A heterarchy of values determined by the topology of nervous nets

Because of the dromic character of purposive activities, the closed circuits sustaining them and their interaction can be treated topologically. It is found that to the value anomaly, whenA is preferred toB,B toC, butC toA, there corresponds a diadrome, or circularity in the net which is not the path of any drome and which cannot be mapped without a diallel on a surface sufficient to map the dromes. Thus the apparent inconsistency of preference is shown to indicate consistency of an order too high to permit construction of a scale of values, but submitting to finite topological analysis based on the finite number of nervous cells and their possible connections.     

The construction of a simultaneous functional order in nervous systems

The functional order of a collection of nervous elements is available to the system itself, as opposed to the anatomical geometrical order which exists only for external observers. It has been shown before (Part I) that covariances or coincidences in the signal activity of a neural net can be used in the construction of a simultaneous functional order in which a modality is represented as a concatenation of districts with a lattice structure. In this paper we will show how the resulting functional order in a nervous net can be related to the geometry of the underlying detector array. In particular, we will present an algorithm to construct an abstract geometrical complex from this functional order. The algebraic structure of this complex reflects the topological and geometrical structure of the underlying detector array. We will show how the activated subcomplexes of a complex can be related to segments of the detector array that are activated by the projection of a stimulus pattern. The homology of an abstract complex (and therefore of all of its subcomplexes) can be obtained from simple combinatorial operations on its coincidence scheme. Thus, both the geometry of a detector array and the topology of projections of stimulus patterns may have an objective existence for the neural system itself.     

The construction of a simultaneous functional order in nervous systems

In a previous paper (Part I) we introduced a model that constructs a simultaneous functional order in a set of neuronal elements by monitoring the coincidences in their signal activities (the so-called coincidence-model). The simultaneous signal activity in a neural net will be constrained both by its physical restrictions and by environmental constraints. In this paper we present the results of simulation experiments that were performed to study the influence of environmental constraits on the resulting functional order in a set of neural elements corresponding to a onedimensional detector array. We show that the coincidence-model produces a functional order that encodes the physical constraints of the environment. Moreover, we demonstrate that the signal activity in the neural net (the perceptions) can be related to events in the outer world. We provide some examples to demonstrate that our model may prove useful to gain insight into certain developmental disorders.     

The construction of a simultaneous functional order in nervous systems

The signal activity in a neural net will be constrained both by its physical structure and by environmental constraints. By monitoring its signal activity a neural system can build up a simultaneous functional order that encodes these constraints. We have previously (Part I) presented two models that construct a simultaneous functional order in a collection of neural elements using either signal-covariances or signal-coincides. In this paper we present the results of simulation experiments that were performed to study the influence of the physical constraints of a neural system on the simultaneous functional order produced by both models. In the simulation experiments we used a one-dimensional detector array. We delineate the physical constraints such an array has to satisfy in order to induce a functional order relation that allows an isomorphism with a geometrical order. We show that for an appropriate choice of the system parameters both models can produce a simultaneous functional order with sufficient internal coherence to allow isomorphisms with a triangulation. In this case the dimensionality and the coherence of the detector array are objectively available to the system itself.     

The construction of a simultaneous functional order in nervous systems

We have developed two algorithms that construct a simultaneous functional order in a collection of neural elements using purely functional relations. The input of the first algorithm is a matrix describing the total of covariances of signals carried by the members of the neural collection. The second algorithm proceeds from a matrix describing a primitive inclusion relation among the members of the neural collection that can be determined from coincidences in their signal activity. From this information both algorithms compute a partial functional order in the collection of neural elements. Such an order has an objective existence for the system itself and not only for an external observer. By either merging individual neurons or recruiting previously unspecified ones the partial order is locally transformed into a lattice order. Thus, the simultaneous functional order in a nervous net may become isomorphic with a geometrical order if the system has eneough internal coherence. Simulation experiments were done, both for the neuron-merging and the neuron-recruitment routines, to study the number of individuals in the resulting lattice order as a function of the number of individuals in the underlying partially ordered set.     

