Adding Adhesion to a Chemical Signaling Model for Somite Formation

Somites are condensations of mesodermal cells that form along the two sides of the neural tube during early vertebrate development. They are one of the first instances of a periodic pattern, and give rise to repeated structures such as the vertebrae. A number of theories for the mechanisms underpinning somite formation have been proposed. For example, in the “clock and wavefront” model (Cooke and Zeeman in J. Theor. Biol. 58:455–476, 1976), a cellular oscillator coupled to a determination wave progressing along the anterior-posterior axis serves to group cells into a presumptive somite. More recently, a chemical signaling model has been developed and analyzed by Maini and coworkers (Collier et al. in J. Theor. Biol. 207:305–316, 2000; Schnell et al. in C. R. Biol. 325:179–189, 2002; McInerney et al. in Math. Med. Biol. 21:85–113, 2004), with equations for two chemical regulators with entrained dynamics. One of the chemicals is identified as a somitic factor, which is assumed to translate into a pattern of cellular aggregations via its effect on cell–cell adhesion. Here, the authors propose an extension to this model that includes an explicit equation for an adhesive cell population. They represent cell adhesion via an integral over the sensing region of the cell, based on a model developed previously for adhesion driven cell sorting (Armstrong et al. in J. Theor. Biol. 243:98–113, 2006). The expanded model is able to reproduce the observed pattern of cellular aggregates, but only under certain parameter restrictions. This provides a fuller understanding of the conditions required for the chemical model to be applicable. Moreover, a further extension of the model to include separate subpopulations of cells is able to reproduce the observed differentiation of the somite into separate anterior and posterior halves. N.J. Armstrong was supported by a Doctoral Training Account Studentship from EPSRC. K.J. Painter and J.A. Sherratt were supported in part by Integrative Cancer Biology Program Grant CA113004 from the US National Institute of Health and in part by BBSRC grant BB/D019621/1 for the Centre for Systems Biology at Edinburgh.     

A Computational Analysis of Localized Ca<Superscript>2+</Superscript>-Dynamics Generated by Heterogeneous Release Sites

We investigate the role of heterogeneous expression of IP₃R and RyR in generating diverse elementary Ca²⁺ signals. It has been shown empirically (Wojcikiewicz and Luo in Mol. Pharmacol. 53(4):656–662, 1998; Newton et al. in J. Biol. Chem. 269(46):28613–28619, 1994; Smedt et al. in Biochem. J. 322(Pt. 2):575–583, 1997) that tissues express various proportions of IP₃ and RyR isoforms and this expression is dynamically regulated (Parrington et al. in Dev. Biol. 203(2):451–461, 1998; Fissore et al. in Biol. Reprod. 60(1):49–57, 1999; Tovey et al. in J. Cell Sci. 114(Pt. 22):3979–3989, 2001). Although many previous theoretical studies have investigated the dynamics of localized calcium release sites (Swillens et al. in Proc. Natl. Acad. Sci. U.S.A. 96(24):13750–13755, 1999; Shuai and Jung in Proc. Natl. Acad. Sci. U.S.A. 100(2):506–510, 2003a; Shuai and Jung in Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 67(3 Pt. 1):031905, 2003b; Thul and Falcke in Biophys. J. 86(5):2660–2673, 2004; DeRemigio and Smith in Cell Calcium 38(2):73–86, 2005; Nguyen et al. in Bull. Math. Biol. 67(3):393–432, 2005), so far all such studies focused on release sites consisting of identical channel types. We have extended an existing mathematical model (Nguyen et al. in Bull. Math. Biol. 67(3):393–432, 2005) to release sites with two (or more) receptor types, each with its distinct channel kinetics. Mathematically, the release site is represented by a transition probability matrix for a collection of nonidentical stochastically gating channels coupled through a shared Ca²⁺ domain. We demonstrate that under certain conditions a previously defined mean-field approximation of the coupling strength does not accurately reproduce the release site dynamics. We develop a novel approximation and establish that its performance in these instances is superior. We use this mathematical framework to study the effect of heterogeneity in the Ca²⁺-regulation of two colocalized channel types on the release site dynamics. We consider release sites consisting of channels with both Ca²⁺-activation and inactivation (“four-state channels”) and channels with Ca²⁺-activation only (“two-state channels”) and show that for the appropriate parameter values, synchronous channel openings within a release site with any proportion of two-state to four-state channels are possible, however, the larger the proportion of two-state channels, the more sensitive the dynamics are to the exact spatial positioning of the channels and the distance between channels. Specifically, the clustering of even a small number of two-state channels interferes with puff/spark termination and increases puff durations or leads to a tonic response.     

