Equivalence transformations for dendritic Y-junctions: a new definition of dendritic sub-unit

A sequence of equivalence transformations is used to represent the mathematical model of a simply branched neuron with non-homogeneous membrane properties and non-uniform geometry by an entirely equivalent model of an unbranched structure. The analysis indicates how neuronal morphology, in combination with its biophysical properties, shapes neuronal output in response to current input. The equivalence transformations described here reveal the types of operations that are likely to feature in the analysis of complex multi-branched structures, neuronal or otherwise. These transformations provide a new definition of dendritic sub-unit and a basis of a mechanism for characterising local and non-local signal processing within dendritic structures. It is anticipated that the capacity to transform biological neurons into an equivalent unbranched structure will make an important contribution to the understanding of the functional role of neuron geometry as well as to the construction of silicon neurons with realistic biological properties.     

A generalized tapering equivalent cable model for dendritic neurons

A mathematical model has been developed which collapses a dendritic neuron of complex geometry into a single electrotonically tapering equivalent cable. The modified cable equation governing the transient distribution of subthreshold membrane potential in a branching tree is transformed, becoming amenable to analytic solution. This transformation results in a Riccati differential equation whose six solutions (expressed in terms of elementary functions) control the amount and degree of taper found in the equivalent cable model. To illustrate the theory, an analytic solution (in series form) of the modified cable equation is obtained for a voltage-clamp present at the soma of a quadratically tapering equivalent cable whose distal end is sealed.     

Innervation of the cercal sensilla on the ovipositor of the Australian sheep blowfly (Lucilia cuprina)

ABSTRACT. The ovipositor of the female sheep blowfly, Lucilia cuprina (Wied.) (Diptera: Calliphoridae), has a complement of cercal sensilla that includes long, medium and short tactile hairs, two campaniform domes, four olfactory pegs, and ten double-channelled gustatory hairs. This sensory array is suited to assess oviposition site resources, prior to and during the laying of an egg batch.
The tactile hairs and campaniform sensilla are each innervated by a single, tubular body containing dendrite. The olfactory pegs are each innervated by a single, moderately branched dendrite, which gains access to the external environment via pores at the bottom of deep grooves in the peg wall. The gustatory hairs fall into two categories. Four hairs have a single, tubular body containing dendrite at their base, and four unbranched dendrites running up to the hair tip which has a terminal pore. Six of the taste hairs have no tubular body containing dendrite at the base, and three unbranched dendrites running up to a terminal pore.     

Coding of odor intensity in a steady-state deterministic model of an olfactory receptor neuron

The coding of odor intensity by an olfactory receptor neuron model was studied under steady-state stimulation. Our model neuron is an elongated cylinder consisting of the following three components: a sensory dendritic region bearing odorant receptors, a passive region consisting of proximal dendrite and cell body, and an axon. First, analytical solutions are given for the three main physiological responses: (1) odorant-dependent conductance change at the sensory dendrite based on the Michaelis-Menten model, (2) generation and spreading of the receptor potential based on a new solution of the cable equation, and (3) firing frequency based on a Lapicque model. Second, the magnitudes of these responses are analyzed as a function of odorant concentration. Their dependence on chemical, electrical, and geometrical parameters is examined. The only evident gain in magnitude results from the activation-to-conductance conversion. An optimal encoder neuron is presented that suggests that increasing the length of the sensory dendrite beyond about 0.3 space constant does not increase the magnitude of the receptor potential. Third, the sensivities of the responses are examined as functions of (1) the concentration at half-maximum response, (2) the lower and upper concentrations actually discriminated, and (3) the width of the dynamic range. The overall gain in sensitivity results entirely from the conductance-to-voltage conversion. The maximum conductance at the sensory dendrite appears to be the main tuning constant of the neuron because it determines the shift toward low concentrations and the increase in dynamic range. The dynamic range of the model cannot exceed 5.7 log units, for a sensitivity increase at low odor concentration is compensated by a sensitivity decrease at high odor concentration.     