The primary and higher order structures of sea urchin ovoperoxidase as determined by cDNA cloning and predicted by homology modeling.

At fertilization, sea urchin ovoperoxidase (OPO) is incorporated into a nascent fertilization envelope in association with proteoliaisin and plays an essential role in its hardening. By cDNA cloning based on the previously reported partial amino acid sequences of Hemicentrotus pulcherrimus OPO, the cDNA and deduced amino acid sequences of the enzyme precursor were determined. Its 814-residue sequence consists of 125-residue signal- plus pro-peptides and 689-residue mature enzyme and has 92.2 and 81.4% identity with the OPOs of Strongylocentrotus purpuratus and Lytechinus variegatus, respectively. Compared with human myeloperoxidase, it has 30.3% identity and 9.6% similarity and has an additional C-terminal sequence of about 100 residues, suggesting its possible role as the site for interaction with proteoliaisin, if not for the entire sequence. The linker peptide sequence between L- and H-chains (e.g., ASFVTG and FSFFTG) cleaved off upon activation in mammalian promyeloperoxidases is intrinsically lacking in OPO, uniquely rendering the single 70K polypeptide a basic unit. The positions of distal and proximal histidines, distal arginine, and six disulfide bridges are highly conserved among mammalian and sea urchin peroxidases. The secondary structure was predicted by EMBL-PHD on the Internet for the whole sequence of mature OPO, and both secondary and tertiary structures were predicted by Swiss-Model for the partial sequences residues 18-65 and 123-570 with canine myeloperoxidase as a template. The overall architecture of the OPO molecule is close to that of human myeloperoxidase but its secondary structure has some differences based on the sequence variation, as depicted by RasMol. Another software, Swiss-PdbViewer, produced a slightly but significantly different image of the OPO structure for the same predicted atomic coordinates. A discrepancy was also found between the secondary structures of human myeloperoxidase in the PDB file and in its Swiss-PdbViewer presentation.     

A statistical consequence of the logical calculus of nervous nets

A formal method is derived for converting logical relations among the actions of neurons in a net into statistical relations among the frequencies of their impulses.     

Some remarks on the boolean algebra of nervous nets in mathematical biophysics

Recent demonstration by the author has shown that the fundamental equations of the mathematical biophysics of the central nervous system can be considered as describing the behavior of very large numbers of neurons, of which each one follows discontinuous laws, such as discussed by W. S. McCulloch and W. Pitts. In that light some of the old problems are discussed. The comparative merits of the “microscopic” and “macroscopic” approaches are discussed for the problem of the point to point correspondence between the retina and the cortex, with the number of connecting fibers much less than the number of cells. Some aspects of discrimination of intensities are also discussed. Finally, a few generalizations of the McCulloch-Pitts treatment are suggested, and a nervous network is constructed which illustrates some aspects of the perception of numbers.     

FCP: functional coverage of the proteome by structures

MOTIVATION: Tools and resources for translating the remarkable growth witnessed in recent years in the number of protein structures determined experimentally into actual gain in the functional coverage of the proteome are becoming increasingly necessary. We introduce FCP, a publicly accessible web tool dedicated to analyzing the current state and trends of the population of structures within protein families. FCP offers both graphical and quantitative data on the degree of functional coverage of enzymes and nuclear receptors by existing structures, as well as on the bias observed in the distribution of structures along their respective functional classification schemes. AVAILABILITY: http://cgl.imim.es/fcp CONTACT: jmestres@imim.es.     

Lipoprotein lipase: size of the functional unit determined by radiation inactivation

Radiation inactivation was used to determine the functional molecular weight of lipoprotein lipase (LPL) in rat heart and adipose tissues. This technique reveals the size of the smallest unit required to carry out the enzyme function. Supernatant fractions of the tissue homogenates were exposed to high energy electrons at -135 degrees C. LPL activity showed a simple exponential decay in all samples tested. Because changes in nutritional state shift the distribution of LPL between the capillary endothelial and parenchymal cells within heart and adipose tissues, fasted and refed rats were used for the radiation studies. The functional molecular weight was calculated to be 127,000 +/- 15,000 (mean +/- SD) daltons for heart and adipose. Thus, the smallest unit required for enzyme function was the same in both of these tissues and did not vary with nutritional state. The data suggest that, compared with LPL monomer sizes reported in the range 55,000 to 72,000, this active unit constitutes a dimer.     

