Inheritance of steroid-independent male sexual behavior in male offspring of B6D2F1 mice

The importance of gonadal steroids in modulating male sexual behavior is well established. Individual differences in male sexual behavior, independent of gonadal steroids, are prevalent across a wide range of species, including man. However, the genetic mechanisms underlying steroid-independent male sexual behavior are poorly understood. A high proportion of B6D2F1 hybrid male mice demonstrates steroid-independent male sexual behavior (identified as “maters”), providing a mouse model that opens up avenues of investigation into the mechanisms regulating male sexual behavior in the absence of gonadal hormones. Recent studies have revealed several proteins that play a significant factor in regulating steroid-independent male sexual behavior in B6D2F1 male mice, including amyloid precursor protein (APP), tau, and synaptophysin. The specific goals of our study were to determine whether steroid-independent male sexual behavior was a heritable trait by determining if it was dependent upon the behavioral phenotype of the B6D2F1 sire, and whether the differential expression of APP, tau, and synaptophysin in the medial preoptic area found in the B6D2F1 sires that did and did not mate after gonadectomy was similar to those found in their male offspring. After adult B6D2F1 male mice were bred with C57BL/6J female mice, they and their male offspring (BXB₁) were orchidectomized and identified as either maters or “non-maters”. A significant proportion of the BXB₁ maters was sired only from B6D2F1 maters, indicating that the steroid-independent male sexual behavior behavioral phenotype of the B6D2F1 hybrid males, when crossed with C57BL/6J female mice, is inherited by their male offspring. Additionally, APP, tau, and synaptophysin were elevated in in the medial preoptic area in both the B6D2F1 and BXB₁ maters relative to the B6D2F1 and BXB₁ non-maters, respectively, suggesting a potential genetic mechanism for the inheritance of steroid-independent male sexual behavior.     

Is tau ready for admission to the prion club?

Aggregation-prone proteins associated with neurodegenerative disease, such as α synuclein and β amyloid, now appear to share key prion-like features with mammalian prion protein, such as the ability to recruit normal proteins to aggregates and to translocate between neurons. These features may shed light on the genesis of stereotyped lesion development patterns in conditions such as Alzheimer disease and Lewy Body dementia. We discuss the qualifications of tau protein as a possible “prionoid” mediator of lesion spread based on recent characterizations of the secretion, uptake and transneuronal transfer of human tau isoforms in a variety of tauopathy models, and in human patients. In particular, we consider (1) the possibility that prionoid behavior of misprocessed tau in neurodegenerative disease may involve other aggregation-prone proteins, including PrP itself, and (2) whether “prionlike” tau lesion propagation might include mechanisms other than protein-protein templating.     

Steroid-independent male sexual behavior in B6D2F2 male mice

It is well established that male sexual behavior (MSB) is regulated by gonadal steroids; however, individual differences in MSB, independent of gonadal steroids, are prevalent across a wide range of species, and further investigation is necessary to advance our understanding of steroid-independent MSB. Studies utilizing B6D2F1 hybrid male mice in which a significant proportion retain MSB after long-term orchidectomy, identified as steroid-independent-maters (SI-maters), have begun to unravel the genetic underpinnings of steroid-independent MSB. A recent study demonstrated that steroid-independent MSB is a heritable behavioral phenotype that is mainly passed down from B6D2F1 hybrid SI-maters when crossed with C57BL6J female mice. To begin to uncover whether the strain of the dam plays a role in the inheritance of steroid-independent MSB, B6D2F1 hybrid females were crossed with B6D2F1 hybrid males. While the present study confirms the finding that steroid-independent MSB is a heritable behavioral phenotype and that SI-mater sires are more likely to pass down some components of MSB than SI-non-maters to their offspring, it also reveals that the B6D2F2 male offspring that were identified as SI-maters that displayed the full repertoire of steroid-independent MSB had the same probability of being sired from either a B6D2F1 SI-mater or SI-non-mater. These results, in conjunction with previous findings, indicate that the specific chromosomal loci pattern that codes for steroid-independent MSB in the B6D2F2 male offspring may result regardless of whether the father was a SI-mater or SI-non-mater, and that the maternal strain may be an important factor in the inheritance of steroid-independent MSB.     

