Fast Kalman filtering on quasilinear dendritic trees

Optimal filtering of noisy voltage signals on dendritic trees is a key problem in computational cellular neuroscience. However, the state variable in this problem—the vector of voltages at every compartment—is very high-dimensional: realistic multicompartmental models often have on the order of N = 10⁴ compartments. Standard implementations of the Kalman filter require O(N ³) time and O(N ²) space, and are therefore impractical. Here we take advantage of three special features of the dendritic filtering problem to construct an efficient filter: (1) dendritic dynamics are governed by a cable equation on a tree, which may be solved using sparse matrix methods in O(N) time; and current methods for observing dendritic voltage (2) provide low SNR observations and (3) only image a relatively small number of compartments at a time. The idea is to approximate the Kalman equations in terms of a low-rank perturbation of the steady-state (zero-SNR) solution, which may be obtained in O(N) time using methods that exploit the sparse tree structure of dendritic dynamics. The resulting methods give a very good approximation to the exact Kalman solution, but only require O(N) time and space. We illustrate the method with applications to real and simulated dendritic branching structures, and describe how to extend the techniques to incorporate spatially subsampled, temporally filtered, and nonlinearly transformed observations.     

An hypothesis of freese and the DNA-protein coding problem

Freese’s Hypothesis states that a single specific alteration in the sequence of nucleotides of an information-bearing DNA molecule results in a specific mutational effect. Within the framework of the DNA-protein coding problem developed elsewhere, and assuming the quasi-ergodicity of the general coding process, it is shown that Freese’s Hypothesis allows us to derive expressions for the length of the smallest mutable DNA molecule and to obtain a bound for the maximal number of allelic molecules of fixed length. To illustrate these ideas, calculations are carried out on appropriate data from bacternophage and man, and the results are shown to differ by a factor of 10 (modulo the rather crude approximations used). It is further shown that, if ρ(N) and ϱ(N) are respectively the number of information-bearing words of lengthN in a given code and the number of words of lengthN, then the number lim ρ(N)/ϱ(N) depends sensitively on the parameter ∈ which specifiesN→∞ the given code. The implications of this result for the spontaneous aggregation of a sufficient number of information-bearing words to characterize an organism are discussed. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under Contract No. AF 49(638)-917.     

Crystal structure,DNA binding studies,nucleolytic property and topoisomerase I inhibition of zinc complex with 1,10-phenanthroline and 3-methyl-picolinic acid

Crystal structure analysis of the zinc complex establishes it as a distorted octahedral complex, bis(3-methylpicolinato-κ² N,O)₂(1,10-phenanthroline-κ² N,N)-zinc(II) pentahydrate, [Zn(3-Me-pic)₂(phen)]·5H₂O. The trans-configuration of carbonyl oxygen atoms of the carboxylate moieties and orientation of the two planar picolinate ligands above and before the phen ligand plane seems to confer DNA sequence recognition to the complex. It cannot cleave DNA under hydrolytic condition but can slightly be activated by hydrogen peroxide or sodium ascorbate. Circular Dichroism and Fluorescence spectroscopic analysis of its interaction with various duplex polynucleotides reveals its binding mode as mainly intercalation. It shows distinct DNA sequence binding selectivity and the order of decreasing selectivity is ATAT > AATT > CGCG. Docking studies lead to the same conclusion on this sequence selectivity. It binds strongly with G-quadruplex with human tolemeric sequence 5′-AG₃(T₂AG₃)₃-3′, can inhibit topoisomerase I efficiently and is cytotoxic against MCF-7 cell line.     

A simple, practical and complete O-time Algorithm for RNA folding using the Four-Russians Speedup

Background  

The problem of computationally predicting the secondary structure (or folding) of RNA molecules was first introduced more than thirty years ago and yet continues to be an area of active research and development. The basic RNA-folding problem of finding a maximum cardinality, non-crossing, matching of complimentary nucleotides in an RNA sequence of length n, has an O(n ³)-time dynamic programming solution that is widely applied. It is known that an o(n ³) worst-case time solution is possible, but the published and suggested methods are complex and have not been established to be practical. Significant practical improvements to the original dynamic programming method have been introduced, but they retain the O(n ³) worst-case time bound when n is the only problem-parameter used in the bound. Surprisingly, the most widely-used, general technique to achieve a worst-case (and often practical) speed up of dynamic programming, the Four-Russians technique, has not been previously applied to the RNA-folding problem. This is perhaps due to technical issues in adapting the technique to RNA-folding.     