The functional size of ferrochelatase determined in situ by radiation inactivation.

Ferrochelatase (EC 4.99.1.1) catalyzes the final step of heme biosynthesis, the insertion of iron(II) into protoporphyrin. It is an integral protein of the inner mitochondrial membrane. The functional size of bovine hepatic ferrochelatase has been studied in situ using radiation inactivation analysis. The functional unit required for enzymic activity in intact mitochondria was found to have a mass of 82 +/- 13 kDa. In contrast, the structural unit (evaluated in immunoblots following sodium dodecyl sulfate-polyacrylamide gel electrophoresis) has a mass of 40 +/- 10 kDa. Similar results were obtained when irradiation was performed on sodium cholate-solubilized mitochondria. The presence or absence of dithiothreitol during irradiation had no effect on target sizes obtained from either intact or solubilized mitochondria. Pairwise comparison of the functional and structural target sizes from each set of irradiated samples yielded a ratio of 2.0 +/- 0.4. Previous studies using sodium dodecyl sulfate-polyacrylamide gel electrophoresis and gel filtration chromatography have shown that a Mr 40,000 peptide is associated with ferrochelatase activity. This study shows that the functional size of bovine ferrochelatase is approximately 80 kDa; the data are most consistent with a model for active ferrochelatase composed of two structural subunits of about 40 kDa each.     

Comparison of the structures of three carboxypeptidase A-phosphonate complexes determined by X-ray crystallography

The structures of the complexes of carboxypeptidase A (CPA) with two tight-binding phosphonate inhibitors have been determined by X-ray crystallography. The inhibitors, Cbz-Phe-ValP-(O)-Phe[ZFVP(O)F] and Cbz-Ala-GlyP-(O)-Phe[ZAGP(O)F], bind noncovalently to CPA with dissociation constants (Ki's) of 11 fM and 710 pM, respectively. The CPA-ZFVP(O)F complex crystallizes in the space group P2(1)2(1)2(1) with unit cell parameters a = 65.3 A, b = 63.4 A, and c = 76.0 A, and the CPA-ZAGP(O)F complex crystallizes in the space group P2(1)2(1)2(1) with unit cell parameters a = 63.4 A, b = 65.9 A, and c = 74.4 A. Both structures were determined by molecular replacement to a resolution of 2.0 A. The final crystallographic residuals are 0.189 for the CPA-ZFVP(O)F complex and 0.191 for the CPA-ZAGP(O)F complex. The CPA-ZFVP(O)F complex exhibits the lowest Ki yet determined for an enzyme-inhibitor interaction. Comparison of the CPA-ZFVP(O)F structure with that of the CPA-ZAAP(O)F complex [Kim, H., & Lipscomb, W.N. (1990) Biochemistry 29, 5546-5555] indicates the likely important contributions of hydrophobic and weakly polar enzyme-inhibitor interactions to the exceptional stability of the CPA-ZFVP(O)F complex. Among these interactions is a network of four aromatic rings of CPA and ZFVP(O)F in a configuration that allows stabilizing aromatic-aromatic edge-to-face interactions from one ring to the next. A comparison of the structures of the CPA-ZFVP(O)F, CPA-ZAAP(O)F and CPA-ZAGP(O)F complexes shows that all three phosphonates assume a similar binding mode in the active-site binding groove of CPA. For ZAGP(O)F, the glycyl P1 residue does not lead to an anomalous or a partially disordered binding mode as seen in some previous complexes of CPA involving dipeptide analogue inhibitors with glycyl P1 residues. The additional enzyme-inhibitor interactions for these tripeptide phosphonates secure a binding mode in which a Pi portion of the inhibitor is clearly bound by the corresponding Si binding subsite. These three phosphonates have been implicated as transition-state analogues of the CPA-catalyzed reaction. The phosphinyl groups of these phosphonates coordinate to the active-site zinc in a manner that has been proposed as a characteristic feature of the general-base (Zn-hydroxyl or Zn-water) mechanism for the CPA-catalyzed reaction. Further mechanistic proposals are made for Arg-127, whose probable role in binding substrates is apparent in these CPA-phosphonate complexes.     