Regioselective approach to colchiceine tropolone ring functionalization at C(9) and C(10) yielding new anticancer hybrid derivatives containing heterocyclic structural motifs

The influence of base type, temperature, and solvent on regioselective C(9)/C(10) “click” modifications within the tropolone ring of colchiceine (2) is investigated. New ether derivatives of 2, bearing alkyne, azide, vinyl, or halide aryl groups enable assembly of the alkaloid part with heterocycles or important biomolecules such as saccharides, geldanamycin or AZT into hybrid scaffolds by dipolar cycloaddition (CuAAC) or Heck reaction. Compared to colchicine (1) or colchiceine (2), ether congeners, as e.g. 3e [IC₅₀s_(3e) ∼ 0.9 nM], show improved or similar anticancer effects, whereby the bulkiness of the substituents and the substitution pattern of the tropolone proved to be essential. Biological studies reveal that expanding the ether arms by terminal basic heterocycles as quinoline or pyridine, decreases the toxicity in HDF cells at high anticancer potency (IC₅₀s ∼ 1–2 nM). Docking of ether and hybrid derivatives into the colchicine pocket of α_GTP/β tubulin dimers reveals a relationship between the favourable binding mode and the attractive anticancer potency.     

Subtle Population Genetic Structure in Yelloweye Rockfish (Sebastes ruberrimus) Is Consistent with a Major Oceanographic Division in British Columbia,Canada

The boundaries between oceanographic domains often function as dispersal barriers for many temperate marine species with a dispersive pelagic larval phase. Yelloweye rockfish (Sebastes ruberrimus, YR) are widely distributed across the northeastern Pacific Ocean, inhabiting coastal rocky reefs from the Aleutian Islands in Alaska through southern California. This species exhibits an extended pelagic larval duration and has the capacity for long distance larval transport. We assayed 2,862 YR individuals from 13 general areas in the northeast Pacific Ocean for allelic variation at nine microsatellite loci. Bayesian model-based clustering analyses grouped individuals from the Strait of Georgia (SG) into a distinct genetic cluster, while individuals from outer coastal water locations (OCLs) were partitioned equally across two genetic clusters, including the cluster associated with the SG fish. Pairwise F_ST values were consistently an order of magnitude higher for comparisons between the SG and OCLs than they were for all OCL-OCL comparisons (∼0.016 vs. ∼0.001). This same pattern was observed across two time points when individuals were binned into an “old” and “young” group according to birth year (old: ∼0.020 vs. 0.0003; young: ∼0.020 vs. ∼0.004). Additionally, mean allelic richness was markedly lower within the SG compared to the OCLs (8.00 vs. 10.54–11.77). These results indicate that the Strait of Georgia “deep-basin” estuary oceanographic domain acts as a dispersal barrier from the outer coastal waters via the Juan de Fuca Strait. Alternatively, selection against maladapted dispersers across this oceanographic transition may underlie the observed genetic differentiation between the Georgia basin and the outer coastal waters, and further work is needed to confirm the SG-OCL divide acts as a barrier to larval dispersal.     

The Oxytricha trifallax Macronuclear Genome: A Complex Eukaryotic Genome with 16,000 Tiny Chromosomes

The macronuclear genome of the ciliate Oxytricha trifallax displays an extreme and unique eukaryotic genome architecture with extensive genomic variation. During sexual genome development, the expressed, somatic macronuclear genome is whittled down to the genic portion of a small fraction (∼5%) of its precursor “silent” germline micronuclear genome by a process of “unscrambling” and fragmentation. The tiny macronuclear “nanochromosomes” typically encode single, protein-coding genes (a small portion, 10%, encode 2–8 genes), have minimal noncoding regions, and are differentially amplified to an average of ∼2,000 copies. We report the high-quality genome assembly of ∼16,000 complete nanochromosomes (∼50 Mb haploid genome size) that vary from 469 bp to 66 kb long (mean ∼3.2 kb) and encode ∼18,500 genes. Alternative DNA fragmentation processes ∼10% of the nanochromosomes into multiple isoforms that usually encode complete genes. Nucleotide diversity in the macronucleus is very high (SNP heterozygosity is ∼4.0%), suggesting that Oxytricha trifallax may have one of the largest known effective population sizes of eukaryotes. Comparison to other ciliates with nonscrambled genomes and long macronuclear chromosomes (on the order of 100 kb) suggests several candidate proteins that could be involved in genome rearrangement, including domesticated MULE and IS1595-like DDE transposases. The assembly of the highly fragmented Oxytricha macronuclear genome is the first completed genome with such an unusual architecture. This genome sequence provides tantalizing glimpses into novel molecular biology and evolution. For example, Oxytricha maintains tens of millions of telomeres per cell and has also evolved an intriguing expansion of telomere end-binding proteins. In conjunction with the micronuclear genome in progress, the O. trifallax macronuclear genome will provide an invaluable resource for investigating programmed genome rearrangements, complementing studies of rearrangements arising during evolution and disease.     

