain itself indefinitely if it is coupled to an external source of energy and materials. However, although this constitutes an important step towards understanding the difference between a living and a non-living system, it is not clear that an (M,R) system with organizational invariance is sufficient to define a living system. To take a further step towards defining what it means to be alive it is necessary to add to a simple (M,R) system some property that represents its identity, and which can be maintained and modified in subsequent generations.     

The role of low avidity T cells in the protection against type 1 diabetes: a modeling investigation

Cytotoxic T lymphocytes (CTLs) play a dominant role in the pathogenesis of autoimmune diabetes, commonly denoted Type 1 Diabetes (T1D). These CTLs (notably CD8⁺ T cells) recognize and kill insulin-secreting pancreatic β cells, reducing their number by ∼90%. The resulting reduction of insulin secretion causes the defective regulation of glucose metabolism, leading to the characteristic symptoms of diabetes. Recognition of β cells as targets by CTLs depends on the interactions between MHC-peptide complexes on the surface of β cells and receptors (TCRs) on T cells. Those CTLs with high affinity TCRs (also called high avidity T cells) cause most of the harm, while those with low affinity TCRs (also called low avidity T cells) play a more mysterious role. Recent experimental evidence suggests that low avidity T cells accumulate as memory T cells during the disease and may be protective in NOD mice (a strain prone to developing T1D), delaying disease progression. It has been hypothesized that such low avidity T cells afford disease protection either by crowding the islets of Langerhans, where β cells reside, or by killing antigen presenting cells (APCs).In this paper, we explore the hypothesized mechanisms for this protective effect in the context of a series of models for (1) the interactions of low and high avidity T cells, (2) the effect of APCs and (3) the feedback from β cell killing to autoantigen-induced T cell proliferation. We analyze properties of these models, noting consistency of predictions with observed behaviour. We then use the models to examine the influence of various treatment strategies on the progression of the disease. The model reveals that progressive accumulation of memory low avidity autoreactive T cells during disease progression makes treatments aimed at expanding these protective T cell types more effective close to, or at the onset of clinical disease. It also provides evidence for the hypothesis that low avidity T cells kill APCs (rather than the alternate hypothesis that they crowd the islets).     

Modeling species-specific diacylglycerol dynamics in the RAW 264.7 macrophage

A mathematical model of the G protein signaling pathway in RAW 264.7 macrophages downstream of P2Y₆ receptors activated by the ubiquitous signaling nucleotide uridine 5’-diphosphate is developed. The model, which is based on time-course measurements of inositol trisphosphate, cytosolic calcium, and diacylglycerol, focuses particularly on differential dynamics of multiple chemical species of diacylglycerol. When using the canonical pathway representation, the model predicted that key interactions were missing from the current network structure. Indeed, the model suggested that accurate depiction of experimental observations required an additional branch to the signaling pathway. An intracellular pool of diacylglycerol is immediately phosphorylated upon stimulation of an extracellular receptor for uridine 5’-diphosphate and subsequently used to aid replenishment of phosphatidylinositol. As a result of sensitivity analysis of the model parameters, key predictions can be made regarding which of these parameters are the most sensitive to perturbations and are therefore most responsible for output uncertainty.     

Alternative NMR method for quantitative determination of acyl positional distribution in triacylglycerols and related compounds

High-resolution 13C NMR spectroscopy has been used to analyze the positional distribution of fatty acids in model triacylglycerols. A novel method for quantitative determination of the positional distribution of unsaturated chains in triacylglycerols simultaneously with the ratio of saturated/unsaturated acyl chains has been proposed, utilizing the chemical shift differences of the aliphatic atoms C4, C5, and C6. The use of HSQC-TOCSY spectra allows unequivocal proof of the position of the unsaturated chain as well as complete assignment of the 13C NMR signals in tripalmitin.     

