Systematic derivation of partition functions for ligand binding to two-dimensional lattices

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.

Comparing in vitro, in situ, and in vivo experimental data in a three-dimensional model of mammalian cochlear mechanics

Normal mammalian hearing is refined by amplification of the motion of the cochlear partition. This partition, comprising the organ of Corti sandwiched between the basilar and tectorial membranes, contains the outer hair cells that are thought to drive this amplification process. Force generation by outer hair cells has been studied extensively in vitro and in situ, but, to understand cochlear amplification fully, it is necessary to characterize the role played by each of the components of the cochlear partition in vivo. Observations of cochlear partition motion in vivo are severely restricted by its inaccessibility and sensitivity to surgical trauma, so, for the present study, a computer model has been used to simulate the operation of the cochlea under different experimental conditions. In this model, which uniquely retains much of the three-dimensional complexity of the real cochlea, the motions of the basilar and tectorial membranes are fundamentally different during in situ- and in vivo-like conditions. Furthermore, enhanced outer hair cell force generation in vitro leads paradoxically to a decrease in the gain of the cochlear amplifier during sound stimulation to the model in vivo. These results suggest that it is not possible to extrapolate directly from experimental observations made in vitro and in situ to the normal operation of the intact organ in vivo.

Extension of the thermodynamics of small systems to open metastable states: An example

By using a simplified model of small open liquid-like clusters with surface effects, in the gas phase, it is shown how the statistical thermodynamics of small systems can be extended to include metastable supersaturated gaseous states not too far from the gas–liquid equilibrium transition point. To accomplish this, one has to distinguish between mathematical divergence and physical convergence of the open-system partition function.

Compression, gain, and nonlinear distortion in an active cochlear model with subpartitions

The propagation of inhomogeneous, weakly nonlinear waves is considered in a cochlear model having two degrees of freedom that represent the transverse motions of the tectorial and basilar membranes within the organ of Corti. It is assumed that nonlinearity arises from the saturation of outer hair cell active force generation. I use multiple scale asymptotics and treat nonlinearity as a correction to a linear hydroelastic wave. The resulting theory is used to explain experimentally observed features of the response of the cochlear partition to a pure tone, including: the amplification of the response in a healthy cochlea vs a dead one; the less than linear growth rate of the response to increasing sound pressure level; and the amount of distortion to be expected at high and low frequencies at basal and apical locations, respectively. I also show that the outer hair cell nonlinearity generates retrograde waves.

Intracellular localization of P1 ParB protein depends on ParA and parS

The P1 partition system promotes faithful plasmid segregation during the Escherichia coli cell cycle. This system consists of two proteins, ParA and ParB, that act on a plasmid site called parS. By immunofluorescence microscopy, we observed that ParB localizes to discrete foci that are most often located close to the one-quarter and three-quarters positions of cell length. The visualization of ParB foci depended completely on the presence of parS, although their visualization was independent of the chromosomal context of parS (in P1 or the bacterial chromosome). In integration host factor-defective mutants, in which ParB binding to parS is weakened, only a fraction of the total pool of ParB had converged into foci. Taken together, these results indicate that parS recruits a pool of ParB into foci and that the resulting ParB–parS complexes serve as substrates for the segregation reaction. In the absence of ParA, the position of ParB foci in cells is perturbed, indicating that at least one of the roles of ParA is to direct ParB–parS complexes to the proper one-quarter positions from a cell pole. Finally, inhibition of cell division did not inhibit localization of ParB foci in cells, indicating that the positioning signals in the E. coli host that are needed for P1 partition do not depend on early division events.

The Yeast Dynactin Complex Is Involved in Partitioning the Mitotic Spindle between Mother and Daughter Cells during Anaphase B

Although vertebrate cytoplasmic dynein can move to the minus ends of microtubules in vitro, its ability to translocate purified vesicles on microtubules depends on the presence of an accessory complex known as dynactin. We have cloned and characterized a novel gene, NIP100, which encodes the yeast homologue of the vertebrate dynactin complex protein p150glued. Like strains lacking the cytoplasmic dynein heavy chain Dyn1p or the centractin homologue Act5p, nip100Δ strains are viable but undergo a significant number of failed mitoses in which the mitotic spindle does not properly partition into the daughter cell. Analysis of spindle dynamics by time-lapse digital microscopy indicates that the precise role of Nip100p during anaphase is to promote the translocation of the partially elongated mitotic spindle through the bud neck. Consistent with the presence of a true dynactin complex in yeast, Nip100p exists in a stable complex with Act5p as well as Jnm1p, another protein required for proper spindle partitioning during anaphase. Moreover, genetic depletion experiments indicate that the binding of Nip100p to Act5p is dependent on the presence of Jnm1p. Finally, we find that a fusion of Nip100p to the green fluorescent protein localizes to the spindle poles throughout the cell cycle. Taken together, these results suggest that the yeast dynactin complex and cytoplasmic dynein together define a physiological pathway that is responsible for spindle translocation late in anaphase.

