Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods

Hodgkin–Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many biological properties of interest, including channel complement and density, that give rise to a neuron’s electrophysiological behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach. This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using test data simulated from neuronal models comprising several common channels, we show that short (<50 ms) intracellular recordings from neurons stimulated with a complex time-varying current yield accurate and precise estimates of the model parameters as well as accurate predictions of the future behavior of the neuron. We also show that this method is robust to errors in model specification, supporting model development for biological preparations in which the channel expression and other biophysical properties of the neurons are not fully known.     

Screening for hereditary hemochromatosis: are DNA-based tests the answer?

Universal screening for hereditary hemochromatosis (HH) has been proposed by many experts, with understandable enthusiasm: HH can cause fatal complications, which are preventable with early treatment. The disorder involves excess iron accumulation that can result in tissue iron overload, with secondary cirrhosis, diabetes, heart failure, impotence and arthritis. These complications are preceded by years of iron accumulation, and most are believed to be preventable by removal of excess iron by phlebotomy. Thus, early identification and treatment - the quintessential functions of health screening - seem to make sense for HH. However, the available screening tests are imperfect. While they can identify many persons at increased risk from HH, the proportion that will develop serious clinical manifestations related to iron overload is not known with certainty. DNA-based tests do not provide a simple resolution to these questions.     

Intricacies of hedgehog signaling pathways: a perspective in tumorigenesis

The hedgehog (HH) signaling pathway is a crucial negotiator of developmental proceedings in the embryo governing a diverse array of processes including cell proliferation, differentiation, and tissue patterning. The overall activity of the pathway is significantly curtailed after embryogenesis as well as in adults, yet it retains many of its functional capacities. However, aberration in HH signaling mediates the initiation, proliferation and continued sustenance of malignancy in different tissues to varying degrees through different mechanisms. In this review, we provide an overview of the role of constitutively active aberrant HH signaling pathway in different types of human cancer and the underlying molecular and genetic mechanisms that drive tumorigenesis in that particular tissue. An insight into the various modes of anomalous HH signaling in different organs will provide a comprehensive knowledge of the pathway in these tissues and open a window for individually tailored, tissue-specific therapeutic interventions. The synergistic cross talking of HH pathway with many other regulatory molecules and developmentally inclined signaling pathways may offer many avenues for pharmacological advances. Understanding the molecular basis of abnormal HH signaling in cancer will provide an opportunity to inhibit the deregulated pathway in many aggressive and therapeutically challenging cancers where promising options are not available.     

Food hoarding is increased by food deprivation and decreased by leptin treatment in Syrian hamsters

Compensatory increases in food intake are commonly observed after a period of food deprivation in many species, including laboratory rats and mice. Thus it is interesting that Syrian hamsters fail to increase food intake after a period of food deprivation, despite a fall in plasma leptin concentrations similar to those seen in food-deprived rats and mice. In previous laboratory studies, food-deprived Syrian hamsters increased the amount of food hoarded. We hypothesized that leptin treatment during food deprivation would attenuate food-deprivation-induced increases in hoarding. Baseline levels of hoarding were bimodally distributed, with no hamsters showing intermediate levels of hoarding. Both high (HH) and low hoarding (LH) hamsters were included in each experimental group. Fifty-six male hamsters were either food deprived or given ad libitum access to food for 48 h. One-half of each group received intraperitoneal injections of leptin (4 mg/kg) or vehicle every 12 h during the food-deprivation period. Within the HH group, the hoarding score increased significantly in food-deprived but not fed hamsters (P < 0.05). Leptin treatment significantly decreased hoarding in the food-deprived HH hamsters (P < 0.05). The LH hamsters did not increase hoarding regardless of whether they were food deprived or had ad libitum access to food. These results are consistent with the idea that HH hamsters respond to energetic challenges at least in part by changing their hoarding behavior and that leptin might be one factor that mediates this response.     

