Dimensional reduction and universal f( alpha ) in magnetic chains.
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Reduction-of-dimensionality kinetics at reaction-limited cell surface receptors.
It has been suggested for several years that reactions between ligands and cell surface receptors can be speeded up by nonspecific adsorption of the ligand to the cell surface followed by two-dimensional surface diffusion to the receptor, a mechanism referred to as "reduction-of-dimensionality" (RD) rate enhancement. Most of the theoretical treatments of this and related problems have assumed that the receptor is an irreversibly absorbing perfect sink. Such receptors induce a depletion zone of ligand probability density around themselves. The reaction rate in this case (called "diffusion-limited") is limited only by the time required for ligands to diffuse through this depletion zone. In some cases, however, the receptor may be far from "perfect" such that a collision with a ligand only rarely leads to binding. Receptors then do not create significant local depletion zones of ligand probability density, and the reaction rate becomes strongly affected by the (small) probability of reaction success per diffusive encounter (the "reaction-limited" case). This article presents a simple theory of RD rate enhancement for reaction-limited receptors that are either reversible or irreversible binders. In contrast to the diffusion-limited theories, the reaction-limited theory presented here: (a) differs quantitatively from diffusion-limited models; (b) is simple and algebraic in closed form; (c) exhibits significant rate enhancement in some realistic cases; (d) depends strongly on the actual Brownian rather than pure diffusive nature of the ligand's motion; (e) depends (for irreversibly binding receptors only) on the kinetic rates (not just equilibria) of reversible adsorption to nontarget regions, in contrast to some previous approximate theories of reduction of dimensionality; and (f) is applicable to actual ligand/receptor systems with binding success probabilities at the opposite extreme from the perfect sink/diffusion-limited models.
Adsorption↗
Electrostatics and reduction of dimensionality produce apparent cooperativity when basic peptides bind to acidic lipids in membranes.
The binding of pentalysine to phospholipid vesicles depends in a sigmoidal manner on the mole fraction of acidic lipid in the vesicles. A simple analysis demonstrates that this apparent cooperativity is probably due to both the reduction of dimensionality that occurs when the first basic residue binds to an acidic lipid in the membrane and the Boltzmann accumulation of the peptide in the electrostatic diffuse double layer produced by the charged lipids.
Electrochemistry↗
Local Context Finder (LCF) reveals multidimensional relationships among mRNA expression profiles of Arabidopsis responding to pathogen infection.
A major task in computational analysis of mRNA expression profiles is definition of relationships among profiles on the basis of similarities among them. This is generally achieved by pattern recognition in the distribution of data points representing each profile in a high-dimensional space. Some drawbacks of commonly used pattern recognition algorithms stem from their use of a globally linear space and/or limited degrees of freedom. A pattern recognition method called Local Context Finder (LCF) is described here. LCF uses nonlinear dimensionality reduction for pattern recognition. Then it builds a network of profiles based on the nonlinear dimensionality reduction results. LCF was used to analyze mRNA expression profiles of the plant host Arabidopsis interacting with the bacterial pathogen Pseudomonas syringae. In one case, LCF revealed two dimensions essential to explain the effects of the NahG transgene and the ndr1 mutation on resistant and susceptible responses. In another case, plant mutants deficient in responses to pathogen infection were classified on the basis of LCF analysis of their profiles. The classification by LCF was consistent with the results of biological characterization of the mutants. Thus, LCF is a powerful method for extracting information from expression profile data.
Arabidopsis↗
Nonlinear dynamics of heart rate variability during experimental hemorrhage in ketamine-anesthetized rats.
Indexes of heart rate variability (HRV) based on linear stochastic models are independent risk factors for arrhythmic death (AD). An index based on a nonlinear deterministic model, a reduction in the point correlation dimension (PD2i), has been shown in both animal and human studies to have a higher sensitivity and specificity for predicting AD. Dimensional reduction subsequent to transient ischemia was examined previously in a simple model system, the intrinsic nervous system of the isolated rabbit heart. The present study presents a new model system in which the higher cerebral centers are blocked chemically (ketamine inhibition of N-methyl-D-aspartate receptors) and the system is perturbed over a longer 15-min interval by continuous hemorrhage. The hypothesis tested was that dimensional reduction would again be evoked, but in association with a more complex relationship between the system variables. The hypothesis was supported, and we interpret the greater response complexity to result from the larger autonomic superstructure attached to the heart. The complexities observed in the nonlinear heartbeat dynamics constitute a new genre of autonomic response, one clearly distinct from a hardwired reflex or a cerebrally determined defensive reaction.
Anesthesia↗
Actor-critic models of the basal ganglia: new anatomical and computational perspectives.