Static and Dynamic Factors Limit Chromosomal Replication Complexity in Escherichia coli,Avoiding Dangers of Runaway Overreplication

We define chromosomal replication complexity (CRC) as the ratio of the copy number of the most replicated regions to that of unreplicated regions on the same chromosome. Although a typical CRC of eukaryotic or bacterial chromosomes is 2, rapidly growing Escherichia coli cells induce an extra round of replication in their chromosomes (CRC = 4). There are also E. coli mutants with stable CRC∼6. We have investigated the limits and consequences of elevated CRC in E. coli and found three limits: the “natural” CRC limit of ∼8 (cells divide more slowly); the “functional” CRC limit of ∼22 (cells divide extremely slowly); and the “tolerance” CRC limit of ∼64 (cells stop dividing). While the natural limit is likely maintained by the eclipse system spacing replication initiations, the functional limit might reflect the capacity of the chromosome segregation system, rather than dedicated mechanisms, and the tolerance limit may result from titration of limiting replication factors. Whereas recombinational repair is beneficial for cells at the natural and functional CRC limits, we show that it becomes detrimental at the tolerance CRC limit, suggesting recombinational misrepair during the runaway overreplication and giving a rationale for avoidance of the latter.     

Human Tau Isoforms Assemble into Ribbon-like Fibrils That Display Polymorphic Structure and Stability

Fibrous aggregates of Tau protein are characteristic features of Alzheimer disease. We applied high resolution atomic force and EM microscopy to study fibrils assembled from different human Tau isoforms and domains. All fibrils reveal structural polymorphism; the “thin twisted” and “thin smooth” fibrils resemble flat ribbons (cross-section ∼10 × 15 nm) with diverse twist periodicities. “Thick fibrils” show periodicities of ∼65–70 nm and thicknesses of ∼9–18 nm such as routinely reported for “paired helical filaments” but structurally resemble heavily twisted ribbons. Therefore, thin and thick fibrils assembled from different human Tau isoforms challenge current structural models of paired helical filaments. Furthermore, all Tau fibrils reveal axial subperiodicities of ∼17–19 nm and, upon exposure to mechanical stress or hydrophobic surfaces, disassemble into uniform fragments that remain connected by thin thread-like structures (∼2 nm). This hydrophobically induced disassembly is inhibited at enhanced electrolyte concentrations, indicating that the fragments resemble structural building blocks and the fibril integrity depends largely on hydrophobic and electrostatic interactions. Because full-length Tau and repeat domain constructs assemble into fibrils of similar thickness, the “fuzzy coat” of Tau protein termini surrounding the fibril axis is nearly invisible for atomic force microscopy and EM, presumably because of its high flexibility.     

Genetically engineered MAPT 10+16 mutation causes pathophysiological excitability of human iPSC-derived neurons related to 4R tau-induced dementia

Human iPSC lines represent a powerful translational model of tauopathies. We have recently described a pathophysiological phenotype of neuronal excitability of human cells derived from the patients with familial frontotemporal dementia and parkinsonism (FTDP-17) caused by the MAPT 10+16 splice-site mutation. This mutation leads to the increased splicing of 4R tau isoforms. However, the role of different isoforms of tau protein in initiating neuronal dementia-related dysfunction, and the causality between the MAPT 10+16 mutation and altered neuronal activity have remained unclear. Here, we employed genetically engineered cells, in which the IVS10+16 mutation was introduced into healthy donor iPSCs to increase the expression of 4R tau isoform in exon 10, aiming to explore key physiological traits of iPSC-derived MAPT IVS10+16 neurons using patch-clamp electrophysiology and multiphoton fluorescent imaging techniques. We found that during late in vitro neurogenesis (from ~180 to 230 days) iPSC-derived cortical neurons of the control group (parental wild-type tau) exhibited membrane properties compatible with “mature” neurons. In contrast, MAPT IVS10+16 neurons displayed impaired excitability, as reflected by a depolarized resting membrane potential, an increased input resistance, and reduced voltage-gated Na⁺- and K⁺-channel-mediated currents. The mutation changed the channel properties of fast-inactivating Na_v and decreased the Na_v1.6 protein level. MAPT IVS10+16 neurons exhibited reduced firing accompanied by a changed action potential waveform and severely disturbed intracellular Ca²⁺ dynamics, both in the soma and dendrites, upon neuronal depolarization. These results unveil a causal link between the MAPT 10+16 mutation, hence overproduction of 4R tau, and a dysfunction of human cells, identifying a biophysical basis of changed neuronal activity in 4R tau-triggered dementia. Our study lends further support to using iPSC lines as a suitable platform for modelling tau-induced human neuropathology in vitro.Subject terms: Mechanisms of disease, Cellular neuroscience, Dementia     