A Closer Look at Amphetamine-Induced Reverse Transport and Trafficking of the Dopamine and Norepinephrine Transporters

Amphetamine (AMPH) and its derivatives are regularly used in the treatment of a wide array of disorders such as attention-deficit hyperactivity disorder (ADHD), obesity, traumatic brain injury, and narcolepsy (Prog Neurobiol 75:406–433, 2005; J Am Med Assoc 105:2051–2054, 1935; J Am Acad Child Adolesc Psychiatry 41:514–521, 2002; Neuron 43:261–269, 2004; Annu Rev Pharmacol Toxicol 47:681–698, 2007; Drugs Aging 21:67–79, 2004). Despite the important medicinal role for AMPH, it is more widely known for its psychostimulant and addictive properties as a drug of abuse. The primary molecular targets of AMPH are both the vesicular monoamine transporters (VMATs) and plasma membrane monoamine—dopamine (DA), norepinephrine (NE), and serotonin (5-HT)—transporters. The rewarding and addicting properties of AMPH rely on its ability to act as a substrate for these transporters and ultimately increase extracellular levels of monoamines. AMPH achieves this elevation in extracellular levels of neurotransmitter by inducing synaptic vesicle depletion, which increases intracellular monoamine levels, and also by promoting reverse transport (efflux) through plasma membrane monoamine transporters (J Biol Chem 237:2311–2317, 1962; Med Exp Int J Exp Med 6:47–53, 1962; Neuron 19:1271–1283, 1997; J Physiol 144:314–336, 1958; J Neurosci 18:1979–1986, 1998; Science 237:1219–1223, 1987; J Neurosc 15:4102–4108, 1995). This review will focus on two important aspects of AMPH-induced regulation of the plasma membrane monoamine transporters—transporter mediated monoamine efflux and transporter trafficking.     

A general linear framework for the comparison and evaluation of models of sensorimotor synchronization

Sensorimotor synchronization (SMS), the temporal coordination of a rhythmic movement with an external rhythm, has been studied most often in tasks that require tapping along with a metronome. Models of SMS use information about the timing of preceding stimuli and responses to predict when the next response will be made. This article compares the theoretical structure and empirical predictions of four two-parameter models proposed in the literature: Michon (Timing in temporal tracking, Van Gorcum, Assen, 1967), Hary and Moore (Br J Math Stat Psychol 40:109–124, 1987b), Mates (Biol Cybern 70:463–473, 1994a; Biol Cybern 70:475–484, 1994b), and Schulze et al. (Mus Percept 22:461–467, 2005). By embedding these models within a general linear framework, the mathematical equivalence of the Michon, Hary and Moore, and Schulze et al. models is demonstrated. The Mates model, which differs from the other three, is then tested empirically with new data from a tapping experiment in which the metronome alternated between two tempi. The Mates model predictions are found to be invalid for about one-third of the trials, suggesting that at least one of the model’s underlying assumptions is incorrect. The other models cannot be refuted as easily, but they do not predict some features of the data very accurately. Comparison of the models’ predictions in a training/test procedure did not yield any significant differences. The general linear framework introduced here may help in the formulation of new models that make better predictions.     

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.     

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.     

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.     

