Effects of base substituents on the hydration of B- and Z-DNA: correlations to the B- to Z-DNA transition.

We present a study of how substituent groups of naturally occurring and modified nucleotide bases affect the degree of hydration of right-handed B-DNA and left-handed Z-DNA. A comparison of poly(dG-dC) and poly(dG-dm5C) titrations with the lipotropic salts of the Hofmeister series infers that the methyl stabilization of cytosines as Z-DNA is primarily a hydrophobic effect. The hydration free energies of various alternating pyrimidine-purine sequences in the two DNA conformations were calculated as solvent free energies from solvent accessible surfaces. Our analysis focused on the N2 amino group of purine bases that sits in the minor groove of the double helix. Removing this amino group from guanine to form inosine (I) destabilizes Z-DNA, while adding this group to adenines to form 2-aminoadenine (A') stabilizes Z-DNA. These predictions were tested by comparing the salt concentrations required to crystallize hexanucleotide sequences that incorporate d(CG), d(CI), d(TA) and d(TA') base pairs as Z-DNA. Combining the current results with our previous analysis of major groove substituents, we derived a thermodynamic cycle that relates the systematic addition, deletion, or substitution of each base substituent to the B- to Z-DNA transition free energy.     

Kinetics of the salt-induced B- to Z-DNA transition

The salt-induced B- to Z-DNA conformational transition is a cooperative- and time-dependent process. From a modified form of the logistic equation which describes an equilibrium between two states we have deduced a kinetic function to quantify the degree of the B to Z transition of a synthetic (dG-dC) ⋅ (dG-dC) polynucleotide. This function was obtained by introduction of time as a variable in the logistic function so that the equilibrium constant, K, is replaced by a new constant K _s , characteristic of the type of salt used. This constant is defined as the salt concentration needed to reach the B-Z transition-midpoint in the time unit. The equation fits the data obtained by circular dichroism (CD) for changes in molecular ellipticity of poly(dG-m⁵dC) ⋅ poly(dG-m⁵dC) and poly(dG-dC) ⋅ poly(dG-dC) incubated with various concentrations of mono-, di-, and trivalent salts at a constant temperature. The derived expression may be a very useful tool for studying the kinetics of the B- to Z-DNA transition. Received: 1 December 1997 / Revised version: 16 March 1998 / Accepted: 27 March 1998     

Location of B- and Z-DNA in the chromosomes of a primitive eukaryote dinoflagellate

The usual conformation of DNA is a right-handed double helix (B-DNA). DNA with stretches of alternating purine-pyrimidine (G-C or A-T) can form a left-handed helix (Z-DNA). The transition B----Z, facilitated by the presence of divalent cations, cytosine methylation, or constraints on DNA such as superhelicity may play a role in the regulation of gene expression and/or in DNA compaction (Zarling, D. A., D. J. Arndt-Jovin, M. Robert-Nicoud, L. P. McIntosh, R. Tomae, and T. M. Jovin. 1984. J. Mol. Biol. 176:369-415). Divalent cations are also important in the structure of the quasi-permanently condensed chromosomes of dinoflagellate protists (Herzog, M., and M.-O. Soyer. 1983. Eur. J. Cell Biol. 30:33-41) which also have superhelicity in their DNA. The absence of histones in dinoflagellate chromosomes suggest that the search for Z-DNA sequences might be fruitful and could provide one indication of the physiological role of this particular DNA conformation. We report a complete immunofluorescent and immunogold analysis of the nuclei of the dinoflagellate Prorocentrum micans E. using monoclonal and polyclonal anti-B and anti-Z-DNA antibodies. Positive labeling was obtained with immunofluorescence using squash preparations and cryosections, both of which showed the intranuclear presence of the two DNA conformations. In ultrathin sections of aldehyde-prefixed, osmium-fixed, and epoxy-embedded cells, we have localized B-DNA and Z-DNA either with single or double immunolabeling using IgG labeled with 5- and 7-nm gold particles, respectively. Chromosomal nucleofilaments of dividing or nondividing chromosomes, as seen in ultrathin sections in their arch-shaped configuration, are abundantly labeled with anti-B-DNA antibody. Extrachromosomal anti-B-DNA labeling is also detected on the nucleoplasm that corresponds to DNA loops; we confirm the presence of these loops previously described external to the chromosomes (Soyer, M.-O., and O. K. Haapala. 1974. Chromosoma (Berl.). 47:179-192). B labeling is also visible in the nucleolus organizer region (NOR) and in the fibrillo-granular area (containing transcribing rDNA) of the nucleolus. Z-DNA was localized in limited areas inside the chromosomes, often at the periphery and near the segregation fork of dividing chromosomes. In the nucleolus, Z-DNA is observed only in the NOR area and never in the fibrillo-granular area. For both types of antibody experiments, controls using gold-labeled IgG without primary antibody were negative. A quantitative evaluation of the distribution of the gold-labeled IgG and a parametric test support the validity of these experiments.(ABSTRACT TRUNCATED AT 400 WORDS)     