Tubulin Polyglycylation: Differential Posttranslational Modification of Dynamic Cytoplasmic and Stable Axonemal Microtubules in Paramecium

Polyglycylation, a posttranslational modification of tubulin, was discovered in the highly stable axonemal microtubules of Paramecium cilia where it involves the lateral linkage of up to 34 glycine units per tubulin subunit. The observation of this type of posttranslational modification mainly in axonemes raises the question as to its relationship with axonemal organization and with microtubule stability. This led us to investigate the glycylation status of cytoplasmic microtubules that correspond to the dynamic microtubules in Paramecium. Two anti-glycylated tubulin monoclonal antibodies (mAbs), TAP 952 and AXO 49, are shown here to exhibit different affinities toward mono- and polyglycylated synthetic tubulin peptides. Using immunoblotting and mass spectrometry, we show that cytoplasmic tubulin is glycylated. In contrast to the highly glycylated axonemal tubulin, which is recognized by the two mAbs, cytoplasmic tubulin reacts exclusively with TAP 952, and the α- and β- tubulin subunits are modified by only 1–5 and 2–9 glycine units, respectively. Our analyses suggest that most of the cytoplasmic tubulin contains side chain lengths of 1 or 2 glycine units distributed on several glycylation sites. The subcellular partition of distinct polyglycylated tubulin isoforms between cytoplasmic and axonemal compartments implies the existence of regulatory mechanisms for glycylation. By following axonemal tubulin immunoreactivity with anti-glycylated tubulin mAbs upon incubation with a Paramecium cellular extract, the presence of a deglycylation enzyme is revealed in the cytoplasm of this organism. These observations establish that polyglycylation is reversible and indicate that, in vivo, an equilibrium between glycylating and deglycylating enzymes might be responsible for the length of the oligoglycine side chains of tubulin.

Heterothermal acclimation: An experimental paradigm for studying the control of thermal acclimation in crabs

A method for the study of the control of the attainment of thermal acclimation has been applied to the crabs, Cancer pagurus and Carcinus maenas. Crabs were heterothermally acclimated by using an anterior–posterior partition between two compartments, one at 8°C and the other at 22°C. One compartment held a three-quarter section of the crab including the central nervous system (CNS), eye stalks, and ipsilateral legs; the other held a quarter section including the contralateral legs. Criteria used to assess the acclimation responses were comparisons of muscle plasma membrane fatty acid composition and “fluidity.” In both species, the major fatty acids of phosphatidylcholine were 16:0, 18:1, 20:5, and 22:6, whereas phosphatidylethanolamine contained significantly less 16:0 but more 18:0; these fatty acids comprised 80% of the total. Differences in fatty acid composition were demonstrated between fractions obtained from the ipsilateral and contralateral legs from the same heterothermally acclimated individual. In all acclimation states (except 22CNS, phosphatidylcholine fraction), membrane lipid saturation was significantly increased with acclimation at 22° as compared with 8°C. Membrane fluidity was determined by using 1,3-diphenyl-1,3,5 hexatriene (DPH) fluorescence polarization. In both species, membranes from legs held at 8° were more fluid than from legs held at 22°C irrespective of the acclimation temperature of the CNS. Heterothermal acclimation demonstrated that leg muscle membrane composition and fluidity respond primarily to local temperature and were not predominately under central direction. The responses between 8°C- and 22°C-acclimated legs were more pronounced when the CNS was cold-acclimated, so a central influence cannot be excluded.

A host–guest system to study structure–function relationships of membrane fusion peptides

We designed a host–guest fusion peptide system, which is completely soluble in water and has a high affinity for biological and lipid model membranes. The guest sequences are those of the fusion peptides of influenza hemagglutinin, which are solubilized by a highly charged unstructured C-terminal host sequence. These peptides partition to the surface of negatively charged liposomes or erythrocytes and elicit membrane fusion or hemolysis. They undergo a conformational change from random coil to an obliquely inserted (≈33° from the surface) α-helix on binding to model membranes. Partition coefficients for membrane insertion were measured for influenza fusion peptides of increasing lengths (n = 8, 13, 16, and 20). The hydrophobic contribution to the free energy of binding of the 20-residue fusion peptide at pH 5.0 is −7.6 kcal/mol (1 cal = 4.18 J). This energy is sufficient to stabilize a “stalk” intermediate if a typical number of fusion peptides assemble at the site of membrane fusion. The fusion activity of the fusion peptides increases with each increment in length, and this increase strictly correlates with the hydrophobic binding energy and the angle of insertion.