NANOG regulates glioma stem cells and is essential in vivo acting in a cross‐functional network with GLI1 and p53

A cohort of genes associated with embryonic stem (ES) cell behaviour, including NANOG, are expressed in a number of human cancers. They form an ES‐like signature we first described in glioblastoma multiforme (GBM), a highly invasive and incurable brain tumour. We have also shown that HEDGEHOG‐GLI (HH‐GLI) signalling is required for GBM growth, stem cell expansion and the expression of this (ES)‐like stemness signature. Here, we address the function of NANOG in human GBMs and its relationship with HH‐GLI activity. We find that NANOG modulates gliomasphere clonogenicity, CD133⁺ stem cell cell behavior and proliferation, and is regulated by HH‐GLI signalling. However, GLI1 also requires NANOG activity forming a positive loop, which is negatively controlled by p53 and vice versa. NANOG is essential for GBM tumourigenicity in orthotopic xenografts and it is epistatic to HH‐GLI activity. Our data establish NANOG as a novel HH‐GLI mediator essential for GBMs. We propose that this function is conserved and that tumour growth and stem cell behaviour rely on the status of a functional GLI1‐NANOG‐p53 network.     

Impulses and Physiological States in Theoretical Models of Nerve Membrane

Van der Pol''s equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting “BVP model” has two variables of state, representing excitability and refractoriness, and qualitatively resembles Bonhoeffer''s theoretical model for the iron wire model of nerve. This BVP model serves as a simple representative of a class of excitable-oscillatory systems including the Hodgkin-Huxley (HH) model of the squid giant axon. The BVP phase plane can be divided into regions corresponding to the physiological states of nerve fiber (resting, active, refractory, enhanced, depressed, etc.) to form a “physiological state diagram,” with the help of which many physiological phenomena can be summarized. A properly chosen projection from the 4-dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable.     

A 3D model for the human hepatic asialoglycoprotein receptor (ASGP-R)

The human hepatic Asialoglycoprotein Receptor (ASGP-R) consists of two different types of liver specific membrane glycoproteins that bind to terminal galactose and N-acetylgalactosamine residues of serum glycoproteins. The two different polypeptide chains are referred to as two receptor subunits, HH1 and HH2, which are both involved in the activity of the functional receptor. This receptor has served as a model for understanding receptor-mediated endocytosis and carbohydrate mediated recognition phenomena. Here models for the C-terminal extracellular region of both HH1 and HH2 subunit are presented. The standard homology building procedure was modified in order to make it suitable for the modeling problem at hand. The models for the extracellular regions of HH1 and HH2 were initially constructed by exploiting several fragments, belonging to proteins of known 3D structure, and showing high local sequence similarity with respect to the glycoproteins of interest. Putative binding sites were first hypothesized on the basis of the comparison with other complexes of lectins, the crystal structure of which was available in the Protein Data Bank. A model for the complex involving the HH2 subunit and the typical high affinity ligand N-acetylgalactosamine (NacGal) was refined as the first by a suitable combination of MD simulations and Energy Minimization calculations, since it seemed to quickly converge to a plausible structure. An intermediate model for HH1 was then rebuilt on the basis of the refined model for HH2. It was then submitted to a sequence of molecular dynamics simulations with templates which took into account the secondary structure prediction for a final refinement. The structures of small regions of the models, located around the binding sites, were compared with more recent crystallographic data regarding a complex involving the mutant of Mannose Binding Protein QPDWGH (1BCH entry in the Protein Data Bank) and NacGal. This mutant shows high local sequence similarity with HH1 and HH2 at the binding sites. On the basis of the above comparison, different locations of the binding sites were also considered. In addition to other expected interactions, two hydrophobic interactions were observed in the models with Trp residues (positions 243 in HH1 and 181 or 267 in HH2 respectively) and His residues (positions 256 in HHI and 184 in HH2.respectively). The quality of the models was evaluated by the Procheck program and they seemed plausible. This observation together with analogies found between binding sites of the models and IBCH supported the validity of the models. A further validation element arose by comparison between experimental binding data available in the literature about the homologous rat receptor subunits and theoretical interaction energies evaluated, by means of the DOCK 3.5 program, in models for the rat subunits obtained from the corresponding human ones. The new modeling procedure used here appears to be a well-suited method for structural analysis of small regions, located around the ligands, in proteins of unknown 3D structure.     