Free radical oxidation (autoxidation) of alkenones and other lipids in cells of Emiliania huxleyi

Cells of the coccolithophorid Emiliania huxleyi strain CS-57 grown under an atmosphere of air+0.5% CO(2) showed oxidative damage after 10 days growth with concomitant and major changes to the lipid composition. The fatty acid profile was strongly altered and lacked appreciable amounts of the polyunsaturated fatty acids (PUFA: C(18:5), C(18:3) and C(22:6)) typical of healthy cells. Oxidation products of these PUFA could not be detected, but monounsaturated fatty acids proved to be good indicators of oxidative processes. The presence (after NaBH(4)-reduction) of a high proportion of 11-hydroxyoctadec-cis-9-enoic and 8-hydroxyoctadec-cis-9-enoic acids showed that the degradation of oleic acid involved mainly free radical oxidation processes (70-75% autoxidation and 20-25% photooxidation). We also detected large amounts of degradation products of the oxidation product 9,10-epoxyoctadecanoic acid including diols, methoxyhydrins and chlorohydrins. These oxidative effects were found in all the lipid classes examined. Products included significant amounts of chlorophyll side-chain autooxidation products Z- and E-3,7,11,15-tetramethylhexadec-3-ene-1,2-diols and Z-and E-3,7,11,15-tetramethylhexadec-2-ene-1,4-diols, while phytyldiol was present in relatively low proportions. Delta(5)-3beta,7-epimeric unsaturated steroidal diols arising from the autooxidation of the Delta(5) double bond of epi-brassicasterol and minor amounts of Delta(4)-3beta,6-diols were also detected. Long-chain unsaturated ketone (alkenone) content per cell was much higher in the presence of 0.5% CO(2) likely due to carbon storage under these conditions. The proportions of di- and tri-unsaturated alkenones was relatively stable throughout the growth cycle in the absence of additional CO(2), but not when grown with 0.5% CO(2). The detection of characteristic alkenone autoxidation products in cells grown under these latter conditions allowed us to attribute the significant increase in index observed to the involvement of free radical oxidation processes.     

Conformation-driven and semiquinone-gated proton-pump mechanism in the NADH-ubiquinone oxidoreductase (complex I)

A novel mechanism for proton/electron transfer is proposed for NADH-quinone oxidoreductase (complex I) based on the following findings: (1) EPR signals of the protein-bound fast-relaxing semiquinone anion radicals (abbreviated as Q(Nf)-) are observable only in the presence of proton-transmembrane electrochemical potential; (2) Iron-sulfur cluster N2 and Q(Nf)- are directly spin-coupled; and (3) The projection of the interspin vector extends only 5A along the membrane normal [Yano, T., Dunham, W.R. and Ohnishi, T. (2005) Biochemistry, 44, 1744-1754]. We propose that the proton pump is operated by redox-driven conformational changes of the quinone binding protein. In the input state, semiquinone is reduced to quinol, acquiring two protons from the N (matrix) side of the mitochondrial inner membrane and an electron from the low potential (NADH) side of the respiratory chain. A conformational change brings the protons into position for release at the P (inter-membrane space) side of the membrane via a proton-well. Concomitantly, an electron is donated to the quinone pool at the high potential side of the coupling site. The system then returns to the original state to repeat the cycle. This hypothesis provides a useful frame work for further investigation of the mechanism of proton translocation in complex I.     

Characterization of two types of osteoclasts from human peripheral blood monocytes

The two osteoclastogenesis pathways, receptor activator nuclear factor (NF)-kappaB ligand (RANKL)-mediated and fusion regulatory protein-1 (FRP-1)-mediated osteoclastogenesis, have recently been reported. There were significant differences in differentiation and activation mechanisms between the two pathways. When monocytes were cultured with FRP-1 without adding M-CSF, essential for the RANKL system, TRAP-positive polykaryocyte formation occurred. FRP-1-mediated osteoclasts formed larger pits on mineralized calcium phosphate plates than RANKL+M-CSF-mediated osteoclasts did. Lacunae on dentin surfaces induced by FRP-1-mediated osteoclasts were inclined to be single and isolated. However, osteoclasts induced by RANKL+M-CSF made many connected pits on dentin surfaces as if they crawled on there. Interestingly, FRP-1 osteoclastogenesis was enhanced by M-CSF/IL-1alpha, while chemotactic behavior to the dentin slices was not effected. There were differences in pH and concentration of HCO3- at culture endpoint and in adherent feature to dentin surfaces. Our findings indicate there are two types of osteoclasts with distinct properties.