A large number of computational models of information processing in the basal ganglia have been developed in recent years. Prominent in these are actor-critic models of basal ganglia functioning, which build on the strong resemblance between dopamine neuron activity and the temporal difference prediction error signal in the critic, and between dopamine-dependent long-term synaptic plasticity in the striatum and learning guided by a prediction error signal in the actor. We selectively review several actor-critic models of the basal ganglia with an emphasis on two important aspects: the way in which models of the critic reproduce the temporal dynamics of dopamine firing, and the extent to which models of the actor take into account known basal ganglia anatomy and physiology. To complement the efforts to relate basal ganglia mechanisms to reinforcement learning (RL), we introduce an alternative approach to modeling a critic network, which uses Evolutionary Computation techniques to 'evolve' an optimal RL mechanism, and relate the evolved mechanism to the basic model of the critic. We conclude our discussion of models of the critic by a critical discussion of the anatomical plausibility of implementations of a critic in basal ganglia circuitry, and conclude that such implementations build on assumptions that are inconsistent with the known anatomy of the basal ganglia. We return to the actor component of the actor-critic model, which is usually modeled at the striatal level with very little detail. We describe an alternative model of the basal ganglia which takes into account several important, and previously neglected, anatomical and physiological characteristics of basal ganglia-thalamocortical connectivity and suggests that the basal ganglia performs reinforcement-biased dimensionality reduction of cortical inputs. We further suggest that since such selective encoding may bias the representation at the level of the frontal cortex towards the selection of rewarded plans and actions, the reinforcement-driven dimensionality reduction framework may serve as a basis for basal ganglia actor models. We conclude with a short discussion of the dual role of the dopamine signal in RL and in behavioral switching.
Animals↗
Most ovine mitral annular three-dimensional size reduction occurs before ventricular systole and is abolished with ventricular pacing.
BACKGROUND: Conventional surgical thinking indicates that mitral annular (MA) size reduction plays a key role in mitral valve closure, and most MA size and shape changes are thought to occur during left ventricular (LV) systole. The influences of left atrial (LA) and LV systole on MA size and shape, however, remain debated. METHODS AND RESULTS: Eight radiopaque markers were placed equidistantly around the MA and imaged using high-speed simultaneous biplane videofluoroscopy in seven closed-chest, sedated sheep before and during asynchronous LV pacing. Marker images were used to compute the three-dimensional coordinates of each marker every 16.7 ms throughout the cardiac cycle, allowing calculation of three-dimensional MA area, septal-lateral (SL) dimension, and commissure-commissure (CC) dimension under control and LV pacing conditions. Maximum MA area occurred in early diastole, and minimum MA area near end-diastole; maximum area reduction was 12+/-1% (P< or =.001). Interestingly, 89+/-3% of area reduction occurred before LV systole. During this "presystolic" period, SL decreased by 8+/-1% and CC by 2+/-1%; the SL/CC ratio fell from 0.73+/-0.02 to 0.69+/-0.01 (P< or =.005), indicating a less circular shape at end-diastole. With LV pacing, total MA area reduction was similar (13+/-2 versus 12+/-1%, P=NS versus control); however, all MA area reduction occurred during LV systole with minimum MA area occurring at end-systole. Presystolic shortening in both SL and CC dimensions was lost, and presystolic ellipticalization disappeared. CONCLUSIONS: Changes in MA size and shape coincident with LA systole included area reduction and shape change prior to the onset of LV contraction. These presystolic changes vanished when LA systole was absent (LV pacing). Thus, LA systole plays a pivotal role in MA size reduction and shape alteration. The unexpected timing of these MA dynamics should be taken into account during mitral valve reparative procedures.
Animals↗
Rates of membrane-associated reactions: reduction of dimensionality revisited.
The hypothesis that reactions associated with intracellular membranes enjoy a kinetic advantage from a reduced dimensionality for diffusion is inconsistent with available data on lateral diffusion rates, membrane-substrate affinities, and endogenous concentrations of enzymes and their aqueous substrates.
Animals↗
Polytypism in columnar group 14 halide salts: structures of (Et2NH2)3Pb3X9 x nH2O (X = Cl, Br) and (beta-alaninium)2SnI4.