The role of a metastable RNA secondary structure in hepatitis delta virus genotype III RNA editing

RNA editing plays a critical role in the life cycle of hepatitis delta virus (HDV). The host editing enzyme ADAR1 recognizes specific RNA secondary structure features around the amber/W site in the HDV antigenome and deaminates the amber/W adenosine. A previous report suggested that a branched secondary structure is necessary for editing in HDV genotype III. This branched structure, which is distinct from the characteristic unbranched rod structure required for HDV replication, was only partially characterized, and knowledge concerning its formation and stability was limited. Here, we examine the secondary structures, conformational dynamics, and amber/W site editing of HDV genotype III RNA using a miniaturized HDV genotype III RNA in vitro. Computational analysis of this RNA using the MPGAfold algorithm indicated that the RNA has a tendency to form both metastable and stable unbranched secondary structures. Moreover, native polyacrylamide gel electrophoresis demonstrated that this RNA forms both branched and unbranched rod structures when transcribed in vitro. As predicted, the branched structure is a metastable structure that converts readily to the unbranched rod structure. Only branched RNA was edited at the amber/W site by ADAR1 in vitro. The structural heterogeneity of HDV genotype III RNA is significant because not only are both conformations of the RNA functionally important for viral replication, but the ratio of the two forms could modulate editing by determining the amount of substrate RNA available for modification.     

Developmental pathways for shaping spike inflorescence architecture in barley and wheat

Grass species display a wide array of inflorescences ranging from highly branched compound/panicle inflorescences to unbranched spike inflorescences. The unbranched spike is a characteristic feature of the species of tribe Triticeae, including economically important crops,such as wheat and barley. In this review, we describe two important developmental genetic mechanisms regulating spike inflorescence architecture in barley and wheat.These include genetic regulation of(i) row-type pathway specific to Hordeum species and(ii) unbranched spike development in barley and wheat. For a comparative understanding, we describe the branched inflorescence phenotypes of rice and maize along with unbranched Triticeae inflorescences. In the end, we propose a simplified model describing a probable mechanism leading to unbranched spike formation in Triticeae species.     

Sensilla and Cuticular Appendages on the Female Abdomen of Lasioptera rubi (Schrank) (Diptera,Cecidomyiidae)

Studies by SEM and TEM revealed 6 types of integumental appendages on female uromeres VIII-X in Lasioptera rubi: microtrichia, not innervated; spines, probably without sensory function; nonporous sensory hairs, each containing one dendrite ending with a tubular body indicating a tactile function; uniporous sensory hairs, each innervated partly by 3 dendrites indicating a chemosensory function, partly by an additional dendrite with a tubular body indicating a tactile function; scoop-like sensilla, each containing partly a branched structure of dendrites in the distal half of the sensillum indicating an olfactory function, partly an unbranched dendrite ending at a pore near the base of the sensillum, most probably registrating chemical stimuli by contact or gustation; finally, nonporous bristles, all or some of them innervated, in a manner indicating a tactile function. In addition, two scolopophorous proprioceptors were found inside uromere X. The nonporous sensory hairs, the uniporous sensory hairs and the scolopophores may be used by the midge to determine the mechanical and chemical properties of potential oviposition sites. The spines and nonporous bristles may function as conidia carriers.     

Dendritic Integration in Olfactory Sensory Neurons: A Steady-State Analysis of How the Neuron Structure and Neuron Environment Influence the Coding of Odor Intensity

Response properties of the receptor potential at steady state were analyzed in a biophysical model of an olfactory sensory neuron embedded in a multicell environment. The neuron structure was described as a set of several identical dendrites (or cilia) bearing the transduction mechanisms, joined to a nonsensory part—dendritic knob, soma, and axon. The different ionic compositions of the media surrounding the neuron sensory and nonsensory parts and the extraneuronal voltage sources, which both result from the presence of auxiliary cells, were also taken into account. Analytical solutions were found to describe how the receptor potential at the nonsensory part responds to a uniform change in the odorant-dependent conductance resulting from odorant stimulation of the sensory dendrites. We investigated the influence of various geometrical and electrical parameters on the receptor-potential response in the classical model neuron within a homogeneous environment and in the model neuron surrounded with auxiliary cells. First, it was found that the maximum amplitude of the receptor potential is independent of the neuron structure in the absence of auxiliary cells but not in their presence. In the latter case, the amplitude decreases with the length and number of sensory dendrites and with the input resistance of the nonsensory part. Second, the sensitivity (as measured by the increase in membrane conductance at half-maximum response) of the neuron model in the absence of auxiliary cells is higher, but its dynamic range is narrower than in their presence. The dynamic range is wide and the sensitivity low when the input resistance of the nonsensory part is small and the sensory dendrite is unbranched. Both sensitivity and dynamic range are higher for a longer dendrite. These results help understand the morphology of insect olfactory sensilla and can be generalized to other neuron types.     