Comparison of experimentally determined protein structures by solution of Bloch equations

Nuclear Overhauser enhancement (NOESY) spectra were theoretically generated by solving the generalized Bloch equations with the appropriate initial conditions. The input to the equations were the coordinates of the protons of two similar crystal structures of basic pancreatic trypsin inhibitor. The two NOESY spectra obtained were compared to published experimental spectra of the protein in solution. It was found that the two crystal structures of basic pancreatic trypsin inhibitor give different theoretical spectra. The solution of the Bloch equations is very sensitive to small variations in the distance between protons (approx. 0.2 A), and to differences in the surrounding configurations. The method allows a detailed comparison of the crystal and solution structures of proteins. The structure of the trypsin inhibitor in solution was found to be similar to either one or the other crystal forms in different regions of the molecule.     

Solution structures of alpha-conotoxin G1 determined by two-dimensional NMR spectroscopy

Two-dimensional NMR data have been used to generate solution structures of alpha-conotoxin G1, a potent peptide antagonist of the acetylcholine receptor. Structural information was obtained in the form of proton-proton internuclear distance constraints, and initial structures were produced with a distance geometry algorithm. Energetically more favorable structures were generated by using the distance geometry structures as input for a constrained energy minimization program. The results of both of these calculations indicate that the overall backbone conformation of the molecule is well-defined by the NMR data whereas the side-chain conformations are generally less well-defined. The main structural features derived from the NMR data were the presence of tight turns centered on residues Pro5 and Arg9. The solution structures are compared with previous proposed models of conotoxin G1, and the NMR data are interpreted in conjunction with chemical modification studies and structural properties of other antagonists of the acetylcholine receptor to gain insight into structure-activity relationships in these peptide toxins.     

Differences in the solution structures of the parallel beta-helical pectate lyases as determined by limited proteolysis

The pectate lyase family of proteins has been shown to fold into a novel domain motif, the right-handed parallel beta-helix. As a means of gaining insight to the solution structure of the pectate lyases, the enzymes were subjected to limited proteolytic digestion by the endoproteases AspN, GluC and trypsin. The effects of proteolytic cleavage on enzymatic activity were determined, and the early products of proteolysis were identified by capillary electrophoresis, MALDI-TOF mass spectrometry and HPLC. A single peptide bond between Lys158 and Asp159 in pectate lyase B (PLb) was cleaved by both AspN and trypsin, with no detectable hydrolysis of PLb by GluC. Pectate lyase E (PLe) was hydrolyzed by trypsin between Lys164 and Asp165, a bond on an analogous loop structure found to be susceptible to proteolytic attack in PLb. AspN and GluC preferentially hydrolyzed peptide bonds (at Asp127 and Glu124, respectively) on another loop extending from the central beta-helical core of PLe. A single beta-strand of the central cylinder of the pectate lyase C (PLc) molecule was susceptible to all three proteases used. These data demonstrate that the most susceptible peptide bonds to proteolytic scission within the native enzymes lie on or near one of the three parallel beta-sheets that compose the core domain motif Despite the proximity of the proteolytic cleavages to the catalytic sites of the enzymes, significant retention of lyase activity was observed after partial proteolysis, indicating preservation of functional tertiary structure in the proteolytic products.     

