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.     

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.     

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.     

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.     

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.     

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.     

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.     

Patterning, prestress, and peeling dynamics of myocytes

As typical anchorage-dependent cells myocytes must balance contractility against adequate adhesion. Skeletal myotubes grown as isolated strips from myoblasts on micropatterned glass exhibited spontaneous peeling after one end of the myotube was mechanically detached. Such results indicate the development of a prestress in the cells. To assess this prestress and study the dynamic adhesion strength of single myocytes, the shear stress of fluid aspirated into a large-bore micropipette was then used to forcibly peel myotubes. The velocity at which cells peeled from the surface, V(peel), was measured as a continuously increasing function of the imposed tension, T(peel), which ranges from approximately 0 to 50 nN/ micro m. For each cell, peeling proved highly heterogeneous, with V(peel) fluctuating between 0 micro m/s ( approximately 80% of time) and approximately 10 micro m/s. Parallel studies of smooth muscle cells expressing GFP-paxillin also exhibited a discontinuous peeling in which focal adhesions fractured above sites of strong attachment (when pressure peeled using a small-bore pipette). The peeling approaches described here lend insight into the contractile-adhesion balance and can be used to study the real-time dynamics of stressed adhesions through both physical detection and the use of GFP markers; the methods should prove useful in comparing normal versus dystrophic muscle cells.     

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.     

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 graph-theoretic method for the basic reproduction number in continuous time epidemiological models

In epidemiological models of infectious diseases the basic reproduction number is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for can be obtained from the digraphs in the reduction process.     

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).     

X-ray photochemistry in iron complexes from Fe(0) to Fe(IV) - Can a bug become a feature?

Under intense soft X-ray irradiation, we have observed time-dependent changes in the soft X-ray spectra of virtually all the Fe coordination complexes that we have examined, indicating chemical transformation of the compound under study. Each compound, with oxidation states ranging from Fe(IV) to Fe(0), has been studied with either Fe L-edge spectroscopy or N K-edge spectroscopy. We find that very often a well-defined spectroscopic change occurs, at least initially, which is apparently capable of straightforward interpretation in terms of X-ray induced photoreduction, photooxidation or ligand photolysis. We briefly discuss the probable chemical nature of the changes and then estimate the rate of chemical change, thereby establishing the necessary radiation dose. We also demonstrate that the photochemistry not only depends on the Fe oxidation state but also the coordination chemistry of the complex. It seems that a proper understanding of such X-ray photochemical effects could well greatly assist the assignment of soft X-ray spectra of uncharacterized metal sites.     

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.     

Molecular characterization of β1,4-galactosyltransferase 7 genetic mutations linked to the progeroid form of Ehlers-Danlos syndrome (EDS)

β1,4-Galactosyltransferase 7 (β4GalT7) is a key enzyme initiating glycosaminoglycan (GAG) synthesis. Based on in vitro and ex vivo kinetics studies and structure-based modelling, we molecularly characterized β4GalT7 mutants linked to the progeroid form of Ehlers-Danlos syndrome (EDS), a severe connective tissue disorder. Our results revealed that loss of activity upon L206P substitution due to altered protein folding is the primary cause for the GAG synthesis defect in patients carrying the compound A186D and L206P mutations. We showed that R270C substitution strongly reduced β4GalT7 affinity towards xyloside acceptor, thus affecting GAG chains formation. This study establishes the molecular basis for β4GalT7 defects associated with altered GAG synthesis in EDS.