Estimating the probability for a protein to have a new fold: A statistical computational model

Structural genomics aims to solve a large number of protein structures that represent the protein space. Currently an exhaustive solution for all structures seems prohibitively expensive, so the challenge is to define a relatively small set of proteins with new, currently unknown folds. This paper presents a method that assigns each protein with a probability of having an unsolved fold. The method makes extensive use of protomap, a sequence-based classification, and scop, a structure-based classification. According to protomap, the protein space encodes the relationship among proteins as a graph whose vertices correspond to 13,354 clusters of proteins. A representative fold for a cluster with at least one solved protein is determined after superposition of all scop (release 1.37) folds onto protomap clusters. Distances within the protomap graph are computed from each representative fold to the neighboring folds. The distribution of these distances is used to create a statistical model for distances among those folds that are already known and those that have yet to be discovered. The distribution of distances for solved/unsolved proteins is significantly different. This difference makes it possible to use Bayes' rule to derive a statistical estimate that any protein has a yet undetermined fold. Proteins that score the highest probability to represent a new fold constitute the target list for structural determination. Our predicted probabilities for unsolved proteins correlate very well with the proportion of new folds among recently solved structures (new scop 1.39 records) that are disjoint from our original training set.

Estimating the probability of initiated cell death before tumor induction

The effects of cell toxicity are known to be inherent in carcinogenesis induced by radiation or chemical carcinogens. The event of cell death precludes tumor induction from occurring. A long standing problem is to estimate the proportion of initiated cells that die before tumor induction. No experimental techniques are currently available for directly gauging the rate of cell death over extended periods of time. The obstacle can be surmounted by newly developed theoretical methods of carcinogenesis modeling. In this paper, we apply such methods to published data on multiple lung tumors in mice receiving different schedules of urethane. Bioassays of this type play an important role in testing environmental chemicals for carcinogenic activity. Our estimates for urethane-induced carcinogenesis show that, unexpectedly, many initiated cells die early in the course of tumor promotion. We present numerical estimates for the probability of initiated cell death for different schedules (and doses) of urethane administration.

The estimation of statistical parameters for local alignment score distributions

The distribution of optimal local alignment scores of random sequences plays a vital role in evaluating the statistical significance of sequence alignments. These scores can be well described by an extreme-value distribution. The distribution’s parameters depend upon the scoring system employed and the random letter frequencies; in general they cannot be derived analytically, but must be estimated by curve fitting. For obtaining accurate parameter estimates, a form of the recently described ‘island’ method has several advantages. We describe this method in detail, and use it to investigate the functional dependence of these parameters on finite-length edge effects.

Vaccination for protection of retinal ganglion cells against death from glutamate cytotoxicity and ocular hypertension: Implications for glaucoma

Our group recently demonstrated that autoimmune T cells directed against central nervous system-associated myelin antigens protect neurons from secondary degeneration. We further showed that the synthetic peptide copolymer 1 (Cop-1), known to suppress experimental autoimmune encephalomyelitis, can be safely substituted for the natural myelin antigen in both passive and active immunization for neuroprotection of the injured optic nerve. Here we attempted to determine whether similar immunizations are protective from retinal ganglion cell loss resulting from a direct biochemical insult caused, for example, by glutamate (a major mediator of degeneration in acute and chronic optic nerve insults) and in a rat model of ocular hypertension. Passive immunization with T cells reactive to myelin basic protein or active immunization with myelin oligodendrocyte glycoprotein-derived peptide, although neuroprotective after optic nerve injury, was ineffective against glutamate toxicity in mice and rats. In contrast, the number of surviving retinal ganglion cells per square millimeter in glutamate-injected retinas was significantly larger in mice immunized 10 days previously with Cop-1 emulsified in complete Freund's adjuvant than in mice injected with PBS in the same adjuvant (2,133 ± 270 and 1,329 ± 121, respectively, mean ± SEM; P < 0.02). A similar pattern was observed when mice were immunized on the day of glutamate injection (1,777 ± 101 compared with 1,414 ± 36; P < 0.05), but not when they were immunized 48 h later. These findings suggest that protection from glutamate toxicity requires reinforcement of the immune system by antigens that are different from those associated with myelin. The use of Cop-1 apparently circumvents this antigen specificity barrier. In the rat ocular hypertension model, which simulates glaucoma, immunization with Cop-1 significantly reduced the retinal ganglion cell loss from 27.8% ± 6.8% to 4.3% ± 1.6%, without affecting the intraocular pressure. This study may point the way to a therapy for glaucoma, a neurodegenerative disease of the optic nerve often associated with increased intraocular pressure, as well as for acute and chronic degenerative disorders in which glutamate is a prominent participant.

