From calcium blips to calcium puffs: Theoretical analysis of the requirements for interchannel communication

In the cytoplasm of cells of different types, discrete clusters of inositol 1,4,5-trisphosphate-sensitive Ca2+ channels generate Ca2+ signals of graded size, ranging from blips, which involve the opening of only one channel, to moderately larger puffs, which result from the concerted opening of a few channels in the same cluster. These channel clusters are of unknown size or geometrical characteristics. The aim of this study was to estimate the number of channels and the interchannel distance within such a cluster. Because these characteristics are not attainable experimentally, we performed computer stochastic simulations of Ca2+ release events. We conclude that, to ensure efficient interchannel communication, as experimentally observed, a typical cluster should contain two or three tens of inositol 1,4,5-trisphosphate-sensitive Ca2+ channels in close contact.

Folding protein models with a simple hydrophobic energy function: The fundamental importance of monomer inside/outside segregation

The present study explores a “hydrophobic” energy function for folding simulations of the protein lattice model. The contribution of each monomer to conformational energy is the product of its “hydrophobicity” and the number of contacts it makes, i.e., E(h⃗, c⃗) = −Σi=1N cihi = −(h⃗.c⃗) is the negative scalar product between two vectors in N-dimensional cartesian space: h⃗ = (h1, … , hN), which represents monomer hydrophobicities and is sequence-dependent; and c⃗ = (c1, … , cN), which represents the number of contacts made by each monomer and is conformation-dependent. A simple theoretical analysis shows that restrictions are imposed concomitantly on both sequences and native structures if the stability criterion for protein-like behavior is to be satisfied. Given a conformation with vector c⃗, the best sequence is a vector h⃗ on the direction upon which the projection of c⃗ − c̄⃗ is maximal, where c̄⃗ is the diagonal vector with components equal to c̄, the average number of contacts per monomer in the unfolded state. Best native conformations are suggested to be not maximally compact, as assumed in many studies, but the ones with largest variance of contacts among its monomers, i.e., with monomers tending to occupy completely buried or completely exposed positions. This inside/outside segregation is reflected on an apolar/polar distribution on the corresponding sequence. Monte Carlo simulations in two dimensions corroborate this general scheme. Sequences targeted to conformations with large contact variances folded cooperatively with thermodynamics of a two-state transition. Sequences targeted to maximally compact conformations, which have lower contact variance, were either found to have degenerate ground state or to fold with much lower cooperativity.

TROSY in triple-resonance experiments: New perspectives for sequential NMR assignment of large proteins

The NMR assignment of 13C, 15N-labeled proteins with the use of triple resonance experiments is limited to molecular weights below ∼25,000 Daltons, mainly because of low sensitivity due to rapid transverse nuclear spin relaxation during the evolution and recording periods. For experiments that exclusively correlate the amide proton (1HN), the amide nitrogen (15N), and 13C atoms, this size limit has been previously extended by additional labeling with deuterium (2H). The present paper shows that the implementation of transverse relaxation-optimized spectroscopy ([15N,1H]-TROSY) into triple resonance experiments results in several-fold improved sensitivity for 2H/13C/15N-labeled proteins and approximately twofold sensitivity gain for 13C/15N-labeled proteins. Pulse schemes and spectra recorded with deuterated and protonated proteins are presented for the [15N, 1H]-TROSY-HNCA and [15N, 1H]-TROSY-HNCO experiments. A theoretical analysis of the HNCA experiment shows that the primary TROSY effect is on the transverse relaxation of 15N, which is only little affected by deuteration, and predicts sensitivity enhancements that are in close agreement with the experimental data.

A universal scaling law between gray matter and white matter of cerebral cortex

Neocortex, a new and rapidly evolving brain structure in mammals, has a similar layered architecture in species over a wide range of brain sizes. Larger brains require longer fibers to communicate between distant cortical areas; the volume of the white matter that contains long axons increases disproportionally faster than the volume of the gray matter that contains cell bodies, dendrites, and axons for local information processing, according to a power law. The theoretical analysis presented here shows how this remarkable anatomical regularity might arise naturally as a consequence of the local uniformity of the cortex and the requirement for compact arrangement of long axonal fibers. The predicted power law with an exponent of 4/3 minus a small correction for the thickness of the cortex accurately accounts for empirical data spanning several orders of magnitude in brain sizes for various mammalian species, including human and nonhuman primates.