Using O2 to probe membrane immersion depth by 19F NMR

A fluorinated detergent, CF3(CF2)5C2H4-O-maltose, was reconstituted into a lipid bilayer model membrane system to demonstrate the feasibility of determining solvent accessibility and membrane immersion depth of each fluorinated group by 19F NMR. Apolar oxygen, which is known to partition with an increasing concentration gradient toward the hydrophobic membrane interior, exhibits a range of paramagnetic relaxation effects on 19F nuclei, depending on its depth in the membrane. This effect, which is predominately associated with spin-lattice relaxation rates (R1) and chemical shifts, can be amplified greatly with minimal line broadening by increasing the partial pressure of O2 at least 100-fold (i.e., PO2 greater than 20 bar). The differences of longitudinal relaxation rates at 20 bar of oxygen pressure to those under ambient pressure (R120bar − R10) are largest for those fluorine groups expected to be most deeply buried in the membrane bilayer. This result contrasts with the reverse trend, which is observed on addition of a membrane surface-associated paramagnetic species, 4-(N,N-dimethyl-N-hexadecyl) ammonium-2,2,6,6-tetramethylpiperidine-1-oxyl iodide (CAT-16) at ambient pressures. Thus, differential relaxation rates may be observed in 19F-labeled membrane-associated molecules resulting from the addition of apolar oxygen under high pressure. The results demonstrate that the degree of solvent accessibility and membrane immersion depth of specific fluorinated species in membrane-associated macromolecules can be probed by 19F NMR.

Segregation of Heterotrimeric G Proteins in Cell Surface Microdomains: Gq Binds Caveolin to Concentrate in Caveolae, whereas Gi and Gs Target Lipid Rafts by Default

Select lipid-anchored proteins such as glycosylphosphatidylinositol (GPI)-anchored proteins and nonreceptor tyrosine kinases may preferentially partition into sphingomyelin-rich and cholesterol-rich plasmalemmal microdomains, thereby acquiring resistance to detergent extraction. Two such domains, caveolae and lipid rafts, are morphologically and biochemically distinct, contain many signaling molecules, and may function in compartmentalizing cell surface signaling. Subfractionation and confocal immunofluorescence microscopy reveal that, in lung tissue and in cultured endothelial and epithelial cells, heterotrimeric G proteins (Gi, Gq, Gs, and Gβγ) target discrete cell surface microdomains. Gq specifically concentrates in caveolae, whereas Gi and Gs concentrate much more in lipid rafts marked by GPI-anchored proteins (5′ nucleotidase and folate receptor). Gq, apparently without Gβγ subunits, stably associates with plasmalemmal and cytosolic caveolin. Gi and Gs interact with Gβγ subunits but not caveolin. Gi and Gs, unlike Gq, readily move out of caveolae. Thus, caveolin may function as a scaffold to trap, concentrate, and stabilize Gq preferentially within caveolae over lipid rafts. In N2a cells lacking caveolae and caveolin, Gq, Gi, and Gs all concentrate in lipid rafts as a complex with Gβγ. Without effective physiological interaction with caveolin, G proteins tend by default to segregate in lipid rafts. The ramifications of the segregated microdomain distribution and the Gq-caveolin complex without Gβγ for trafficking, signaling, and mechanotransduction are discussed.

Nitric oxide partitioning into mitochondrial membranes and the control of respiration at cytochrome c oxidase

An emerging and important site of action for nitric oxide (NO) within cells is the mitochondrial inner membrane, where NO binds to and inhibits members of the electron transport chain, complex III and cytochrome c oxidase. Although it is known that inhibition of cytochrome c oxidase by NO is competitive with O2, the mechanisms that underlie this phenomenon remain unclear, and the impact of both NO and O2 partitioning into biological membranes has not been considered. These properties are particularly interesting because physiological O2 tensions can vary widely, with NO having a greater inhibitory effect at low O2 tensions (<20 μM). In this study, we present evidence for a consumption of NO in mitochondrial membranes in the absence of substrate, in a nonsaturable process that is O2 dependent. This consumption modulates inhibition of cytochrome c oxidase by NO and is enhanced by the addition of exogenous membranes. From these data, it is evident that the partition of NO into mitochondrial membranes has a major impact on the ability of NO to control mitochondrial respiration. The implications of this conclusion are discussed in the context of mitochondrial lipid:protein ratios and the importance of NO as a regulator of respiration in pathophysiology.