Synthesis of (E)-5-(2-cIOdovinyl)-3′-0-(1-Methyl-1,4-Dihydropyridyl-3 -Carbonyl)-2′-Fluoro-2′-Deoxyuridine (Ivfru-Cds) for Brain Targetted Delivery of Ivfru,an Antiviral Nucleoside

Abstract

(E)-5-(2-lodovinyl)-2′-fluoro-3′-0-(1-methyl-1,4-dihydropyridyl-3-carbonyl)-2′-deoxyuridine (11) was synthesized for future evaluation as a lipophilic, brain-selective, pyrimidine phosphorylase-resistant, antiviral agent for the treatment of Herpes simplex encephalitis (HSE). Treatment of (E)-5-(2-iodovinyl)-2′-fluoro-2′-deoxyuridine (6) with TBDMSCI in the presence of imidazole in DMF yielded the protected 5′-O-t-butyldimethylsilyl derivative (7). Subsequent reaction with nicotinoyl chloride hydrochloride in pyridine afforded (E)-5-(-2-iodovinyl)-2′-fluoro-3′-O-(3-pyridylcarbonyl)-5′-O-t-butyldimethylsily-2′-deoxyuridine (8). Deprotection of the silyl ether moiety of 8 with n-Bu₄N⁺F^? and quaternization of the resulting 3′-O-(3-pyridylcarbonyl) derivative 9 using iodomethane afforded the corresponding 1-methylpyridinium salt 10. The latter was reduced with sodium dithionite to yield (E)-5-(2-iodovinyl)-2′-fluoro-3′-O-(1-methyl-1,4-dihydropyridyl-3-carbonyl)-2′-deoxyuridine (11).     

Ribosylation of the Base Residue of Inosine Derivatives by Phase-Transfer Catalysis

Abstract

Reaction of 2′,3′,5′-O-silylated inosine derivative 1 with 2, 3-O-isopropylidene-5-O-tritylribosyl chloride (3) in a two-phase (CH₂Cl₂-aq. NaOH) system in the presence of Bu₄NBr gave three products, i. e., 6-O-α-, 6-O-β-, and N ¹-β-isomers of glycosides 4, 5a, and 5b. A similar PTC reaction of 1 with 2, 3, 5-tri-O-benzylribosyl bromide (9) gave four regio- and stereo-isomers involving the N¹-β-glycoside 10. Reaction of 1 with 2, 3, 5-tri-O-benzoylribosyl bromide (11) afforded three products involving the desired N¹-β-glycoside 12b, which could be deprotected to give N ¹-ribosylinosine (15b) as a useful intermediate for the synthesis of cIDPR.

     

Spin Trapping by Use of N-Tert-Butylhydroxylamine. Involvement of Fenton Reactions

Spin trapping of short-lived R. radicals is done by use of N-tert-butylhydroxylamine (1) and H²O². The hydroxylamine is oxidized to the radical t-BuN(O)H (2) which is converted into the spin trap 2-methyl-2-nitrosopropane (3). Simultaneously, hydroxyl radicals. OH are formed from H²O². The latter radical species abstracts hydrogen atoms from suitable molecules HR to give R. radicals, which are trapped with the formation of aminooxyl radicals, i. e., t-BuN(O)R (4) detectable by EPR spectroscopy. The reaction is enhanced by the presence of iron ions. The cleavage of H²O² into. OH radicals is considered to involve both a radical-driven (t-BuN(O)H 2) and an iron-driven Fenton reaction.     

Ordering process of self-organizing maps improved by asymmetric neighborhood function

The Self-organizing map (SOM) is an unsupervised learning method based on the neural computation, which has found wide applications. However, the learning process sometime takes multi-stable states, within which the map is trapped to an undesirable disordered state including topological defects on the map. These topological defects critically aggravate the performance of the SOM. In order to overcome this problem, we propose to introduce an asymmetric neighborhood function for the SOM algorithm. Compared with the conventional symmetric one, the asymmetric neighborhood function accelerates the ordering process even in the presence of the defect. However, this asymmetry tends to generate a distorted map. This can be suppressed by an improved method of the asymmetric neighborhood function. In the case of one-dimensional SOM, it is found that the required steps for perfect ordering is numerically shown to be reduced from O(N ³) to O(N ²). We also discuss the ordering process of a twisted state in two-dimensional SOM, which can not be rectified by the ordinary symmetric neighborhood function.     

DNA sequence-specific ligands: XIV. Synthesis of fluorescent biologically active dimeric bisbenzimidazoles DB(3, 4, 5, 7, 11)

Five fluorescent symmetrical dimeric bisbenzimidazoles DB(n) containing four 2,6-substituted benzimidazole cores and differing in the length of the oligomethylene linker between two bisbenzimidazole rings (n = 3, 4, 5, 7, 11) have been synthesized. The ability of the dimeric bisbenzimidazoles to form complexes with the double-stranded DNA has been shown by spectral methods. Upon binding to the double-stranded DNA, DB(n) are localized in the narrow groove. The data on the inhibition of the DNA methyltransferase Dnmt3a by DB(n) indicate that dimeric bisbenzimidazoles DB(3) and DB(11) site-specifically bind to the oligonucleotide duplex.     