DNA associations: packing calculations in A-, B-, and Z-DNA structures.

A detailed theoretical study has been carried out to examine the modes of DNA-DNA interactions on the basis of hard-sphere contact criteria. Two helices of identical structure and length are oriented side-by-side and their relative positions are controlled by translations along and rotations about specific axes. Short atomic contacts between pairs of atoms in the structures are assessed and contact-free configurations are compiled. The computed contact-free arrangements of A, B, and Z double helices are found to be remarkably similar to the packing motifs observed in DNA crystals and stretched fibers. Equally interesting in the study are the broad ranges of sterically acceptable arrangements that preserve the overall packing morphology of neighboring duplexes: Among the most notable morphological features in the helical complexes are extended "super" major and minor grooves which might facilitate the wrapping and packaging of DNA chains in supramolecular assemblies. The hard-sphere computations, however, are insufficient for quantitative interpretation of the packing of DNA helices in the solid state. The results are, nevertheless, a useful starting point for energy based studies as well as relevant to the analysis of long-range interactions in DNA supercoils and cruciforms.     

The role of methylation in the intrinsic dynamics of B- and Z-DNA

Methylation of cytosine at the 5-carbon position (5 mC) is observed in both prokaryotes and eukaryotes. In humans, DNA methylation at CpG sites plays an important role in gene regulation and has been implicated in development, gene silencing, and cancer. In addition, the CpG dinucleotide is a known hot spot for pathologic mutations genome-wide. CpG tracts may adopt left-handed Z-DNA conformations, which have also been implicated in gene regulation and genomic instability. Methylation facilitates this B-Z transition but the underlying mechanism remains unclear. Herein, four structural models of the dinucleotide d(GC)(5) repeat sequence in B-, methylated B-, Z-, and methylated Z-DNA forms were constructed and an aggregate 100 nanoseconds of molecular dynamics simulations in explicit solvent under physiological conditions was performed for each model. Both unmethylated and methylated B-DNA were found to be more flexible than Z-DNA. However, methylation significantly destabilized the BII, relative to the BI, state through the Gp5mC steps. In addition, methylation decreased the free energy difference between B- and Z-DNA. Comparisons of α/γ backbone torsional angles showed that torsional states changed marginally upon methylation for B-DNA, and Z-DNA. Methylation-induced conformational changes and lower energy differences may contribute to the transition to Z-DNA by methylated, over unmethylated, B-DNA and may be a contributing factor to biological function.     

Effect of Z-DNA on nucleosome placement

Histone octamers were reconstituted on plasmids carrying the alternating nucleotide sequence (G-C)15. The plasmids, radioactively labeled at one of two neighboring sites near the (G-C) insert, were digested with micrococcal nuclease. Nucleosome core particles were isolated and the monomer DNA subjected to restriction analysis. Quite different results are obtained if the reconstitution is carried out with relaxed plasmids, in which the (G-C) insert is in the B form, or with supercoiled plasmids, where it is in the Z form. With supercoiled plasmids, there is a marked reduction (compared with relaxed plasmids) in the abundance of labeled monomers, the result of a large decrease in core particles carrying any (G-C) sequence. Some core particles formed on supercoiled (Z) plasmids are positioned either just outside the (G-C) sequence, or with the sequence occupying the terminal position within the core particle. In contrast, monomers obtained from relaxed plasmids incorporate the (G-C) sequence in the B form more or less randomly in the interior of the core particle; species showing discrete positioning make only a minor contribution. We conclude that DNA in the Z form cannot be incorporated within core particles, except at their termini, and that a transition from the B to the Z form in vivo might result in a significantly altered local placement of nucleosomes.     