The crystal structures of three hybrid organoammonium metal halide salts composed of edge-sharing MX(6) octahedra have been determined. The genesis of these structures can be traced to the parent hexagonal MX(2) structure via dimensional reduction and recombination arguments. The structures of (Et(2)NH(2))(3)Pb(3)X(9) x nH(2)O (X = Br, I) contain unique columnar (Pb(3)X(9))(n)(3)(n)(-) structures, built up of edge-shared PbX(6) octahedra. The interaction of the Et(2)NH(2)(+) cations with the parent PbX(2) structures leads to a rearrangement of the lattice into the observed columnar structure. Groups of six Et(2)NH(2)(+) cations are hydrogen bonded to these columns, girdling them at their narrowest points. These hydrogen bonds contribute to the formation of the zigzag nature of the columnar inorganic framework. The resultant structures are recombinate analogues (polytypes) of the (Pb(3)X(9))(n)(3)(n)(-) stacks that would be obtained by the dimensional reduction process of the parent layer PbX(2) structure into simple edge-shared ribbons of PbX(6) octahedra. These structures can be described in terms of the stacking of planar bibridged Pb(3)X(8)(2-) units decorated with a single halide ion at a terminal lead ion site. In a similar fashion, (beta-alaH)(2)Sn(2)I(6) contains corrugated (Sn(2)I(6))(n)(2)(n)(-) columns (beta-ala = beta-alanine), with the cations sitting in the clefts of the columns.
Journal Article↗
Mandibular skeletal dysmorphology in micrognathic mice.
The primary manifestations of micrognathia were microglossia, midline fusion of the right and left sides of the mandible, total absence of incisor and molar toothbuds and, in many cases, absence or perhaps premature resorption of Meckel's cartilage. In addition, there was altered osteogenesis as evidenced by disrupted trabecular patterns, as well as an overall dimensional reduction of the mandible both antero-posteriorly and laterally. Strikingly similar results were reported by Johnson (1926), who studied the progeny of x-irradiated mice. How specifically our results correlate with this much earlier work is a matter for further analysis. It seems clear that the critical factor in the development of micrognathia is not so much an abnormal formation of the bony mandible, but a deficiency of tongue development, specifically its intrinsic musculature. Thus, mandibular micrognathia involves not only a dysmorphology of the first branchial arch, but also the mesenchymal cell migration from the occipital somites. Taken together, the picture is one that suggests an underlying cause that may have its inception at a much earlier developmental stage, when ectomesenchymal migration from the region of the neural tube occurs. In any event, we can report confidently that spontaneous micrognathia in prenatal mice is not a simple dimensional reduction of the lower jaw, but a more complex morphological phenomenon.
Animals↗
Characterization of a partially denatured state of a protein by two-dimensional NMR: reduction of the hydrophobic interactions in ubiquitin.
A stable, partially structured state of ubiquitin, the A-state, is formed at pH 2.0 in 60% methanol/40% water at 298 K. Detailed characterization of the structure of this state has been carried out by 2D NMR spectroscopy. Assignment of slowly exchanging amide resonances protected from the solvent in the native and A-state shows that gross structural reorganization of the protein has not occurred and that the A-state contains a subset of the interactions present in the native state (N-state). Vicinal coupling constants and NOESY data show the presence of the first two strands of the five-strand beta-sheet that is present in the native protein and part of the third beta-strand. The hydrophobic face of the beta-sheet in the A-state is covered by a partially structured alpha-helix, tentatively assigned to residues 24-34, that is considerably more flexible than the alpha-helix in the N-state. There is evidence for some fixed side-chain--side-chain interactions between these two units of structure. The turn-rich area of the protein, which contains seven reverse turns and a short piece of 3(10) helix, does not appear to be structured in the A-state and is approaching random coil.
Amino Acid Sequence↗
Effect of the reduction of dimensionality on the exchange parameters in semimagnetic semiconductors.
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Journal Article↗
Using the chern-simons action for a self-consistent determination of the magnetic screening mass in thermal QCD.
We present a self-consistent determination of the screening mass for chromomagnetic fields in QCD within the framework of dimensional reduction. The three-dimensional Chern-Simons density is used as a mass term for a self-consistent perturbative calculation that yields a value of m approximately 1.604(g(2)N/2pi)T for the magnetic screening mass.
Journal Article↗
Evaluation of reaction rate enhancement by reduction in dimensionality.
The paths followed by ligands as they react with or dissociate from cell surface receptors may include weak association with nonreceptor portions of the surface followed by lateral diffusion in the plane of the membrane to a receptor. The change in dimensionality of the diffusion process by utilization of these nonspecific paths has been invoked by a number of investigators as a mechanism for enhancing reaction rate in biological systems. This paper extends our previous work on the calculation of diffusive rate constants for ligand-receptor paths. We find that they have little effect on rate constants unless the number of free receptors per cell has been reduced to less than or equal to 10(2). This number represents better than 90% occupancy for most eukaryotes, suggesting that the dimensional change mechanism is of limited consequence. We show further that when the free receptor number is low enough for rate enhancement, then the primary parameter of consequence is D'K*/D, where D' and D are the two- and three-dimensional diffusion coefficients, respectively, and K* the nonspecific affinity. A 10-fold rate enhancement with 100 free receptors requires that this parameter be of order 10(-3). This value is barely within the lower limit imposed by currently available experimental information, casting doubt on the relevance of nonspecific paths in cellular systems.