Equilibration rates in lipid monolayers

A theoretical analysis is given for the rate of change of domain sizes in lipid monolayers at the air–water interface. The calculation is applicable to liquid domains formed from binary mixtures of lipids that form two coexisting liquid phases. Under conditions where the two lipid molecules have approximately equal areas, the equilibration rate does not involve macroscopic hydrodynamic flow in the subphase but rather depends on the diffusion coefficient of the lipid molecules. The calculation shows that the equilibration rate in binary mixtures of cholesterol and phosphatidylcholine is remarkably slow, the radius of a typical 20-μm diameter domain changing by as little as a part in a million per second. Under these circumstances, equilibration times of the order of days or weeks are expected. Even with such long times, the final state reached by the monolayer will in general be a state of metastable equilibrium, rather than true equilibrium.

An initiation element in the yeast CUP1 promoter is recognized by RNA polymerase II in the absence of TATA box-binding protein if the DNA is negatively supercoiled

Purified RNA polymerase II initiated transcription from the yeast CUP1 promoter fused to a C-less cassette if the DNA was negatively supercoiled. Relaxed plasmid was not transcribed. Transcription did not require addition of any other transcription factors. TATA box-binding protein (TBP) was not detectable in the polymerase preparation and the TATA box was not required. Deletion analysis of the CUP1 promoter revealed that a 25-bp element containing the initiation region was sufficient for recognition by polymerase. Two transcription start sites were mapped, one of which is identical to one of the two major start sites observed in vivo. Our observations can be accounted for by using a theoretical analysis of the probability of DNA melting within the plasmid as a function of superhelix density: the CUP1 initiation element is intrinsically unstable to superhelical stress, permitting entry of the polymerase, which then scans the DNA to locate the start site. In support of this analysis, the CUP1 promoter was sensitive to mung bean nuclease. These observations and a previous theoretical analysis of yeast genes support the idea that promoters are stress points within the DNA superhelix. The role of transcription factors might be to mark the promoter and to regulate specific melting of promoter DNA.

Statistical significance of protein structure prediction by threading

In this study, we estimate the statistical significance of structure prediction by threading. We introduce a single parameter ɛ that serves as a universal measure determining the probability that the best alignment is indeed a native-like analog. Parameter ɛ takes into account both length and composition of the query sequence and the number of decoys in threading simulation. It can be computed directly from the query sequence and potential of interactions, eliminating the need for sequence reshuffling and realignment. Although our theoretical analysis is general, here we compare its predictions with the results of gapless threading. Finally we estimate the number of decoys from which the native structure can be found by existing potentials of interactions. We discuss how this analysis can be extended to determine the optimal gap penalties for any sequence-structure alignment (threading) method, thus optimizing it to maximum possible performance.

CKAAPs DB: a conserved key amino acid positions database

The Conserved Key Amino Acid Positions DataBase (CKAAPs DB) provides access to an analysis of structurally similar proteins with dissimilar sequences where key residues within a common fold are identified. The derivation and significance of CKAAPs starting from pairwise structure alignments is described fully in Reddy et al. [Reddy,B.V.B., Li,W.W., Shindyalov,I.N. and Bourne,P.E. (2000) Proteins, in press]. The CKAAPs identified from this theoretical analysis are provided to experimentalists and theoreticians for potential use in protein engineering and modeling. It has been suggested that CKAAPs may be crucial features for protein folding, structural stability and function. Over 170 substructures, as defined by the Combinatorial Extension (CE) database, which are found in approximately 3000 representative polypeptide chains have been analyzed and are available in the CKAAPs DB. CKAAPs DB also provides CKAAPs of the representative set of proteins derived from the CE and FSSP databases. Thus the database contains over 5000 representative poly­peptide chains, covering all known structures in the PDB. A web interface to a relational database permits fast retrieval of structure-sequence alignments, CKAAPs and associated statistics. Users may query by PDB ID, protein name, function and Enzyme Classification number. Users may also submit protein alignments of their own to obtain CKAAPs. An interface to display CKAAPs on each structure from a web browser is also being implemented. CKAAPs DB is maintained by the San Diego Supercomputer Center and accessible at the URL http://ckaaps.sdsc.edu.

Diffusion and formation of microtubule asters: physical processes versus biochemical regulation.

Microtubule asters forming the mitotic spindle are assembled around two centrosomes through the process of dynamic instability in which microtubules alternate between growing and shrinking states. By modifying the dynamics of this assembly process, cell cycle enzymes, such as cdc2 cyclin kinases, regulate length distributions in the asters. It is believed that the same enzymes control the number of assembled microtubules by changing the "nucleating activity" of the centrosomes. Here we show that assembly of microtubule asters may be strongly altered by effects connected with diffusion of tubulin monomers. Theoretical analysis of a simple model describing assembly of microtubule asters clearly shows the existence of a region surrounding the centrosome depleted in GTP tubulin. The number of assembled microtubules may in some cases be limited by this depletion effect rather than by the number of available nucleation sites on the centrosome.