Gonadal Steroid Hormones and Hypothalamic Opioid Circuitry

Endogenous opioid peptides derived from several gene families are localized within hypothalamic regions known to be involved in the regulation of reproduction. For example, the proenkephalin gene products, met- and leu-enkephalin, and the proopiomelanocortin (POMC) gene product, β-endorphin, are found in the rat medial preoptic area (MPOA). Moreover, the expression of these peptides and their receptors varies across the estrous cycle in the female rat. We have examined the gonadal steroid regulation of μ-opiate receptors and opioid peptides in the MPOA, and POMC mRNA expression in neurons that innervate the MPOA. μ-Opiate receptors in the MPOA are sexually dimorphic and gonadal steroid hormone-dependent. Hormonal priming of ovariectomized rats with estrogen and progesterone (P) upregulates MPOA μ-receptors 27, but not 3, hr after P treatment. Inhibition of protein synthesis during the first 6 hr after P prevents receptor upregulation, The density of β-endorphin fibers in the MPOA also increases following hormone treatment, and POMC mRNA expression in neurons that innervate the MPOA is induced by hormone treatment beginning 13 hr after P treatment. This delayed response might be ubiquitous among POMC neurons, as those innervating the median eminence also exhibit increased POMC mRNA expression along a similar time course. The results suggest that hormonal feedback regulates opioid peptides which act at μ-receptors in the MPOA to influence reproductive behavior and cyclicity. These opioid functions represent an important component in the complex regulatory processes which control reproduction.     

Infection Density Dynamics of the Citrus Greening Bacterium “Candidatus Liberibacter asiaticus” in Field Populations of the Psyllid Diaphorina citri and Its Relevance to the Efficiency of Pathogen Transmission to Citrus Plants

Huanglongbing, or citrus greening, is a devastating disease of citrus plants recently spreading worldwide, which is caused by an uncultivable bacterial pathogen, “Candidatus Liberibacter asiaticus,” and vectored by a phloem-sucking insect, Diaphorina citri. We investigated the infection density dynamics of “Ca. Liberibacter asiaticus” in field populations of D. citri with experiments using field-collected insects to address how “Ca. Liberibacter asiaticus” infection density in the vector insect is relevant to pathogen transmission to citrus plants. Of 500 insects continuously collected from “Ca. Liberibacter asiaticus”-infected citrus trees with pathological symptoms in the spring and autumn of 2009, 497 (99.4%) were “Ca. Liberibacter asiaticus” positive. The infections were systemic across head-thorax and abdomen, ranging from 10³ to 10⁷ bacteria per insect. In spring, the infection densities were low in March, at ∼10³ bacteria per insect, increasing up to 10⁶ to 10⁷ bacteria per insect in April and May, and decreasing to 10⁵ to 10⁶ bacteria per insect in late May, whereas the infection densities were constantly ∼10⁶ to 10⁷ bacteria per insect in autumn. Statistical analysis suggested that several factors, such as insect sex, host trees, and collection dates, may be correlated with “Ca. Liberibacter asiaticus” infection densities in field D. citri populations. Inoculation experiments with citrus seedlings using field-collected “Ca. Liberibacter asiaticus”-infected insects suggested that (i) “Ca. Liberibacter asiaticus”-transmitting insects tend to exhibit higher infection densities than do nontransmitting insects, (ii) a threshold level (∼10⁶ bacteria per insect) of “Ca. Liberibacter asiaticus” density in D. citri is required for successful transmission to citrus plants, and (iii) D. citri attaining the threshold infection level transmits “Ca. Liberibacter asiaticus” to citrus plants in a stochastic manner. These findings provide valuable insights into understanding, predicting, and controlling this notorious citrus pathogen.     