(S)-α-methyl,α-amino acids: a new stereocontrolled synthesis

A new and convenient stereocontrolled synthesis of the optically pure (S)-α-methyl,α-amino acids 6(a–d) that exploits the chiral synthon 1,4-N,N-[(S)-1-phenylethyl]-piperazine-2,5-dione (1) is described. The (S)-1-phenylethyl group, bonded to each of the N-atoms of the 2,5-diketopiperazine, acts as a chiral inductor in the first alkylation, while the steric hindrance appears to be the determining factor of stereocontrol in third and forth alkylation.     

AnO(N 2 logN) restriction map comparison and search algorithm

We present anO(R logP) time,O(M+P ² ) space algorithm for searching a restriction map withM sites for the best matches to a shorter map withP sites, whereR, the number of matching site pairs, is bounded byMP. As first proposed by Watermanet al. (1984,Nucl. Acids Res. 12, 237–242) the objective function used to score matches is additive in the number of unaligned sites and the discrepancies in the distances between adjacent aligned sites. Our algorithm is basically a sparse dynamic programming computation in which “candidate lists” are used to model the future contribution of all previously computed entries to those yet to be computed. A simple modification to the algorithm computes the distance between two restriction maps withM andN sites, respectively, inO(MN(logM+logN)) time. This author’s work was supported in part by National Library of Medicine Grant R01-LM4960. This author’s work was supported in part by National Library of Medicine Grant R01-LM5110.     

Kinetic processes initiated by a nanosecond high-current discharge in hot air

Results from numerical investigations of kinetic processes initiated by a pulsed nanosecond discharge in hot (T ₀ ≥ 1000 K) air at atmospheric pressure are presented. The calculated results on the dynamics of the electron density, the population of the N₂(B³Π _g ) and N₂(C³Π _u ) states, and the atomic oxygen density in the axial discharge region agree with experiment. The method for determining the gas temperature by measuring the rotational structure of the transitions N₂(C³Π _u , ν) → N₂(B³Π _g , ν′) of the 2⁺ nitrogen system is analyzed. It is shown that, in relatively weak reduced electric fields typical of secondary discharge pulses, the electron impact excitation of the N₂(C³Π _u ) state from the ground state N₂(X¹Σ _g ⁺) can be accompanied by its additional step population from the N₂(B³Π _g ), N₂(a′Σ _u ⁻), and other electronic states. This effect substantially influences the rotational distribution of nitrogen molecules in the N₂(C³Π _u , ν) state; moreover, the temperature determined from this distribution can be substantially higher than the true gas temperature.     

Molecular-Dynamics Simulations for the Density Autocorrelation Function in a Supercooled Fluid Phase

Abstract

We have re-calculated the self part of the density autocorrelation function F_s(k, t) (incoherent scattering function) for the binary soft-sphere fluid with a much longer molecular-dynamics (MD) simulation than our previous MD calculations, and with a larger system size (N = 4000) to a longer time window as well as to study a system-size dependence, if it exists. The full density autocorrelation function F(k, t) was also computed. It is found that all F(k, t)'s that we have computed in this work can be fitted over a wide range of time steps (at least over three figures of the decay) by a Williams-Watts stretched exponential function F_s(k, t) = A exp [— (t/t ₀)^β], where A, β and t ₀ are adjustable parameters. Other significant dynamical behaviours were also presented in mean square displacements and non-Gaussian parameters for highly supercooled fluids with N = 4000. The present results are compatible to our previous computations with N = 500, but a significant size dependence is suggested.     

Di-<Emphasis Type="Italic">tert</Emphasis>-butylsilylene-directed α-selective synthesis of <Emphasis Type="Italic">p</Emphasis>-nitrophenyl T-antigen analogues

Seven analogues of p-nitrophenyl T-antigen [Galβ(1→3)GalNAcα(1→O)PNP] have been synthesized as potential substrates for elucidation of the substrate specificity of endo-α-N-acetylgalactosaminidase. These compounds, which are commercially unavailable, include: GlcNAcβ(1→3){GlcNAcβ(1→6)}GalNAcα(1→O)PNP [core 4 type], GalNAcα(1→3)GalNAcα(1→O)PNP [core 5 type], GlcNAcβ(1→6)GalNAcα(1→O)PNP [core 6 type], GalNAcα(1→6)GalNAcα(1→O)PNP [core 7 type], Galα(1→3)GalNAcα(1→O)PNP [core 8 type], Glcβ(1→3)GalNAcα(1→O)PNP and GalNAcβ(1→3)GalNAcα(1→O)PNP. The assembly of these synthetic probes was accomplished efficiently, based on di-tert-butylsilylene(DTBS)-directed α-galactosylation as a key reaction.     

