Nonattacking Queens in a Rectangular Strip

The function that counts the number of ways to place nonattacking identical chess or fairy chess pieces in a rectangular strip of fixed height and variable width, as a function of the width, is a piecewise polynomial which is eventually a polynomial and whose behavior can be described in some detail. We deduce this by converting the problem to one of counting lattice points outside an affinographic hyperplane arrangement, which Forge and Zaslavsky solved by means of weighted integral gain graphs. We extend their work by developing both generating functions and a detailed analysis of deletion and contraction for weighted integral gain graphs. For chess pieces we find the asymptotic probability that a random configuration is nonattacking, and we obtain exact counts of nonattacking configurations of small numbers of queens, bishops, knights, and nightriders.Comment: 21 pages, 3 figures, preprint of published version copyright Springer Basel AG 2011, Published online February 15, 2011, submitted March 15, 200

Modularity map of the network of human cell differentiation

Cell differentiation in multicellular organisms is a complex process whose mechanism can be understood by a reductionist approach, in which the individual processes that control the generation of different cell types are identified. Alternatively, a large scale approach in search of different organizational features of the growth stages promises to reveal its modular global structure with the goal of discovering previously unknown relations between cell types. Here we sort and analyze a large set of scattered data to construct the network of human cell differentiation (NHCD) based on cell types (nodes) and differentiation steps (links) from the fertilized egg to a crying baby. We discover a dynamical law of critical branching, which reveals a fractal regularity in the modular organization of the network, and allows us to observe the network at different scales. The emerging picture clearly identifies clusters of cell types following a hierarchical organization, ranging from sub-modules to super-modules of specialized tissues and organs on varying scales. This discovery will allow one to treat the development of a particular cell function in the context of the complex network of human development as a whole. Our results point to an integrated large-scale view of the network of cell types systematically revealing ties between previously unrelated domains in organ functions.Comment: 32 pages, 7 figure

Defining the Cellular Environment in the Organ of Corti following Extensive Hair Cell Loss: A Basis for Future Sensory Cell Replacement in the Cochlea

Background: Following the loss of hair cells from the mammalian cochlea, the sensory epithelium repairs to close the lesions but no new hair cells arise and hearing impairment ensues. For any cell replacement strategy to be successful, the cellular environment of the injured tissue has to be able to nurture new hair cells. This study defines characteristics of the auditory sensory epithelium after hair cell loss. Methodology/Principal Findings: Studies were conducted in C57BL/6 and CBA/Ca mice. Treatment with an aminoglycoside-diuretic combination produced loss of all outer hair cells within 48 hours in both strains. The subsequent progressive tissue re-organisation was examined using immunohistochemistry and electron microscopy. There was no evidence of significant de-differentiation of the specialised columnar supporting cells. Kir4.1 was down regulated but KCC4, GLAST, microtubule bundles, connexin expression patterns and pathways of intercellular communication were retained. The columnar supporting cells became covered with non-specialised cells migrating from the outermost region of the organ of Corti. Eventually non-specialised, flat cells replaced the columnar epithelium. Flat epithelium developed in distributed patches interrupting regions of columnar epithelium formed of differentiated supporting cells. Formation of the flat epithelium was initiated within a few weeks post-treatment in C57BL/6 mice but not for several months in CBA/Ca’s, suggesting genetic background influences the rate of re-organisation

Systemic aminoglycosides are trafficked via endolymph into cochlear hair cells

Aminoglycoside antibiotics rapidly enter and kill cochlear hair cells via apical mechanoelectrical transduction (MET) channels in vitro. In vivo, it remains unknown whether systemically-administered aminoglycosides cross the blood-labyrinth barrier into endolymph and enter hair cells. Here we show, for the first time, that systemic aminoglycosides are trafficked across the blood-endolymph barrier and preferentially enter hair cells across their apical membranes. This trafficking route is predominant compared to uptake via hair cell basolateral membranes during perilymph infusion

Retention of progenitor cell phenotype in otospheres from guinea pig and mouse cochlea