Characterization of the Denitrification-Associated Phosphorus Uptake Properties of “Candidatus Accumulibacter phosphatis” Clades in Sludge Subjected to Enhanced Biological Phosphorus Removal

To characterize the denitrifying phosphorus (P) uptake properties of “Candidatus Accumulibacter phosphatis,” a sequencing batch reactor (SBR) was operated with acetate. The SBR operation was gradually acclimated from anaerobic-oxic (AO) to anaerobic-anoxic-oxic (A2O) conditions by stepwise increases of nitrate concentration and the anoxic time. The communities of “Ca. Accumulibacter” and associated bacteria at the initial (AO) and final (A2O) stages were compared using 16S rRNA and polyphosphate kinase genes and using fluorescence in situ hybridization (FISH). The acclimation process led to a clear shift in the relative abundances of recognized “Ca. Accumulibacter” subpopulations from clades IIA > IA > IIF to clades IIC > IA > IIF, as well as to increases in the abundance of other associated bacteria (Dechloromonas [from 1.2% to 19.2%] and “Candidatus Competibacter phosphatis” [from 16.4% to 20.0%]), while the overall “Ca. Accumulibacter” abundance decreased (from 55.1% to 29.2%). A series of batch experiments combined with FISH/microautoradiography (MAR) analyses was performed to characterize the denitrifying P uptake properties of the “Ca. Accumulibacter” clades. In FISH/MAR experiments using slightly diluted sludge (∼0.5 g/liter), all “Ca. Accumulibacter” clades successfully took up phosphorus in the presence of nitrate. However, the “Ca. Accumulibacter” clades showed no P uptake in the presence of nitrate when the sludge was highly diluted (∼0.005 g/liter); under these conditions, reduction of nitrate to nitrite did not occur, whereas P uptake by “Ca. Accumulibacter” clades occurred when nitrite was added. These results suggest that the “Ca. Accumulibacter” cells lack nitrate reduction capabilities and that P uptake by “Ca. Accumulibacter” is dependent upon nitrite generated by associated nitrate-reducing bacteria such as Dechloromonas and “Ca. Competibacter.”     

Proinflammatory Cytokines Stimulate Mitochondrial Superoxide Flashes in Articular Chondrocytes In Vitro and In Situ

Objective

Mitochondria play important roles in many types of cells. However, little is known about mitochondrial function in chondrocytes. This study was undertaken to explore possible role of mitochondrial oxidative stress in inflammatory response in articular chondrocytes.

Methods

Chondrocytes and cartilage explants were isolated from wild type or transgenic mice expressing the mitochondrial superoxide biosensor - circularly permuted yellow fluorescent protein (cpYFP). Cultured chondrocytes or cartilage explants were incubated in media containing interleukin-1β (10 ng/ml) or tumor necrosis factor-α (10 ng/ml) to stimulate an inflammatory response. Mitochondrial imaging was carried out by confocal and two-photon microscopy. Mitochondrial oxidative status was evaluated by “superoxide flash” activity recorded with time lapse scanning.

Results

Cultured chondrocytes contain abundant mitochondria that show active motility and dynamic morphological changes. In intact cartilage, mitochondrial abundance as well as chondrocyte density declines with distance from the surface. Importantly, sudden, bursting superoxide-producing events or “superoxide flashes” occur at single-mitochondrion level, accompanied by transient mitochondrial swelling and membrane depolarization. The superoxide flash incidence in quiescent chondrocytes was ∼4.5 and ∼0.5 events/1000 µm²*100 s in vitro and in situ, respectively. Interleukin-1β or tumor necrosis factor-α stimulated mitochondrial superoxide flash activity by 2-fold in vitro and 5-fold in situ, without altering individual flash properties except for reduction in spatial size due to mitochondrial fragmentation.

Conclusions

The superoxide flash response to proinflammatory cytokine stimulation in vitro and in situ suggests that chondrocyte mitochondria are a significant source of cellular oxidants and are an important previously under-appreciated mediator in inflammatory cartilage diseases.     