Fitness consequences of branching in Verbascum thapsus (Scrophulariaceae)

The reserve meristem hypothesis proposes that strong apical dominance suppresses lateral meristems and branches to escape from predictable damage (herbivory). This hypothesis was tested for Verbascum thapsus and its seed predator the weevil Gynmnetron tetrum by two mensurative experiments. The following predictions were made under this hypothesis: the proportion of individuals branched within a population will increase with increased damage, the main stalk of branched plants will be more damaged, and branching increases net seed production. Fifty populations of V. thapsus were extensively surveyed, and one pair of similar-sized individuals (branched vs. unbranched) were selected from each population to determine damage patterns and measure seed production. Two of the predictions of the reserve meristem hypothesis were clearly supported. The proportion of fruits damaged on the main stalk of branched plants was significantly greater than unbranched plants, and branched plants produced significantly more seeds. Hence, the reserve meristem hypothesis is supported as an adaptive interpretation of apical dominance in this species. This study is a potential example of overcompensation following granivory in the field.     

Modelling the electrotonic structure of starburst amacrine cells in the rabbit retina: A functional interpretation of dendritic morphology

A detailed morphometric analysis of a Lucifer yellow-filled Cb amacrine cell was undertaken to provide raw data for the construction of a neuronal cable model. The cable model was employed to determine whether distal input-output regions of dendrites were electrically isolated from the soma and each other. Calculations of steady state electrotonic current spread suggested reasonable electrical communication between cell body and dendrites. In particular, the centripetal voltage attenuation revealed that a synaptic signal introduced at the distal end of the equivalent dendrite could spread passively along the dendrite and reach the soma with little loss in amplitude. A functional interpretation of this results could favour a postsynaptic rather than a presynaptic scheme for the operation of directional selectivity in the rabbit retina. On the other hand, dendrites of starburst amacrine cells process information electrotonically with a bias towards the centrifugal direction and for a restricted range of membrane resistance values the voltage attenuation in the centripetal direction suggests that the action of these dendrites can be confined locally. A functional interpretation of this result favours a presynaptic version of Vaney's cotransmission model which attempts to explain how the neural network of starburst amacrine cells might account for directionally selective responses observed in the rabbit retina.     

The capabilities and limitations of conductance-based compartmental neuron models with reduced branched or unbranched morphologies and active dendrites

Conductance-based neuron models are frequently employed to study the dynamics of biological neural networks. For speed and ease of use, these models are often reduced in morphological complexity. Simplified dendritic branching structures may process inputs differently than full branching structures, however, and could thereby fail to reproduce important aspects of biological neural processing. It is not yet well understood which processing capabilities require detailed branching structures. Therefore, we analyzed the processing capabilities of full or partially branched reduced models. These models were created by collapsing the dendritic tree of a full morphological model of a globus pallidus (GP) neuron while preserving its total surface area and electrotonic length, as well as its passive and active parameters. Dendritic trees were either collapsed into single cables (unbranched models) or the full complement of branch points was preserved (branched models). Both reduction strategies allowed us to compare dynamics between all models using the same channel density settings. Full model responses to somatic inputs were generally preserved by both types of reduced model while dendritic input responses could be more closely preserved by branched than unbranched reduced models. However, features strongly influenced by local dendritic input resistance, such as active dendritic sodium spike generation and propagation, could not be accurately reproduced by any reduced model. Based on our analyses, we suggest that there are intrinsic differences in processing capabilities between unbranched and branched models. We also indicate suitable applications for different levels of reduction, including fast searches of full model parameter space.     

Equivalence of branched and unbranched Michaelian pathways concerning periodic signal transmission

Sinusoidal oscillation transmission through branched metabolic pathways is studied. Two systems are analyzed, which are composed of two convergent reaction branches and differ in the length of one of them. Linear kinetics is assumed first. Michaelis-Menten enzymes are then considered by using previous results that suggest their behavior with respect to propagation of oscillations is close to linearity around the mean input flux. As a result, there exist ways to modulate the activity of the enzymes so that propagation is equivalent for branched and specific unbranched pathways. Cells may have taken advantage of such a possibility in cases where oscillations have a biological role.     