Abstract\ud \ud Background\ud Culturing otospheres from dissociated organ of Corti is an appropriate starting point aiming at the development of cell therapy for hair cell loss. Although guinea pigs have been widely used as an excellent experimental model for studying the biology of the inner ear, the mouse cochlea has been more suitable for yielding otospheres in vitro. The aim of this study was to compare conditions and outcomes of otosphere suspension cultures from dissociated organ of Corti of either mouse or guinea pig at postnatal day three (P3), and to evaluate the guinea pig as a potential cochlea donor for preclinical cell therapy.\ud \ud \ud Methods\ud Organs of Corti were surgically isolated from P3 guinea pig or mouse cochlea, dissociated and cultivated under non-adherent conditions. Cultures were maintained in serum-free DMEM:F12 medium, supplemented with epidermal growth factor (EGF) plus either basic fibroblast growth factor (bFGF) or transforming growth factor alpha (TGFα). Immunofluorescence assays were conducted for phenotype characterization.\ud \ud \ud Results\ud The TGFα group presented a number of spheres significantly higher than the bFGF group. Although mouse cultures yielded more cells per sphere than guinea pig cultures, sox2 and nestin distributed similarly in otosphere cells from both organisms. We present evidence that otospheres retain properties of inner ear progenitor cells such as self-renewal, proliferation, and differentiation into hair cells or supporting cells.\ud \ud \ud Conclusions\ud Dissociated guinea pig cochlea produced otospheres in vitro, expressing sox2 and nestin similarly to mouse otospheres. Our data is supporting evidence for the presence of inner ear progenitor cells in the postnatal guinea pig. However, there is limited viability for these cells in neonatal guinea pig cochlea when compared to the differentiation potential observed for the mouse organ of Corti at the same developmental stage

On a Generalization of Zaslavsky's Theorem for Hyperplane Arrangements

We define arrangements of codimension-1 submanifolds in a smooth manifold which generalize arrangements of hyperplanes. When these submanifolds are removed the manifold breaks up into regions, each of which is homeomorphic to an open disc. The aim of this paper is to derive formulas that count the number of regions formed by such an arrangement. We achieve this aim by generalizing Zaslavsky's theorem to this setting. We show that this number is determined by the combinatorics of the intersections of these submanifolds.Comment: version 3: The title had a typo in v2 which is now fixed. Will appear in Annals of Combinatorics. Version. 2: 19 pages, major revision in terms of style and language, some results improved, contact information updated, final versio

A Protective Mechanism against Antibiotic-Induced Ototoxicity: Role of Prestin

Hearing loss or ototoxicity is one of the major side effects associated with the use of the antibiotics, particularly aminoglycosides (AGs), which are the most commonly used antibiotics worldwide. However, the molecular and cellular events involved in the antibiotic-induced ototoxicity remains unclear. In the present study, we test the possibility that prestin, the motor protein specifically expressed in the basolateral membrane of outer hair cells (OHCs) in the cochlea with electromotility responsible for sound amplification, may be involved in the process of AG-induced apoptosis in OHCs. Our results from both mice model and cultured cell line indicate a previously unexpected role of prestin, in mediating antibiotic-induced apoptosis, the effect of which is associated with its anion-transporting capacity. The observed downregulation of prestin mRNA prior to detectable apoptosis in OHCs and hearing loss in the antibiotic-treated mice is interesting, which may serve as a protective mechanism against hearing loss induced by AGs in the early stage

Cisplatin and Oxaliplatin Toxicity: Importance of Cochlear Kinetics as a Determinant for Ototoxicity