Animals↗
Systems with superabsorbing states
We report on some extensive analyses of a recently proposed model [A. Lipowski, Phys. Rev. E 60, 6255 (1999)] with infinitely many absorbing states. By performing extensive Monte Carlo simulations, we have determined critical exponents and shown strong evidence that this model is not in the directed percolation universality class. The conjecture that this two-dimensional model exhibits a dimensional reduction (behaving as one-dimensional directed percolation) is firmly disproven. The reason for the model not exhibiting standard directed percolation scaling behavior is traced back to the existence of what we call superabsorbing sites, i.e., absorbing sites that cannot be directly activated by the presence of neighboring activity in one or more than one direction. Supporting this claim we present two strong evidences: (i) in one dimension, where superabsorbing sites do not appear at the critical point, the system behaves as directed percolation, and (ii) in a modified two-dimensional variation of the model, defined on a honeycomb lattice, for which superabsorbing sites are very rarely observed, directed percolation behavior is recovered. Finally, a parallel updating version of the model exhibiting a nonequilibrium first-order transition is also reported.
Journal Article↗
Nonparametric regression applied to quantitative structure-activity relationships
Several nonparametric regressors have been applied to modeling quantitative structure-activity relationship (QSAR) data. The simplest regressor, the Nadaraya-Watson, was assessed in a genuine multivariate setting. Other regressors, the local linear and the shifted Nadaraya-Watson, were implemented within additive models--a computationally more expedient approach, better suited for low-density designs. Performances were benchmarked against the nonlinear method of smoothing splines. A linear reference point was provided by multilinear regression (MLR). Variable selection was explored using systematic combinations of different variables and combinations of principal components. For the data set examined, 47 inhibitors of dopamine beta-hydroxylase, the additive nonparametric regressors have greater predictive accuracy (as measured by the mean absolute error of the predictions or the Pearson correlation in cross-validation trails) than MLR. The use of principal components did not improve the performance of the nonparametric regressors over use of the original descriptors, since the original descriptors are not strongly correlated. It remains to be seen if the nonparametric regressors can be successfully coupled with better variable selection and dimensionality reduction in the context of high-dimensional QSARs.
Journal Article↗
Mechanisms of enhanced or impaired DNA target selectivity driven by protein dimerization.
Successful DNA transcription demands coordination between proteins that bind DNA while simultaneously binding to one another to form dimers or higher-order complexes. For proteins with numerous DNA targets throughout the genome, measurements that report on their dwell time or occupancy thus represent a convolution over a population interacting with specific DNA, nonspecific DNA, or protein partners on DNA. Dimerization is known to add contacts that can help a single protein to stably bind DNA. However, we show here that dimerization can also impair measured dwell times and occupancy on target sequences because the population redistributes across DNA. We combine mass-action kinetic models of pairwise reversible reactions between proteins and DNA with theory and spatial stochastic simulations to isolate the role of dimerization on observed DNA dwell times, occupancy, and spatial distribution of proteins on DNA. Three key themes emerge: (i) Protein-protein interactions, in addition to protein-DNA interactions, can localize a protein to DNA, and relative binding rates can thus widely tune dwell times. (ii) Dimensional reduction achieved through nonspecific binding and subsequent 1D diffusion controls the order-of-magnitude of enhancements despite nucleosome barriers. (iii) Dimerization enhances selectivity for locally clustered targets and often impairs binding to widely-spaced targets by sequestration. Compared with ChIP-seq data, our model explains how the distribution of the essential GAF protein throughout the genome is highly selective for clustered targets due to protein interactions. This model framework predicts when even weak dimerization can redistribute and stabilize proteins on DNA as a necessary part of transcription.
DNA binding↗
The Whitney reduction network: a method for computing autoassociative graphs.
This article introduces a new architecture and associated algorithms ideal for implementing the dimensionality reduction of an m-dimensional manifold initially residing in an n-dimensional Euclidean space where n >> m. Motivated by Whitney's embedding theorem, the network is capable of training the identity mapping employing the idea of the graph of a function. In theory, a reduction to a dimension d that retains the differential structure of the original data may be achieved for some d < or = 2m + 1. To implement this network, we propose the idea of a good-projection, which enhances the generalization capabilities of the network, and an adaptive secant basis algorithm to achieve it. The effect of noise on this procedure is also considered. The approach is illustrated with several examples.
Journal Article↗