An analysis of a dendritic neuron model with an active membrane site

We formulate and analyze a mathematical model that couples an idealized dendrite to an active boundary site to investigate the nonlinear interaction between these passive and active membrane patches. The active site is represented mathematically as a nonlinear boundary condition to a passive cable equation in the form of a space-clamped FitzHugh-Nagumo (FHN) equation. We perform a bifurcation analysis for both steady and periodic perturbation at the active site. We first investigate the uncoupled space-clamped FHN equation alone and find that for periodic perturbation a transition from phase locked (periodic) to phase pulling (quasiperiodic) solutions exist. For the model coupling a passive cable with a FHN active site at the boundary, we show for steady perturbation that the interval for repetitive firing is a subset of the interval for the space-clamped case and shrinks to zero for strong coupling. The firing rate at the active site decreases as the coupling strength increases. For periodic perturbation we show that the transition from phase locked to phase pulling solutions is also dependent on the coupling strength.This work was supported in part by NSF Grants MCS 83-00562 and MDS 85-01535     

RNA editing in hepatitis delta virus genotype III requires a branched double-hairpin RNA structure

RNA editing at the amber/W site plays a central role in the replication scheme of hepatitis delta virus (HDV), allowing the virus to produce two functionally distinct forms of the sole viral protein, hepatitis delta antigen (HDAg), from the same open reading frame. Editing is carried out by a cellular activity known as ADAR (adenosine deaminase), which acts on RNA substrates that are at least partially double stranded. In HDV genotype I, editing requires a highly conserved base-paired structure that occurs within the context of the unbranched rod structure characteristic of HDV RNA. This base-paired structure is disrupted in the unbranched rod of HDV genotype III, which is the most distantly related of the three known HDV genotypes and is associated with the most severe disease. Here I show that RNA editing in HDV genotype III requires a branched double-hairpin structure that deviates substantially from the unbranched rod structure, involving the rearrangement of nearly 80 bp. The structure includes a UNCG RNA tetraloop, a highly stable structural motif frequently involved in the folding of large RNAs such as rRNA. The double-hairpin structure is required for editing, and hence for virion formation, but not for HDV RNA replication, which requires the unbranched rod structure. HDV genotype III thus relies on a dynamic conformational switch between the two different RNA structures: the unbranched rod characteristic of HDV RNA and a branched double-hairpin structure that is required for RNA editing. The different mechanisms of editing in genotypes I and III underscore their functional differences and may be related to pathogenic differences as well.     

Fine structure of antennal sensilla coeloconica of culicine mosquitoes

The sensilla coeloconica (pegs in pits) previously mis-identified as campaniform organs, at the tip of the antennae of female Aedes aegypti L. and Culexpipiens (L.) are described. Each sensillum is innervated by three bipolar neurons: the dendrites of two are unbranched whereas the distal portion of the third is folded into tightly packed lamellae. One unbranched dendrite extends to the tip of the peg and the other ends near the base of the peg. The lamellae-bearing dendrite terminates 4-5 μ beneath the base of the peg. Chemo- and thermoreception are the proposed functions for the sensillum.     

Electron-microscopic localization of type II,IX, and V collagen in the organ of Corti of the gerbil

Summary The presence of types II, IX and V collagen was probed in the organ of Corti of the adult gerbil cochlea by use of immunocytochemistry at the light- and electron-microscopic levels. Type II collagen is found in the connective tissues of the osseous spiral lamina and spiral limbus. In the region of the sensory hair cells it is present in the tectorial membrane and antibodies bind to the thick unbranched radial fibers. Type IX collagen co-localizes with type II collagen in the tectorial membrane, where antibodies bind to the thick unbranched radial fibers. Type V collagen is present in the connective tissue of the spiral limbus, the osseous spiral lamina, the eighth nerve, and the tectorial membrane. In the tectorial membrane, the staining with antibodies to type V collagen is more diffuse than that seen for types II and IX collagen and antibodies to type V bind to the thin, highly branched fibers in which the thick fibers are embedded. The results indicate that collagens characteristic of cartilage are localized in the organ of Corti. Within the tectorial membrane, types II and IX collagen form heterotypic thick fibers embedded in a reticular network of type V collagen fibers. These collagens form a highly structured matrix which contributes to the rigidity of the tectorial membrane and allow it to withstand the physical stresses associated with transmission of the stimuli necessary for sensory transduction.