Background Cisplatin is a commonly used platinum anti-cancer drug. Regrettably cisplatin has dose-limiting ototoxic side effects, e.g. the drug can induce an irreversible hearing loss. The ototoxic mechanisms of cisplatin have not been elucidated in the human ear and no clinically useful oto-protectors are yet available. Cisplatin is a necessary part of many treatment regimes. Its beneficial therapeutic effects might be reduced if cisplatin was excluded from the treatment in order to protect the hearing function. In this work the ototoxic effects of cisplatin are studied with the aim to better understand the mechanisms behind the irreversible hearing loss induced by this drug. Oxaliplatin is a second generation platinum-derivative anti-cancer drug, free from ototoxic side effects in clinical practice. The effects of oxaliplatin on the inner ear have been studied in this work and the results are compared with cisplatin treatment. The two drugs differ regarding both anti-cancer effects and side effects, which could be attributed to differences in pharmacokinetic factors, cellular uptake and apoptotic mechanisms. The thioredoxin redox system with the enzyme thioredoxin reductase (TrxR) was studied in cochleae due to a suggested DNA-independent apoptotic mechanism of the hair cells. The cochlear pharmacokinetics of cisplatin was assessed and the transport protein organic cation transporter 2 (OCT2) was studied in relation to the ototoxic effect of cisplatin. Material and methods Cultured human colon carcinoma cells and cell cultures of rat organ of Corti were used for apoptosis studies in vitro following exposure to cisplatin and oxaliplatin. Cisplatin and oxaliplatin were administered i.v. to guinea pigs, followed by in vivo sampling of blood, cerebrospinal fluid (CSF) and scala tympani (ST) perilymph. Liquid chromatography with post-column derivatization was used to determine the concentration of parent drug in the samples. Electrophysiological hearing thresholds and the loss of hair cells were assessed to evaluate their ototoxic effects. Phenformin, a potential blocker of OCT2 was administered and the ototoxic side effect of cisplatin was evaluated. For immunohistochemical studies, cochlea from rat, guinea pig and pig were used, where TrxR and OCT2 were evaluated in the cochlea. TrxR-assays were used to measure the TrxR activity in cochlear tissue, both in vivo and in vitro. Results The results from the in vitro studies showed that addition of either cisplatin or oxaliplatin to the culture medium in organ of Corti cell cultures caused a similar amount of outer hair cell loss and inhibition of TrxR activity. Cisplatin exposure to cultured human colon carcinoma cells also reduced the activity of TrxR. The results from the in vivo studies showed that a considerable concentration of cisplatin was present in ST perilymph as compared with weak concentrations of oxaliplatin after high dose oxaliplatin i.v. Ten minutes after cisplatin administration, its concentration in ST perilymph was 4-fold higher in the basal turn of the cochlea as compared to the apex. Cisplatin could be analysed in ST perilymph for up to 120 min. Phenformin i.v. did not reduce the ototoxic side-effect of cisplatin. Positive immunoreactivity to TrxR was evident in both hair cells and spiral ganglion cells. Futhermore, OCT2 was expressed in the supporting cells of organ of Corti and in the spiral ganglion cells. Conclusion The transport of cisplatin to the vulnerable cells of hearing seems to be of major importance for the ototoxic effects. An early high concentration of cisplatin in the base of the cochlea and delayed elimination of cisplatin from ST perilymph may be related to the cisplatin-induced loss of outer hair cells in the basal turn of the cochlea. Cisplatin and oxaliplatin both cause similar ototoxic effects when the organ of Corti is directly exposed in vitro. The thioredoxin redox system with the TrxR enzyme may well play a critical role in cisplatininduced ototoxicity. The presence of OCT2 in the supporting cells indicates that this transport protein is primarily not involved in the uptake of cisplatin from the systemic circulation but rather from the deeper compartments of the cochlea. The knowledge elicited in this work will hopefully suggest objectives for further studies in order to develop oto-protective treatments to preserve the hearing of cisplatin treated patients

Identification of a Novel Synaptic Protein, TMTC3, Involved in Periventricular Nodular Heterotopia with Intellectual Disability and Epilepsy

Defects in neuronal migration cause brain malformations, which are associated with intellectual disability (ID) and epilepsy. Using exome sequencing, we identified compound heterozygous variants (p.Arg71His and p. Leu729ThrfsTer6) in TMTC3, encoding transmembrane and tetratricopeptide repeat containing 3, in four siblings with nocturnal seizures and ID. Three of the four siblings have periventricular nodular heterotopia (PVNH), a common brain malformation caused by failure of neurons to migrate from the ventricular zone to the cortex. Expression analysis using patient-derived cells confirmed reduced TMTC3 transcript levels and loss of the TMTC3 protein compared to parental and control cells. As TMTC3 function is currently unexplored in the brain, we gathered support for a neurobiological role for TMTC3 by generating flies with post-mitotic neuron-specific knockdown of the highly conserved Drosophila melanogaster TMTC3 ortholog, CG4050/tmtc3. Neuron-specific knockdown of tmtc3 in flies resulted in increased susceptibility to induced seizures. Importantly, this phenotype was rescued by neuron-specific expression of human TMTC3, suggesting a role for TMTC3 in seizure biology. In addition, we observed co-localization of TMTC3 in the rat brain with vesicular GABA transporter (VGAT), a presynaptic marker for inhibitory synapses. TMTC3 is localized at VGAT positive pre-synaptic terminals and boutons in the rat hypothalamus and piriform cortex, suggesting a role for TMTC3 in the regulation of GABAergic inhibitory synapses. TMTC3 did not co-localize with Vglut2, a presynaptic marker for excitatory neurons. Our data identified TMTC3 as a synaptic protein that is involved in PVNH with ID and epilepsy, in addition to its previously described association with cobblestone lissencephaly