Immunohistochemical mapping of perineuronal nets containing chondroitin unsulfate proteoglycan in the rat central nervous system

Subsets of neurons ensheathed by perineuronal nets containing chondroitin unsulfate proteoglycan have been immunohistochemically mapped throughout the rat central nervous system from the olfactory bulb to the spinal cord. A variable proportion of neurons were outlined by immunoreactivity for the monoclonal antibody (Mab 1B5), but only after chondroitinase ABC digestion. In forebrain cortical structures the only immunoreactive nets were around interneurons; in contrast, throughout the brainstem and spinal cord a large proportion of projection neurons were surrounded by intense immunoreactivity. Immunoreactivity was ordinarily found in the neuropil between neurons surrounded by an immunopositive net. By contrast, within the pyriform cortex the neuropil of the plexiform layer was intensely immunoreactive even though no perineuronal net could be found. The presence of perineuronal nets could not be correlated with any single class of neurons; however a few functionally related groups (e.g., motor and motor-related structures: motor neurons both in the spinal cord and in the efferent somatic nuclei of the brainstem, deep cerebellar nuclei, vestibular nuclei; red nucleus, reticular formation; central auditory pathway: ventral cochlear nucleus, trapezoid body, superior olive, nucleus of the lateral lemniscus, inferior colliculus, medial geniculate body) were the main components of the neuronal subpopulation displaying chondroitin unsulfate proteoglycans in the surrounding extracellular matrix. The immunodecorated neurons found in the present study and those shown by different monoclonal antibodies or by lectin cytochemisty, revealed consistent overlapping of their distribution patterns.     

Sterility of males determined by functional features of the mouse spermatozoa bearing t-complex

The mechanisms underlying normal spermatogenesis and its pathology expressed as male sterility determined by t-complex located on chromosome 17 in mice are considered in this review. t-Complex is a very convenient model with diverse markers of expression of the genes involved in development of the functional features of the spermatozoa bearing t-complex. These features include defects of mobility, capacitation, and acrosome reactions, which determine full or partial male sterility. It has been proposed that the defects of capacitation are also inherent in humans and affect male fertility. This homology is confirmed by the presence of the male gene Tcp11 in humans and demonstration of the fact that the protein TCP11 plays a leading role in modulation of the capacitation of murine spermatozoa. Hence it follows that the defects of human genes leading to incomplete binding of the fertilization promoting peptide could play a certain role in a decreased male fertility. All this is essential not only for deeper understanding of the biology of spermatozoa, but also for development of new therapeutic methods of finding and treating the semen pathology.     

The separate profile structures of the functional calcium pump protein and the phospholipid bilayer within isolated sarcoplasmic reticulum membranes determined by X-ray and neutron diffraction

The detailed profile structure of the isolated sarcoplasmic reticulum membrane was studied utilizing a combination of X-ray and neutron diffraction. The water and lipid profile structures within the sarcoplasmic reticulum membrane were determined at 28 A resolution directly by neutron diffraction and selective deuteration of the water and lipid components. The previously determined electron density profile structure of the sarcoplasmic reticulum membrane at 12 A resolution was subjected to model refinement analysis constrained by the neutron diffraction results, thereby providing unique higher resolution calculated lipid and protein profile structures. It was found that the lipid bilayer profile structure of the isolated sarcoplasmic reticulum membrane is asymmetric, primarily the result of more lipid residing in the inner versus the outer monolayer of the sarcoplasmic reticulum lipid bilayer. The asymmetry in the lipid composition was necessarily coincident with a complimentary asymmetry in the protein mass distribution between the two monolayers in order to preserve the overall cross-sectional area of lipid and protein throughout the lipid bilayer region of the sarcoplasmic reticulum membrane profile structure. Approximately 50% of the mass of the total protein was found to be localized externally to the sarcoplasmic reticulum membrane lipid bilayer protruding from the outer lipid monolayer into the extravesicular medium. The structural features of the protein protrusion appear to be rather variable depending upon the environment of the sarcoplasmic reticulum membrane. This highly asymmetric structural organization of the sarcoplasmic reticulum membrane profile is consistent with its primary function of unidirectional calcium transport.