Drying Increases Intracellular Partitioning of Amphiphilic Substances into the Lipid Phase1 : Impact on Membrane Permeability and Significance for Desiccation Tolerance

Previously we proposed that endogenous amphiphilic substances may partition from the aqueous cytoplasm into the lipid phase during dehydration of desiccation-tolerant organ(ism)s and vice versa during rehydration. Their perturbing presence in membranes could thus explain the transient leakage from imbibing organisms. To study the mechanism of this phenomenon, amphiphilic nitroxide spin probes were introduced into the pollen of a model organism, Typha latifolia, and their partitioning behavior during dehydration and rehydration was analyzed by electron paramagnetic resonance spectroscopy. In hydrated pollen the spin probes mainly occurred in the aqueous phase; during dehydration, however, the amphiphilic spin probes partitioned into the lipid phase and had disappeared from the aqueous phase below 0.4 g water g−1 dry weight. During rehydration the probes reappeared in the aqueous phase above 0.4 g water g−1 dry weight. The partitioning back into the cytoplasm coincided with the decrease of the initially high plasma membrane permeability. A charged polar spin probe was trapped in the cytoplasm during drying. Liposome experiments showed that partitioning of an amphiphilic spin probe into the bilayer during dehydration caused transient leakage during rehydration. This was also observed with endogenous amphipaths that were extracted from pollen, implying similar partitioning behavior. In view of the fluidizing effect on membranes and the antioxidant properties of many endogenous amphipaths, we suggest that partitioning with drying may be pivotal to desiccation tolerance, despite the risk of imbibitional leakage.

Resonant tectorial membrane motion in the inner ear: its crucial role in frequency tuning.

The tectorial membrane has long been postulated as playing a role in the exquisite sensitivity of the cochlea. In particular, it has been proposed that the tectorial membrane provides a second resonant system, in addition to that of the basilar membrane, which contributes to the amplification of the motion of the cochlear partition. Until now, technical difficulties had prevented vibration measurements of the tectorial membrane and, therefore, precluded direct evidence of a mechanical resonance. In the study reported here, the vibration of the tectorial membrane was measured in two orthogonal directions by using a novel method of combining laser interferometry with a photodiode technique. It is shown experimentally that the motion of the tectorial membrane is resonant at a frequency of 0.5 octave (oct) below the resonant frequency of the basilar membrane and polarized parallel to the reticular lamina. It is concluded that the resonant motion of the tectorial membrane is due to a parallel resonance between the mass of the tectorial membrane and the compliance of the stereocilia of the outer hair cells. Moreover, in combination with the contractile force of outer hair cells, it is proposed that inertial motion of the tectorial membrane provides the necessary conditions to allow positive feedback of mechanical energy into the cochlear partition, thereby amplifying and tuning the cochlear response.

Dopamine transporters are markedly reduced in Lesch-Nyhan disease in vivo.

Dopamine (DA) deficiency has been implicated in Lesch-Nyhan disease (LND), a genetic disorder that is characterized by hyperuricemia, choreoathetosis, dystonia, and compulsive self-injury. To establish that DA deficiency is present in LND, the ligand WIN-35,428, which binds to DA transporters, was used to estimate the density of DA-containing neurons in the caudate and putamen of six patients with classic LND. Comparisons were made with 10 control subjects and 3 patients with Rett syndrome. Three methods were used to quantify the binding of the DA transporter so that its density could be estimated by a single dynamic positron emission tomography study. These approaches included the caudate- or putamen-to-cerebellum ratio of ligand at 80-90 min postinjection, kinetic analysis of the binding potential [Bmax/(Kd x Vd)] using the assumption of equal partition coefficients in the striatum and the cerebellum, and graphical analysis of the binding potential. Depending on the method of analysis, a 50-63% reduction of the binding to DA transporters in the caudate, and a 64-75% reduction in the putamen of the LND patients was observed compared to the normal control group. When LND patients were compared to Rett syndrome patients, similar reductions were found in the caudate (53-61%) and putamen (67-72%) in LND patients. Transporter binding in Rett syndrome patients was not significantly different from the normal controls. Finally, volumetric magnetic resonance imaging studies detected a 30% reduction in the caudate volume of LND patients. To ensure that a reduction in the caudate volume would not confound the results, a rigorous partial volume correction of the caudate time activity curve was performed. This correction resulted in an even greater decrease in the caudate-cerebellar ratio in LND patients when contrasted to controls. To our knowledge, these findings provide the first in vivo documentation of a dopaminergic reduction in LND and illustrate the role of positron emission tomography imaging in investigating neurodevelopmental disorders.