Characterization of SLCO5A1/OATP5A1, a Solute Carrier Transport Protein with Non-Classical Function

Organic anion transporting polypeptides (OATP/SLCO) have been identified to mediate the uptake of a broad range of mainly amphipathic molecules. Human OATP5A1 was found to be expressed in the epithelium of many cancerous and non-cancerous tissues throughout the body but protein characterization and functional analysis have not yet been performed. This study focused on the biochemical characterization of OATP5A1 using Xenopus laevis oocytes and Flp-In T-REx-HeLa cells providing evidence regarding a possible OATP5A1 function. SLCO5A1 is highly expressed in mature dendritic cells compared to immature dendritic cells (∼6.5-fold) and SLCO5A1 expression correlates with the differentiation status of primary blood cells. A core- and complex- N-glycosylated polypeptide monomer of ∼105 kDa and ∼130 kDa could be localized in intracellular membranes and on the plasma membrane, respectively. Inducible expression of SLCO5A1 in HeLa cells led to an inhibitory effect of ∼20% after 96 h on cell proliferation. Gene expression profiling with these cells identified immunologically relevant genes (e.g. CCL20) and genes implicated in developmental processes (e.g. TGM2). A single nucleotide polymorphism leading to the exchange of amino acid 33 (L→F) revealed no differences regarding protein expression and function. In conclusion, we provide evidence that OATP5A1 might be a non-classical OATP family member which is involved in biological processes that require the reorganization of the cell shape, such as differentiation and migration.     

Genetic Basis of a Violation of Dollo’s Law: Re-Evolution of Rotating Sex Combs in Drosophila bipectinata

Phylogenetic analyses suggest that violations of “Dollo’s law”—that is, re-evolution of lost complex structures—do occur, albeit infrequently. However, the genetic basis of such reversals has not been examined. Here, we address this question using the Drosophila sex comb, a recently evolved, male-specific morphological structure composed of modified bristles. In some species, sex comb development involves only the modification of individual bristles, while other species have more complex “rotated” sex combs that are shaped by coordinated migration of epithelial tissues. Rotated sex combs were lost in the ananassae species subgroup and subsequently re-evolved, ∼12 million years later, in Drosophila bipectinata and its sibling species. We examine the genetic basis of the differences in sex comb morphology between D. bipectinata and D. malerkotliana, a closely related species with a much simpler sex comb representing the ancestral condition. QTL mapping reveals that >50% of this difference is controlled by one chromosomal inversion that covers ∼5% of the genome. Several other, larger inversions do not contribute appreciably to the phenotype. This genetic architecture suggests that rotating sex combs may have re-evolved through changes in relatively few genes. We discuss potential developmental mechanisms that may allow lost complex structures to be regained.     

Multiple Signals Converge on a Differentiation MAPK Pathway

An important emerging question in the area of signal transduction is how information from different pathways becomes integrated into a highly coordinated response. In budding yeast, multiple pathways regulate filamentous growth, a complex differentiation response that occurs under specific environmental conditions. To identify new aspects of filamentous growth regulation, we used a novel screening approach (called secretion profiling) that measures release of the extracellular domain of Msb2p, the signaling mucin which functions at the head of the filamentous growth (FG) MAPK pathway. Secretion profiling of complementary genomic collections showed that many of the pathways that regulate filamentous growth (RAS, RIM101, OPI1, and RTG) were also required for FG pathway activation. This regulation sensitized the FG pathway to multiple stimuli and synchronized it to the global signaling network. Several of the regulators were required for MSB2 expression, which identifies the MSB2 promoter as a target “hub” where multiple signals converge. Accessibility to the MSB2 promoter was further regulated by the histone deacetylase (HDAC) Rpd3p(L), which positively regulated FG pathway activity and filamentous growth. Our findings provide the first glimpse of a global regulatory hierarchy among the pathways that control filamentous growth. Systems-level integration of signaling circuitry is likely to coordinate other regulatory networks that control complex behaviors.     

Transient Potentials in Dendritic Systems of Arbitrary Geometry

A simple graphical calculus is developed that generates analytic solutions for membrane potential transforms at any point on the dendritic tree of neurons with arbitrary dendritic geometries, in response to synaptic “current” inputs. Such solutions permit the computation of transients in neurons with arbitrary geometry and may facilitate analysis of the role of dendrites in such cells.