Magnetic-field-induced vertigo: a theoretical and experimental investigation

Vertigo-like sensations or apparent perception of movement are reported by some subjects and operators in and around high field whole body magnetic resonance body scanners. Induced currents (which modulate the firing rate of the vestibular hair cell), magneto-hydrodynamics (MDH), and tissue magnetic susceptibility differences have all been proposed as possible mechanisms for this effect. In this article, we examine the theory underlying each of these mechanisms and explore resulting predictions. Experimental evidence is summarised in the following findings: 30% of subjects display a postural sway response at a field-gradient product of 1 T(2)m(-1); a determining factor for experience of vertigo is the total unipolar integrated field change over a period greater than 1 s; the perception of dizziness is not necessarily related to a high value of the rate of change of magnetic field; eight of ten subjects reported sensations ranging from mild to severe when exposed to a magnetic field change of the order of 4.7 T in 1.9 s; no subjects reported any response when exposed to 50 ms pulses of dB/dt of 2 Ts(-1) amplitude. The experimental evidence supports the hypothesis that magnetic-field related vertigo results from both magnetic susceptibility differences between vestibular organs and surrounding fluid, and induced currents acting on the vestibular hair cells. Both mechanisms are consistent with theoretical predictions.     

Orientational and rotational velocity correlation functions for water-hydrating B- and Z-DNA double helices

The molecular dynamics simulations reported earlier for the structure and dynamics of water molecules hydrating B- and Z-DNA double helices are analyzed for the orientational correlation functions and the proton rotational velocity autocorrelation functions. The spectra of the rotational velocity autocorrelation functions obtained from the simulation results are compared with the neutron inelastic scattering experiments on hydrated Na-DNA samples. The results predict a small frequency component associated with water molecules bound to the double helices that disappears for waters away from the double helix.     

Quantitative analysis of DNA secondary structure from solvent-accessible surfaces: the B- to Z-DNA transition as a model

Solvent structure and its interactions have been suggested to play a critical role in defining the conformation of polynucleotides and other macromolecules. In this work, we attempt to quantitate solvent effects on the well-studied conformational transition between right-handed B- and left-handed Z-DNA. The solvent-accessible surfaces of the hexamer sequences d(m5CG)3, d(CG)3, d(CA)3, and d(TA)3 were calculated in their B- and Z-DNA conformations. The difference in hydration free energies between the Z and the B conformations (delta delta GH(Z-B] was determined from these surfaces to be -0.494 kcal/mol for C-5 methylated d(CG), 0.228 kcal/mol for unmethylated d(CG), 0.756 kcal/mol for d(CA)-d(TG), and 0.896 kcal/mol for d(TA) dinucleotides. These delta delta GH(Z-B) values were compared to the experimental B- to Z-DNA transition energies of -0.56 kcal/mol that we measured for C-5 methylated d(CG), 0.69-1.30 kcal/mol reported for unmethylated d(CG), 1.32-1.48 kcal/mol reported for d(CA)-d(TG), and 2.3-2.4 kcal/mol for d(TA) dinucleotides. From this comparison, we found that the calculated delta delta GH(Z-B) of these dinucleotides could account for the previous observation that the dinucleotides were ordered as d(m5CG) greater than d(CG) greater than d(CA)-d(TG) greater than d(TA) in stability as Z-DNA. Furthermore, we predicted that one of the primary reasons for the inability of d(TA) sequences to form Z-DNA results from a decrease in exposed hydrophilic surfaces of adjacent base pairs due to the C-5 methyl group of thymine; thus, d(UA) dinucleotides should be more stable as Z-DNA than the analogous d(TA) dinucleotides.(ABSTRACT TRUNCATED AT 250 WORDS)     