ROS-Mediated ABA Signaling

In plants, reactive oxygen species (ROS) are short-lived molecules produced through various cellular mechanisms in response to biotic and abiotic stimuli. ROS function as second messengers for hormone signaling, development, oxygen deprivation, programmed cell death, and plant–pathogen interactions. Recent research on ROS-mediated responses has produced stimulating findings such as the specific sources of ROS production, molecular elements that work in ROS-mediated signaling and homeostasis, and a ROS-regulated gene network (Neill et al., Curr Opin Plant Biol 5:388–395, 2002a; Apel and Hirt, Annu Rev Plant Biol 55:373–399, 2004; Mittler et al., Trends Plant Sci 9:490–498, 2004; Mori and Schroeder, Plant Physiol 135:702–708, 2004; Kwak et al., Plant Physiol 141:323–329, 2006; Torres et al., Plant Physiol 141:373–378, 2006; Miller et al., Physiol Plant 133:481–489, 2008). In this review, we highlight new discoveries in ROS-mediated abscisic acid (ABA) signaling. Drs. Daeshik Cho and June M. Kwak are the corresponding authors for this paper.     

Leader neurons in leaky integrate and fire neural network simulations

In this paper, we highlight the topological properties of leader neurons whose existence is an experimental fact. Several experimental studies show the existence of leader neurons in population bursts of activity in 2D living neural networks (Eytan and Marom, J Neurosci 26(33):8465–8476, 2006; Eckmann et al., New J Phys 10(015011), 2008). A leader neuron is defined as a neuron which fires at the beginning of a burst (respectively network spike) more often than we expect by chance considering its mean firing rate. This means that leader neurons have some burst triggering power beyond a chance-level statistical effect. In this study, we characterize these leader neuron properties. This naturally leads us to simulate neural 2D networks. To build our simulations, we choose the leaky integrate and fire (lIF) neuron model (Gerstner and Kistler 2002; Cessac, J Math Biol 56(3):311–345, 2008), which allows fast simulations (Izhikevich, IEEE Trans Neural Netw 15(5):1063–1070, 2004; Gerstner and Naud, Science 326:379–380, 2009). The dynamics of our lIF model has got stable leader neurons in the burst population that we simulate. These leader neurons are excitatory neurons and have a low membrane potential firing threshold. Except for these two first properties, the conditions required for a neuron to be a leader neuron are difficult to identify and seem to depend on several parameters involved in the simulations themselves. However, a detailed linear analysis shows a trend of the properties required for a neuron to be a leader neuron. Our main finding is: A leader neuron sends signals to many excitatory neurons as well as to few inhibitory neurons and a leader neuron receives only signals from few other excitatory neurons. Our linear analysis exhibits five essential properties of leader neurons each with different relative importance. This means that considering a given neural network with a fixed mean number of connections per neuron, our analysis gives us a way of predicting which neuron is a good leader neuron and which is not. Our prediction formula correctly assesses leadership for at least ninety percent of neurons.     

Bone tissue,lyophilized and stored at room temperature for 15 days or more,is not capable of transmitting HIV,HCV or HBV

Over the past 57 years, 17 recipients of frozen bone have been infected with: HIV (Centers for Disease Control and Prevention in Morb Mortal Wkly Rep MMWR 37(39):597–599, 1988; Li et al. in J Formos Med Assoc 100(5):350–351, 2001; Simonds et al. in NEJM 326(11):726–732, 1992; Schratt et al. in Unfallchirurg 99(9):679–684, 1996); HCV (Eggen and Nordbo in NEJM 326(6):411, 1992; Conrad et al. in J Bone Joint Surg Am 77:214–224, 1995; Trotter in J Bone Joint Surg Am 851(11):2215–2217, 2003; Tugwell et al. in Ann of Internal Med 143(9):648–654, 2005); or HBV (Shutkin in J Bone Joint Surg Am 36:160–162, 1954). However, bone, lyophilized and stored at room temperature, has never transmitted these viral diseases. A literature review was undertaken to determine whether there is any evidence that lyophilized bone is capable of transmitting HIV, HCV and HBV.     

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.     