A conditional probability analysis of cystic fibrosis transmembrane conductance regulator gating indicates that ATP has multiple effects during the gating cycle

ATP-binding cassette (ABC) transporters bind and hydrolyze ATP. In the cystic fibrosis transmembrane conductance regulator Cl− channel, this interaction with ATP generates a gating cycle between a closed (C) and two open (O1 and O2) conformations. To understand better how ATP controls channel activity, we examined gating transitions from the C to the O1 and O2 states and from these open states to the C conformation. We made three main observations. First, we found that the channel can open into either the O1 or O2 state, that the frequency of transitions to both states was increased by ATP concentration, and that ATP increased the relative proportion of openings into O1 vs. O2. These results indicate that ATP can interact with the closed state to open the channel in at least two ways, which may involve binding to nucleotide-binding domains (NBDs) NBD1 and NBD2. Second, ATP prolonged the burst duration and altered the way in which the channel closed. These data suggest that ATP also interacts with the open channel. Third, the channel showed runs of specific types of open–closed transitions. This finding suggests a mechanism with more than one cycle of gating transitions. These data suggest models to explain how ATP influences conformational transitions in cystic fibrosis transmembrane conductance regulator and perhaps other ABC transporters.

A unified statistical framework for sequence comparison and structure comparison

We present an approach for assessing the significance of sequence and structure comparisons by using nearly identical statistical formalisms for both sequence and structure. Doing so involves an all-vs.-all comparison of protein domains [taken here from the Structural Classification of Proteins (scop) database] and then fitting a simple distribution function to the observed scores. By using this distribution, we can attach a statistical significance to each comparison score in the form of a P value, the probability that a better score would occur by chance. As expected, we find that the scores for sequence matching follow an extreme-value distribution. The agreement, moreover, between the P values that we derive from this distribution and those reported by standard programs (e.g., blast and fasta validates our approach. Structure comparison scores also follow an extreme-value distribution when the statistics are expressed in terms of a structural alignment score (essentially the sum of reciprocated distances between aligned atoms minus gap penalties). We find that the traditional metric of structural similarity, the rms deviation in atom positions after fitting aligned atoms, follows a different distribution of scores and does not perform as well as the structural alignment score. Comparison of the sequence and structure statistics for pairs of proteins known to be related distantly shows that structural comparison is able to detect approximately twice as many distant relationships as sequence comparison at the same error rate. The comparison also indicates that there are very few pairs with significant similarity in terms of sequence but not structure whereas many pairs have significant similarity in terms of structure but not sequence.

Heat effects on DNA repair after ionising radiation: hyperthermia commonly increases the number of non-repaired double-strand breaks and structural rearrangements

After ionising radiation double-strand breaks (dsb) are lethal if not repaired or misrepaired. Cell killing is greatly enhanced by hyperthermia and it is questioned here whether heat not only affects dsb repair capacity but also fidelity in a chromosomal context. dsb repair experiments were designed so as to mainly score non-homologous end joining, while homologous recombination was largely precluded. Human male G0 fibroblasts were either preheated (45°C, 20 min) or not before X-irradiation. dsb induction and repair were measured by conventional gel electrophoresis and an assay combining restriction digestion using a rare cutting enzyme (NotI) and Southern hybridisation, which detects large chromosomal rearrangements (>100 kb). dsb induction rate in an X-chromosomal NotI fragment was 4.8 × 10–3 dsb/Gy/Mb. Similar values were found for the genome overall and also when cells were preheated. After 50 Gy, fibroblasts were competent to largely restore the original restriction fragment size. Five per cent of dsb remained non-rejoined and 14% were misrejoined. Correct restitution of restriction fragments occurred preferably during the first hour but continued at a slow rate for 12–16 h. In addition, dsb appeared to misrejoin throughout the entire repair period. After hyperthermia the fractions of non-rejoined and misrejoined dsb were similarly increased to 13 and 51%, respectively. It is suggested that heat increases the probability of dsb being incorrectly rejoined but it is not likely to interfere with one dsb repair pathway in particular.

Hypothesis testing and earthquake prediction.

Requirements for testing include advance specification of the conditional rate density (probability per unit time, area, and magnitude) or, alternatively, probabilities for specified intervals of time, space, and magnitude. Here I consider testing fully specified hypotheses, with no parameter adjustments or arbitrary decisions allowed during the test period. Because it may take decades to validate prediction methods, it is worthwhile to formulate testable hypotheses carefully in advance. Earthquake prediction generally implies that the probability will be temporarily higher than normal. Such a statement requires knowledge of "normal behavior"--that is, it requires a null hypothesis. Hypotheses can be tested in three ways: (i) by comparing the number of actual earth-quakes to the number predicted, (ii) by comparing the likelihood score of actual earthquakes to the predicted distribution, and (iii) by comparing the likelihood ratio to that of a null hypothesis. The first two tests are purely self-consistency tests, while the third is a direct comparison of two hypotheses. Predictions made without a statement of probability are very difficult to test, and any test must be based on the ratio of earthquakes in and out of the forecast regions.