A 3D Model for the Human Hepatic Asialoglycoprotein Receptor (ASGP-R)

Abstract

The human hepatic Asialoglycoprotein Receptor (ASGP-R) consists of two different types of liver specific membrane glycoproteins that bind to terminal galactose and acetylgalactosamine residues of serum glycoproteins. The two different polypeptide chains are referred to as two receptor subunits, HH1 and HH2, which are both involved in the activity of the functional receptor. This receptor has served as a model for understanding receptor-mediated endocytosis and carbohydrate mediated recognition phenomena.

Here models for the C-terminal extracellular region of both HH1 and HH2 subunit are presented. The standard homology building procedure was modified in order to make it suitable for the modeling problem at hand. The models for the extracellular regions of HH1 and HH2 were initially constructed by exploiting several fragments, belonging to proteins of known 3D structure, and showing high local sequence similarity with respect to the glycoproteins of interest. Putative binding sites were first hypothesized on the basis of the comparison with other complexes of lectins, the crystal structure of which was available in the Protein Data Bank. A model for the complex involving the HH2 subunit and the typical high affinity ligand N-acetylgalactosamine (NacGal) was refined as the first by a suitable combination of MD simulations and Energy Minimization calculations, since it seemed to quickly converge to a plausible structure. An intermediate model for HH1 was then rebuilt on the basis of the refined model for HH2. It was then submitted to a sequence of molecular dynamics simulations with templates which took into account the secondary structure prediction for a final refinement. The structures of small regions of the models, located around the binding sites, were compared with more recent crystallographic data regarding a complex involving the mutant of Mannose Binding Protein QPDWGH (1BCH entry in the Protein Data Bank) and NacGal. This mutant shows high local sequence similarity with HH1 and HH2 at the binding sites. On the basis of the above comparison, different locations of the binding sites were also considered. In addition to other expected interactions, two hydrophobic interactions were observed in the models with Trp residues (positions 243 in HH1 and 181 or 267 in HH2 respectively) and His residues (positions 256 in HH1 and 184 in HH2 respectively). The quality of the models was evaluated by the Procheck program and they seemed plausible. This observation together with analogies found between binding sites of the models and 1BCH supported the validity of the models. A further validation element arose by comparison between experimental binding data available in the literature about the homologous rat receptor subunits and theoretical interaction energies evaluated, by means of the DOCK 3.5 program, in models for the rat subunits obtained from the corresponding human ones. The new modeling procedure used here appears to be a well-suited method for structural analysis of small regions, located around the ligands, in proteins of unknown 3D structure.     

Temporal restriction of migratory and lineage potential in rhombomere 1 and 2 neural crest

Migratory cranial neural crest cells differentiate into a wide range of cell types, such as ectomesenchymal tissue (bone and connective tissues) ventrally in the branchial arches and neural tissue (neurons and glia) dorsally. We investigated spatial and temporal changes of migration and differentiation potential in neural crest populations derived from caudal midbrain and rhombomeres 1 and 2 by back-transplanting cells destined for the first branchial arch and trigeminal ganglion from HH8-HH19 quail into HH7-HH11 chicks. Branchial arch cells differentiated down ectomesenchymal lineages but largely lost both the ability to localize to the trigeminal position and neurogenic differentiation capacity by HH12-HH13, even before the arch is visible, and lost long distance migratory ability around HH17. In contrast, neural crest-derived cells from trigeminal ganglia lost ectomesechymal differentiation potential by HH17. Despite this, they retain the ability to migrate into the branchial arches until at least HH19. However, many of the neural crest-derived trigeminal ganglia cells in the branchial arch localized to the non-neural crest core of the arch from HH13 and older donors. These results suggest that long distance migration ability, finer scale localization, and lineage restriction may not be coordinately regulated in the cranial neural crest population.     