The rise and fall of handicap principle: a commentary on the “Modelling and the fall and rise of the handicap principle”

The honesty of animal communication is in the spot lights in the last 30 years. During most of this time the field was dominated by one explanation: Zahavi’s handicap principle (Zahavi, J Theor Biol 67:603–605, 1975; Grafen, J Theor Biol 144:517–546, 1990). Grose (Biol Philos 2011) embarks to explain both the success of the theory and the empirical difficulties that exist despite this success. While I wholeheartedly agree with the criticism offered by Grose and with almost all the claims he makes, the treatment of the issue is far from complete and it still leaves much to be explained. Accordingly, my commentary consist of six sections: in the first section I clear up some technical issues left unexposed, most importantly the role of strategic cost in handicap signalling; in the second section I relate this to empirical testing; in the next section I comment on the historical development of the handicap principle; in the fourth section I review the biological models that came up with conclusions that contradict the handicap principle; in the fifth section I discuss the reasons behind the success of the handicap theory; finally, in the last section I discuss the application of the handicap theory to anthropology and human sciences.     

Shaping bursting by electrical coupling and noise

Gap-junctional coupling is an important way of communication between neurons and other excitable cells. Strong electrical coupling synchronizes activity across cell ensembles. Surprisingly, in the presence of noise synchronous oscillations generated by an electrically coupled network may differ qualitatively from the oscillations produced by uncoupled individual cells forming the network. A prominent example of such behavior is the synchronized bursting in islets of Langerhans formed by pancreatic β-cells, which in isolation are known to exhibit irregular spiking (Sherman and Rinzel, Biophys J 54:411–425, 1988; Sherman and Rinzel, Biophys J 59:547–559, 1991). At the heart of this intriguing phenomenon lies denoising, a remarkable ability of electrical coupling to diminish the effects of noise acting on individual cells. In this paper, building on an earlier analysis of denoising in networks of integrate-and-fire neurons (Medvedev, Neural Comput 21 (11):3057–3078, 2009) and our recent study of spontaneous activity in a closely related model of the Locus Coeruleus network (Medvedev and Zhuravytska, The geometry of spontaneous spiking in neuronal networks, submitted, 2012), we derive quantitative estimates characterizing denoising in electrically coupled networks of conductance-based models of square wave bursting cells. Our analysis reveals the interplay of the intrinsic properties of the individual cells and network topology and their respective contributions to this important effect. In particular, we show that networks on graphs with large algebraic connectivity (Fiedler, Czech Math J 23(98):298–305, 1973) or small total effective resistance (Bollobas, Modern graph theory, Graduate Texts in Mathematics, vol. 184, Springer, New York, 1998) are better equipped for implementing denoising. As a by-product of the analysis of denoising, we analytically estimate the rate with which trajectories converge to the synchronization subspace and the stability of the latter to random perturbations. These estimates reveal the role of the network topology in synchronization. The analysis is complemented by numerical simulations of electrically coupled conductance-based networks. Taken together, these results explain the mechanisms underlying synchronization and denoising in an important class of biological models.     

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.     

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).     

A Mass Action Model of a Fibroblast Growth Factor Signaling Pathway and Its Simplification

We consider a kinetic law of mass action model for Fibroblast Growth Factor (FGF) signaling, focusing on the induction of the RAS-MAP kinase pathway via GRB2 binding. Our biologically simple model suffers a combinatorial explosion in the number of differential equations required to simulate the system. In addition to numerically solving the full model, we show that it can be accurately simplified. This requires combining matched asymptotics, the quasi-steady state hypothesis, and the fact subsets of the equations decouple asymptotically. Both the full and simplified models reproduce the qualitative dynamics observed experimentally and in previous stochastic models. The simplified model also elucidates both the qualitative features of GRB2 binding and the complex relationship between SHP2 levels, the rate SHP2 induces dephosphorylation and levels of bound GRB2. In addition to providing insight into the important and redundant features of FGF signaling, such work further highlights the usefulness of numerous simplification techniques in the study of mass action models of signal transduction, as also illustrated recently by Borisov and co-workers (Borisov et al. in Biophys. J. 89, 951–966, 2005, Biosystems 83, 152–166, 2006; Kiyatkin et al. in J. Biol. Chem. 281, 19925–19938, 2006). These developments will facilitate the construction of tractable models of FGF signaling, incorporating further biological realism, such as spatial effects or realistic binding stoichiometries, despite a more severe combinatorial explosion associated with the latter.