Pharmacogenetics and anti-arrhythmic drug therapy: a theoretical investigation

Pharmacological management of cardiac arrhythmias has been a long and widely sought goal. One of the difficulties in treating arrhythmia stems, in part, from incomplete understanding of the mechanisms of drug block and how intrinsic properties of channel gating affect drug access, binding affinity, and unblock. In the last decade, a plethora of genetic information has revealed that genetics may play a critical role in determining arrhythmia susceptibility and in efficacy of pharmacological therapy. In this context, we present a theoretical approach for investigating effects of drug-channel interaction. We use as an example open-channel or inactivated-channel block by the local anesthetics mexiletine and lidocaine, respectively, of normal and DeltaKPQ mutant Na(+) channels associated with the long-QT syndrome type 3. Results show how kinetic properties of channel gating, which are affected by mutations, are important determinants of drug efficacy. Investigations of Na(+) channel blockade are conducted at multiple scales (single channel and macroscopic current) and, importantly, during the cardiac action potential (AP). Our findings suggest that channel mean open time is a primary determinant of open state blocker efficacy. Channels that remain in the open state longer, such as the DeltaKPQ mutant channels in the abnormal burst mode, are blocked preferentially by low mexiletine concentrations. AP simulations confirm that a low dose of mexiletine can remove early afterdepolarizations and restore normal repolarization without affecting the AP upstroke. The simulations also suggest that inactivation state block by lidocaine is less effective in restoring normal repolarization and adversely suppresses peak Na(+) current.     

Interactions of H1 and H5 histones with polynucleotides of B- and Z-DNA conformations

Interactions of chicken H1 and H5 histones with poly(dA-dT), poly(dG-dC), and the Z-DNA structure brominated poly(dG-dC) were measured by a nitrocellulose filter binding assay and circular dichroism. At low protein:DNA ratios, both H1 and H5 bound more Z-DNA than B-DNA, and binding of Z-DNA was less sensitive to interference by an increase in ionic strength (to 600 mM NaCl). H5 histone bound a higher percentage of all three polynucleotides than did H1 and caused more profound CD spectral changes as well. For spectral studies, histones and DNA were mixed in 2.0 M NaCl and dialyzed stepwise to low ionic strength. Prepared in this way or by direct mixing in 150 mM NaCl, complexes made with right-handed poly(dG-dC) showed a deeply negative psi spectrum (deeper with H5 than with H1). Complexes of histone and Br-poly(dG-dC) showed a reduction in the characteristic Z-DNA spectral features, with H5 again having a greater effect. Complexes of poly(dA-dT) and H5, prepared by mixing them at a protein:DNA ratio of 0.5, displayed a distinctive spectrum that was not achieved with H1 even at higher protein:DNA ratios. It included a new negative band at 287 nm and a large positive band at 255 nm, giving the appearance of an inverted spectrum relative to spectra of various forms of B-DNA. These findings may reflect an ability of the different lysine-rich histones to cause varying conformational changes in the condensation of chromatin in DNA regions of highly biased base sequence.     

Recognition of Z-RNA and Z-DNA determinants by polyamines in solution: experimental and theoretical studies

Protonated polyamines are among the most efficient cations that induce the left-handed Z-form in certain polynucleotides. It is not known, however, whether these cations bind to specific sites on Z-sequences in solution. We have studied potential polyamine binding sites by measuring the effects of polyamines on the binding of purified immunoglobulins (IgGs) to different regions of the Z-helix and by molecular mechanics modeling. The specific binding of anti-Z-DNA and anti-Z-RNA IgGs to Z-helices was studied as a function of spermidine or spermine concentration. The effect of polyamines on the antibody-nucleic acid interaction was different for IgGs with different specificities for various determinants on the Z-helix. Polyamines inhibit the binding of certain anti-Z IgGs directed against specific sites probably at or near the interface between the major convex surface and the phosphate backbone, most likely by competing with the antibody binding site(s). In contrast, polyamines have no effect on other anti-Z IgGs directed against sites determined by the phosphate backbone. Furthermore, these cations can enhance the binding of anti-Z IgG directed against bulky groups at the C-5 position on the major convex surface of the helix; the enhancement may be related to charge neutralization. Under these conditions, no direct binding of antibodies with polyamines was observed. These data suggest the existence of a specific binding site(s) for polyamines on both Z-DNA and Z-RNA in solution. These binding sites have some similarity to those observed in oligonucleotide crystals by Quigley (in "Molecular Structure and Biological Activity," J.F. Griffin and W.L. Duax, eds., Elsevier, Amsterdam (1982), pp. 317-331). The experimental evidence for specific spermine binding sites on the helical surface was supported by molecular mechanics modeling of the interaction of spermine with the major groove of (dG-dC)5.(dG-dC)5 in both the Z- and B-forms. The crystal coordinates of spermine-containing oligonucleotides in both the B- and Z-forms were used as the starting points for modeling studies. The potential energy of spermine bound to the major convex surface of the Z-form was much less favorable than that of spermine bound to the major groove of the B-form. In the presence of sodium ions, however, the Z-form-spermine complexes were favored over the B-form. Thus, both theoretical and experimental studies indicate that polyamines can specifically recognize Z-helical determinants in solution as well as in crystals.     