Shoulder labral pathomechanics with rotator cuff tears

Rotator cuff tears (RCTs), the most common injury of the shoulder, are often accompanied by tears in the superior glenoid labrum. We evaluated whether superior humeral head (HH) motion secondary to RCTs and loading of the long head of the biceps tendon (LHBT) are implicated in the development of this associated superior labral pathology. Additionally, we determined the efficacy of a finite element model (FEM) for predicting the mechanics of the labrum. The HH was oriented at 30° of glenohumeral abduction and neutral rotation with 50 N compressive force. Loads of 0 N or 22 N were applied to the LHBT. The HH was translated superiorly by 5 mm to simulate superior instability caused by RCTs. Superior displacement of the labrum was affected by translation of the HH (P<0.0001), position along the labrum (P<0.0001), and interaction between the location on the labrum and LHBT tension (P<0.05). The displacements predicted by the FEM were compared with mechanical tests from 6 cadaveric specimens and all were within 1 SD of the mean. A hyperelastic constitutive law for the labrum was a better predictor of labral behavior than the elastic law and insensitive to ±1 SD variations in material properties. Peak strains were observed at the glenoid–labrum interface below the LHBT attachment consistent with the common location of labral pathology. These results suggest that pathomechanics of the shoulder secondary to RCTs (e.g., superior HH translation) and LHBT loading play significant roles in the pathologic changes seen in the superior labrum.     

Local and nonlocal interactions in globular proteins and mechanisms of alcohol denaturation.

How important are helical propensities in determining the conformations of globular proteins? Using the two-dimensional lattice model and two monomer types, H (hydrophobic) and P (polar), we explore both nonlocal interactions, through an HH contact energy, as developed in earlier work, and local interactions, through a helix energy, σ. By computer enumeration, the partition functions for short chains are obtained without approximation for the full range of both types of energy. When nonlocal interactions dominate, some sequences undergo coil-globule collapse to a unique native structure. When local interactions dominate, all sequences undergo helix–coil transitions. For two different conformational properties, the closest correspondence between the lattice model and proteins in the Protein Data Bank is obtained if the model local interactions are made small compared to the HH contact interaction, suggesting that helical propensities may be only weak determinants of globular protein structures in water. For some HP sequences, varying σ/ leads to additional sharp transitions (sometimes several) and to “conformational switching” between unique conformations. This behavior resembles the transitions of globular proteins in water to helical states in alcohols. In particular, comparison with experiments shows that whereas urea as a denaturant is best modeled as weakening both local and nonlocal interactions, trifluoroethanol is best modeled as mainly weakening HH interactions and slightly enhancing local helical interactions.     

The Full-length Unprocessed Hedgehog Protein Is an Active Signaling Molecule

The hedgehog (HH) family of ligands plays an important instructional role in metazoan development. HH proteins are initially produced as ∼45-kDa full-length proteins, which undergo an intramolecular cleavage to generate an amino-terminal product that subsequently becomes cholesterol-modified (HH-Np). It is well accepted that this cholesterol-modified amino-terminal cleavage product is responsible for all HH-dependent signaling events. Contrary to this model we show here that full-length forms of HH proteins are able to traffic to the plasma membrane and participate directly in cell-cell signaling, both in vitro and in vivo. We were also able to rescue a Drosophila eye-specific hh loss of function phenotype by expressing a full-length form of hh that cannot be processed into HH-Np. These results suggest that in some physiological contexts full-length HH proteins may participate directly in HH signaling and that this novel activity of full-length HH may be evolutionarily conserved.     

Effects of rectification on synaptic efficacy.

