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.     

Molecular cloning and functional expression of a sodium bicarbonate cotransporter from guinea-pig parotid glands

We recently found that the concentration of HCO3- in guinea-pig saliva is very similar to that of human saliva; however, the entity that regulates HCO3- transport has not yet been fully characterized. In order to investigate the mechanism of HCO3- transport, we identified, cloned, and characterized a sodium bicarbonate (Na(+)/HCO3- cotransporter found in guinea-pig parotid glands (gpNBC1). The gpNBC1 gene encodes a 1079-amino acid protein that has 95% and 96% homology with human and mouse parotid NBC1, respectively. Oocytes expressing gpNBC1 were exposed to HCO3- or Na(+)-free solutions, which resulted in a marked change in membrane potentials (V(m)), suggesting that gpNBC1 is electrogenic. Likewise, a gpNBC1-mediated pH recovery was observed in gpNBC1 transfected human hepatoma cells; however, in the presence of 4, 4-diisothiocyanostilbene-2,2-disulfonic acid, a specific NBC1 inhibitor, such changes in V(m) and pH(i) were not observed. Together, the data show that the cloned guinea-pig gene is a functional, as well as sequence homologue of human NBC1.     

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.     

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.     

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.     

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.     

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.     

A multilevel approach to cancer growth modeling

Cancer growth models may be divided into macroscopic models, which describe the tumor as a single entity, and microscopic ones, which consider the tumor as a complex system whose behavior emerges from the local dynamics of its basic components, the neoplastic cells. Mesoscopic models (e.g. as based on the Local Interaction Simulation Approach [Delsanto, P.P., Mignogna, R., Scalerandi, M., Schechter, R., 1998. In: Delsanto, P.P. Saenz, A.W. (Eds.), New Perspectives on Problems in Classical and Quantum Physics, vol. 2. Gordon & Breach, New Delhi, p. 5174]), which explicitly consider the behavior of cell clusters and their interactions, may be used instead of the microscopic ones, in order to study the properties of cancer biology that strongly depend on the interactions of small groups of cells at intermediate spatial and temporal scales. All these approaches have been developed independently, which limits their usefulness, since they all include relevant features and information that should be cross-correlated for a deeper understanding of the mechanisms involved. In this contribution we consider multicellular tumor spheroids as biological reference systems and propose an intermediate model to bridge the gap between a macroscopic formulation of tumor growth and a mesoscopic one. Thus we are able to establish, as an important result of our formalism, a direct correspondence between parameters characterizing processes occurring at different scales. In particular, we analyze their dependence on an important limiting factor to tumor growth, i.e. the extra-cellular matrix pressure. Since the macro and meso-models stem from totally different roots (energy conservation and clinical observations vs. cell groups dynamics), their consistency may be used to validate both approaches. It may also be interesting to note that the proposed formalism fits well into a recently proposed conjecture of growth laws universality.     

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.     

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.     

Crystal structure of oxidized cytochrome c(6A) from Arabidopsis thaliana

Compared with algal and cyanobacterial cytochrome c(6), cytochrome c(6A) from higher plants contains an additional loop of 12 amino acid residues. We have determined the first crystal structure of cytochrome c(6A) from Arabidopsis thaliana at 1.5 Angstrom resolution in order to help elucidate its function. The overall structure of cytochrome c(6A) follows the topology of class I c-type cytochromes in which the heme prosthetic group covalently binds to Cys16 and Cys19, and the iron has octahedral coordination with His20 and Met60 as the axial ligands. Two cysteine residues (Cys67 and Cys73) within the characteristic 12 amino acids loop form a disulfide bond, contributing to the structural stability of cytochrome c(6A). Our model provides a chemical basis for the known low redox potential of cytochrome c(6A) which makes it an unsuitable electron carrier between cytochrome b(6)f and PSI.     