Stereochemical Effects of Methylphosphonate in B- and Z-DNA Helices: Variation in Hydrophobicity and Effective Widths of Grooves

Abstract

Stereochemical effects of methylphosphonate (MP) in B-DNA and Z-DNA duplexes are studied through molecular mechanics approach. Duplexes of different lengths, tetramers, hexamers, dodecamers are examined to assess the interstrand and intrastrand electrostatic effects due to MPs vis-a-vis phosphates. A variety of models which include duplexes with alternating S-MP and R-MP, alternating phosphate and MP and, duplexes posessing MPs in only one of the strands, are examined by considering both the S- and R-stereoisomers. Majority of the calculations are performed with CG sequences to delineate factors responsible for the stability of B- and Z-DNA as well as B × Z-DNA transition under nonionic conditions. The results show that both B- and Z-DNA duplexes are energetically favoured in the presence of MP due to overwhelming reduction in intrastrand as well as interstrand electrostatic repulsive interactions. The effect is distinct in oligomers longer than tetramers. Comparison of energetics of MP B- and Z-DNA duplexes suggests that an oligodeoxynucleotide such as d(CG)₆ with all phosphates replaced by MPs may favour equally both B- and Z-DNA conformations. The analysis further provides an estimate of electrostatic interactions, operating at the grooves under a variety of conditions. Several specific and localised effects due to S-MP and R-MP are seen at CG and GC steps in various B-DNA and Z-DNA models. S-MP in B- DNA reduces the effective major groove width by nearly 3 Å hence denying access to the functional groups of endonucleases thereby enhancing the resistance of MP-DNA to enzymatic digestion. Further, methyl groups of MP render the surface of the DNA helix to be significantly hydrophobic which may explain higher permeability of MP-DNA in membranes as well as its less soluble nature in aqueous media.     

Generalized Poisson-Boltzmann calculation of the distribution of electrolyte ions around the B- and Z-conformers of DNA

A solution to the three-dimensional Poisson-Boltzmann equation, generalized to include the finite size of the ions, is presented for the environment of DNA in the B- and Z-conformations. The results clearly indicate that despite the lower linear charge density of the left-handed Z-conformer, there is a higher concentration of Na⁺ at the immediate surface of the Z-from than at the surface of the B-form. The average concentration of counterions within a 12-Å radius of the DNA is, nonetheless, higher for the B- than for the Z-form. Calculations of the electrostatic interactions of these conformers with an environment of 0.01M monovalent salt show that the salt exerts a greater stabilizing effect on the left-handed conformer than on the right-handed form.     

Hydration structure and dynamics of B- and Z-DNA in the presence of counterions via molecular dynamics simulations

Following our previous attempts at understanding the structural and dynamical properties of water and counterions hydrating nucleic acids, we have performed molecular dynamics simulations for B- and Z-DNA. In these simulations, the nucleic acids were held rigid. In the case of B-DNA, one turn of B-DNA double helix was considered in the presence of 1500 water molecules and 20 counterions (K⁺). The simulations were performed for 4.0 ps after equilibrating the system. For Z-DNA, we considered one turn of the double helix in the presence of 1851 water molecules and 24 counterions (K⁺). The simulations were carried out for 3.5 ps after equilibration. The average temperature of these simulations was ～ 360 K for Z-DNA and ～ 345 K for B-DNA. In these simulations the hydrogen atoms were explicitly taken into account. For both simulations, a fifth-order predictor-corrector was used for solving the translational equations of motion. The rotational motion of the water molecules was represented in terms of quaternion algebra and the rotational equations of motion were solved with a second-order quaternion method using a sixth-order predictor-corrector method. A time step of 0.5 · 10^?15 s was used in these simulations. The structural and the dynamical properties of water solvating the counterions, and the phosphate groups of the DNA, were computed to understand the hydration structure. Diffusion coefficients and velocity correlation functions were calculated for both ions and the water molecules. The velocity correlation functions for the ions exhibit a caged behavior. The dipole correlation functions for the water molecules indicate that the water molecules close to the helix retain the memory of their initial orientations for longer periods of time than those away from the helix. During the time period of our simulation (3–4 ps) the ion probability distributions show a well-defined pattern and suggest limited mobility for the ions, being close to the helix.     