We have investigated the effects of postsynaptic membrane properties on the shape of synaptic potentials generated by time-varying synaptic conductances. We used numerical simulation techniques to model cells of several different geometrical forms, from an isopotential sphere to a neuron with a soma and a dendritic tree. A variety of postsynaptic membrane properties were tested: (a) a passive resistance-capacitance membrane, (b) a membrane represented by the Hodgkin and Huxley (HH) equations, and (c) a membrane that was passive except for a delayed rectification represented by a voltage- and time-dependent increase in GK. In all cases we investigated the effects of these postsynaptic membrane properties on synaptic potentials produced by synaptic conductances that were fast or slow compared with the membrane time constant. In all cases the effects of postsynaptic rectification occurred on postsynaptic potentials of amplitudes as low as 1 mV. The HH model (compared with the passive model) produced an increased peak amplitude (from the increase in GNa) but a decreased half-width and a decreased time integral (from the increase in GK). These effects of the HH GK change were duplicated by a simple analytical rectifier model.     

Long-term use of high-heeled shoes alters the neuromechanics of human walking

Human movement requires an ongoing, finely tuned interaction between muscular and tendinous tissues, so changes in the properties of either tissue could have important functional consequences. One condition that alters the functional demands placed on lower limb muscle-tendon units is the use of high-heeled shoes (HH), which force the foot into a plantarflexed position. Long-term HH use has been found to shorten medial gastrocnemius muscle fascicles and increase Achilles tendon stiffness, but the consequences of these changes for locomotor muscle-tendon function are unknown. This study examined the effects of habitual HH use on the neuromechanical behavior of triceps surae muscles during walking. The study population consisted of 9 habitual high heel wearers who had worn shoes with a minimum heel height of 5 cm at least 40 h/wk for a minimum of 2 yr, and 10 control participants who habitually wore heels for less than 10 h/wk. Participants walked at a self-selected speed over level ground while ground reaction forces, ankle and knee joint kinematics, lower limb muscle activity, and gastrocnemius fascicle length data were acquired. In long-term HH wearers, walking in HH resulted in substantial increases in muscle fascicle strains and muscle activation during the stance phase compared with barefoot walking. The results suggest that long-term high heel use may compromise muscle efficiency in walking and are consistent with reports that HH wearers often experience discomfort and muscle fatigue. Long-term HH use may also increase the risk of strain injuries.     

Modeling the binding sites of anti-hen egg white lysozyme antibodies HyHEL-8 and HyHEL-26: an insight into the molecular basis of antibody cross-reactivity and specificity

Three antibodies, HyHEL-8 (HH8), HyHEL-10 (HH10), and HyHEL-26 (HH26) are specific for the same epitope on hen egg white lysozyme (HEL), and share >90% sequence homology. Their affinities vary by several orders of magnitude, and among the three antibodies, HH8 is the most cross-reactive with kinetics of binding that are relatively invariable compared to HH26, which is highly specific and has quite variable kinetics. To investigate structural correlates of these functional variations, the Fv regions of HH8 and HH26 were homology-modeled using the x-ray structure of the well-characterized HH10-HEL complex as template. The binding site of HH26 is most charged, least hydrophobic, and has the greatest number of intramolecular salt bridges, whereas that of HH8 is the least charged, most hydrophobic and has the fewest intramolecular salt bridges. The modeled HH26-HEL structure predicts the recently determined x-ray structure of HH26, (Li et al., 2003, Nat. Struct. Biol. 10:482-488) with a root-mean-square deviation of 1.03 A. It is likely that the binding site of HH26 is rendered rigid by a network of intramolecular salt bridges whereas that of HH8 is flexible due to their absence. HH26 also has the most intermolecular contacts with the antigen whereas HH8 has the least. HH10 has these properties intermediate to HH8 and HH26. The structurally rigid binding site with numerous specific contacts bestows specificity on HH26 whereas the flexible binding site with correspondingly fewer contacts enables HH8 to be cross-reactive. Results suggest that affinity maturation may select for high affinity antibodies with either "lock-and-key" preconfigured binding sites, or "preconfigured flexibility" by modulating combining site flexibility.