Diuretic factors and second messengers stimulate secretion of the organic cation TEA by the Malpighian tubules of Drosophila melanogaster

This study showed that four factors which stimulate transepithelial fluid secretion and inorganic ion transport across the main segment of the Malpighian tubules of Drosophila melanogaster also stimulate transepithelial secretion of the prototypical organic cation tetraethylammonium (TEA). TEA fluxes across the Malpighian tubules and gut were measured using a TEA-selective self-referencing (TEA-SeR) microelectrode. TEA flux across isolated Malpighian tubules was also measured using a TEA-selective microelectrode positioned in droplets of fluid secreted by tubules set up in a modified Ramsay assay. TEA flux was stimulated by the intracellular second messengers cAMP and cGMP, which increase the lumen-positive transepithelial potential (TEP), and also by tyramine and leucokinin-I (LK-I), which decrease TEP. The largest increase was measured in response to 1 micromol l-1 LK-I which increased transepithelial TEA flux by 72%. TEA flux in the lower tubule was stimulated slightly (13%) by 1 micromol l-1 tyramine but not by any of the other factors. TEA flux across the midgut was unaffected by cAMP, cGMP or tyramine. This is the first study to demonstrate the effects of insect diuretic factors and second messengers on excretion of organic cations.     

The antioxidative function of eicosapentaenoic acid in a marine bacterium, Shewanella marinintestina IK-1

When the eicosapentaenoic acid (EPA)-deficient mutant strain IK-1Delta8 of the marine EPA-producing Shewanella marinintestina IK-1 was treated with various concentrations of hydrogen peroxide (H(2)O(2)), its colony-forming ability decreased more than that of the wild type. Protein carbonylation, induced by treating cells with 0.01 mM H(2)O(2) under bacteriostatic conditions, was enhanced only in cells lacking EPA. The amount of cells recovered from the cultures was decreased more significantly by the presence of H(2)O(2) for cells lacking EPA than for those producing EPA. Treatment of the cells with 0.1 mM H(2)O(2) resulted in much lower intracellular concentrations of H(2)O(2) being consistently detected in cells with EPA than in those without EPA. These results suggest that cellular EPA can directly protect cells against oxidative damage by shielding the entry of exogenously added H(2)O(2) in S. marinintestina IK-1.     

Pressure equilibrium and jump study on unfolding of 23-kDa protein from spinach photosystem II

Pressure-induced unfolding of 23-kDa protein from spinach photosystem II has been systematically investigated at various experimental conditions. Thermodynamic equilibrium studies indicate that the protein is very sensitive to pressure. At 20 degrees C and pH 5.5, 23-kDa protein shows a reversible two-state unfolding transition under pressure with a midpoint near 160 MPa, which is much lower than most natural proteins studied to date. The free energy (DeltaG(u)) and volume change (DeltaV(u)) for the unfolding are 5.9 kcal/mol and -160 ml/mol, respectively. It was found that NaCl and sucrose significantly stabilize the protein from unfolding and the stabilization is associated not only with an increase in DeltaG(u) but also with a decrease in DeltaV(u). The pressure-jump studies of 23-kDa protein reveal a negative activation volume for unfolding (-66.2 ml/mol) and a positive activation volume for refolding (84.1 ml/mol), indicating that, in terms of system volume, the protein transition state lies between the folded and unfolded states. Examination of the temperature effect on the unfolding kinetics indicates that the thermal expansibility of the transition state and the unfolded state of 23-kDa protein are closer to each other and they are larger than that of the native state. The diverse pressure-refolding pathways of 23-kDa protein in some conditions were revealed in pressure-jump kinetics.     

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.     

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.     

Application of HN(C)N to rapid estimation of 1J(N-C(alpha)) coupling constants correlated to psi torsion angles in proteins: implication to structural genomics

We recently described a triple resonance experiment, HN(C)N, for sequential correlation of H(N) and 15N atoms in (15N, 13C) labeled proteins [J. Biomol. NMR. 20 (2001) 135]. Here, we describe an approach based on this experiment for estimation of one bond N-C(alpha) J-couplings in medium size labeled proteins, which seem to show good correlations with psi torsion angles along the protein backbone. The approach uses the ratio of the intensities of the sequential and diagonal peaks in the F(2)-F(3) planes of the HN(C)N spectrum. The reliability of the approach has been demonstrated using a short peptide wherein the coupling constants have been measured by the present method and also independently from peak splittings in HSQC spectra. The two results agree within 10%. The applicability of the procedure to proteins has been demonstrated using doubly labeled FK506 binding protein (FKBP, molecular mass approximately 12 kDa). Coupling constant estimates have been obtained for 62 out of 100 non-proline residues and they show a correlation with psi torsion angles, as has been reported before. This semi-quantitative application of HN(C)N extends the significance of the experiment especially, in the context of structural genomics, since the single experiment, not only provides a great enhancement in the speed of resonance assignment, but also provides quantitative structural information.