Effect of calcium ions on the organization of iota-carrageenan helices: an X-ray investigation

X-ray fiber diffraction analysis confirms that calcium iota-carrageenan forms a threefold, right-handed, half-staggered, parallel, double helix of pitch 26.42 A stabilized by interchain hydrogen bonds. According to the detailed structural results, three helices are packed in a trigonal unit cell (a=23.61 and c=13.21 A). Strong interactions between the sulfate groups of neighboring helices, mediated by calcium ions and water molecules, are responsible for stabilizing the three-dimensional structure.     

Transitions between B-DNA and Z-DNA: a dilemma

The intramolecular conformational change which occurs in double-stranded (dG-dC) oligonucleotides and polynucleotides in high salt solutions is currently assumed to be a transition between the presently accepted structures for B-DNA and Z-DNA. However, a serious dilemma results from the fact that these two structures are from topologically different families of helical duplexes. Mechanisms for interconversion between the two forms, under typical experimental conditions, are highly improbable from a physical-chemical viewpoint. The alternative possibility is that the structure of one of the forms in the transition is not as assumed. The resulting dilemma is addressed and alternative relationships between right- and left-handed DNA forms are discussed.     

The H2 haplotype regulates the distribution of B cells into B-1a,B-1b and B-2 subsets

The size of B-cell subsets appears to be under genetic control, but the mechanism of this regulation is unknown. By analyzing five congenic strains of mice that differ only in their H2 haplotype, we addressed the issue of whether the MHC genes are involved in the relative proportions of B-1a, B-1b and B-2 cells. Not only were there considerable differences in the percentages of B-1 in B cells between H2s mice which were the highest [78.5+/-0.8% in the peritoneal cavity (PerC), and 26.3+/-0.5% in the spleen] and H2d mice, which were the lowest (15.2+/-0.6% in the PerC, and 10.9+/-0.6% in the spleen), but the percentages of B-1a cells varied inversely to those of B-1. Crosses between H2s and H2d strains showed that the highest B-1 frequencies occurred in F2 progeny expressing the homozygous H2s (70.8+/-2.1% in the PerC, and 30.0+/-0.5 in the spleen), and the lowest in that expressing the homozygous H2d haplotype (8.9+/-0.6% in the PerC, and 8.6+/-0.4% in the spleen). A dose effect of H2 was established in heterozygous F1 and F2 mice. As mice aged, there was a reduction of B-1 cells in the PerC, at the expense of B-1b in the H2s, but not in the H2d mice. Hence, the H2 genes appear to participate in regulating the proportions of B-1a, B-1b and B-2 cells.     

Integrated information in discrete dynamical systems: motivation and theoretical framework

This paper introduces a time- and state-dependent measure of integrated information, , which captures the repertoire of causal states available to a system as a whole. Specifically, quantifies how much information is generated (uncertainty is reduced) when a system enters a particular state through causal interactions among its elements, above and beyond the information generated independently by its parts. Such mathematical characterization is motivated by the observation that integrated information captures two key phenomenological properties of consciousness: (i) there is a large repertoire of conscious experiences so that, when one particular experience occurs, it generates a large amount of information by ruling out all the others; and (ii) this information is integrated, in that each experience appears as a whole that cannot be decomposed into independent parts. This paper extends previous work on stationary systems and applies integrated information to discrete networks as a function of their dynamics and causal architecture. An analysis of basic examples indicates the following: (i) varies depending on the state entered by a network, being higher if active and inactive elements are balanced and lower if the network is inactive or hyperactive. (ii) varies for systems with identical or similar surface dynamics depending on the underlying causal architecture, being low for systems that merely copy or replay activity states. (iii) varies as a function of network architecture. High values can be obtained by architectures that conjoin functional specialization with functional integration. Strictly modular and homogeneous systems cannot generate high because the former lack integration, whereas the latter lack information. Feedforward and lattice architectures are capable of generating high but are inefficient. (iv) In Hopfield networks, is low for attractor states and neutral states, but increases if the networks are optimized to achieve tension between local and global interactions. These basic examples appear to match well against neurobiological evidence concerning the neural substrates of consciousness. More generally, appears to be a useful metric to characterize the capacity of any physical system to integrate information.