Production of singlet oxygen in a non-self-sustained discharge

The production of O₂(a¹Δ_g) singlet oxygen in non-self-sustained discharges in pure oxygen and mixtures of oxygen with noble gases (Ar or He) was studied experimentally. It is shown that the energy efficiency of O₂(a¹Δ_g production can be optimized with respect to the reduced electric field E/N. It is shown that the optimal E/N values correspond to electron temperatures of 1.2–1.4 eV. At these E/N values, a decrease in the oxygen percentage in the mixture leads to an increase in the excitation rate of singlet oxygen because of the increase in the specific energy deposition per O₂ molecule. The onset of discharge instabilities not only greatly reduces the energy efficiency of singlet oxygen production but also makes it impossible to achieve high energy deposition in a non-self-sustained discharge. A model of a non-self-sustained discharge in pure oxygen is developed. It is shown that good agreement between the experimental and computed results for a discharge in oxygen over a wide range of reduced electric fields can be achieved only by taking into account the ion component of the discharge current. The cross section for the electron-impact excitation of O₂(a¹Δ_g and the kinetic scheme of the discharge processes with the participation of singlet oxygen are verified by comparing the experimental and computed data on the energy efficiency of the production of O₂(a¹Δ_g and the dynamics of its concentration. It is shown that, in the dynamics of O₂(a¹Δ_g molecules in the discharge afterglow, an important role is played by their deexcitation in a three-body reaction with the participation of O(³P) atoms. At high energy depositions in a non-self-sustained discharge, this reaction can reduce the maximal attainable concentration of singlet oxygen. The effect of a hydrogen additive to an Ar: O₂ mixture is analyzed based on the results obtained using the model developed. It is shown that, for actual electron beam current densities, a significant energy deposition in a non-self-sustained discharge in the mixtures under study can be achieved due to the high rate of electron detachment from negative ions. In this case, however, significant heating of the mixture can lead to a rapid quenching of O₂(a¹Δ_g molecules by atomic hydrogen.     

Systematic analysis of residual density suggests that a major limitation in well‐refined X‐ray structures of proteins is the omission of ordered solvent

In the residual electron density map of a fully refined X‐ray protein model, there should be no peaks arising from modeling errors or missing atoms. Any residual peaks that do occur should be contributed by random residual intensity differences between the model and the data. If the model is incomplete (i.e., some atoms are missing), there will be more positive peaks than negative ones. On the other hand, if the model includes inappropriately located atoms, there will be an excess of negative peaks. In this study, random residual peaks are quantified using the probability density function P(x), which is defined as the probability for a peak having peak height between x and x + dx. It is found that P(x) is single‐exponential and symmetric for both positive and negative peaks. Thus, P(x) can be used to discriminate residual peaks contributed by random noise in complete models from residual peaks being attributable to modeling errors in incomplete models. For a number of representative structures in the PDB it is found that P(x) has far more large (greater than 5 sigma) positive peaks than large negative peaks. This excess of large positive peaks suggests that the main defect in these refined structures is the omission of ordered water molecules.     

Synthesis of N-Arylinosines

Abstract

2′,3′,5′-Tri-O(tetrahydropyran-2-yl)inosine 1 was treated with iodobenzene or 2-bromopyridine in the presence of cuprous oxide in pyridines to give the N¹ -aryl derivatives 2a, b. Deprotection of the products afforded N¹ -arylinosines 3a, b.     

Effect of Novel Amino Acids and Dipeptides Substituted 3-Morpholino Arecoline Derivatives as Muscarinic Receptor 1 Agonists in Alzheimer’s Dementia Models

A series of novel, potent and selective muscarinic receptor 1 agonists (M1 receptor agonists) that employ a key N-substituted morpholine arecoline moiety has been synthesized as part of research effort for the therapy of Alzheimer’s diseases. The ester group of arecoline (which is reported as mucarinic agonist) has been replaced by N-substituted morpholine ring. The structure activity relationship reveals that the increase in lipophilic carbon chain on the nitrogen atom of the morpholine ring increases the affinity of M1 receptor. In the present study, we are reporting N-amino acid substituted 9(a–k) and dipeptides substituted 10(a–j) and 11(a–j) morpholino arecoline derivatives, along with their in vitro muscarinic binding studies by using [³H]QNB and also in vivo evaluation of memory and learning in male Wistar rats (passive avoidance test plus maze studies) as M1 receptor agonist. Some molecules from the dipeptide series (10b, 10c and 10j) showed potent M1 receptor agonist activity. Other derivatives also showed considerable M1 receptor binding affinity.