Statistical evaluation of pairwise protein sequence comparison with the Bayesian bootstrap

MOTIVATION: Protein sequence comparison methods are routinely used to infer the intricate network of evolutionary relationships found within the rapidly growing library of protein sequences, and thereby to predict the structure and function of uncharacterized proteins. In the present study, we detail an improved statistical benchmark of pairwise protein sequence comparison algorithms. We use bootstrap resampling techniques to determine standard statistical errors and to estimate the confidence of our conclusions. We show that the underlying structure within benchmark databases causes Efron's standard, non-parametric bootstrap to be biased. Consequently, the standard bootstrap underpredicts average performance when used in the context of evaluating sequence comparison methods. We have developed, as an alternative, an unbiased statistical evaluation based on the Bayesian bootstrap, a resampling method operationally similar to the standard bootstrap. RESULTS: We apply our analysis to the comparative study of amino acid substitution matrix families and find that using modern matrices results in a small, but statistically significant improvement in remote homology detection compared with the classic PAM and BLOSUM matrices. AVAILABILITY: The sequence sets and code for performing these analyses are available from http://compbio.berkeley.edu/. Contact: brenner@compbio.berkeley.edu.     

CLUSTAL W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice.

The sensitivity of the commonly used progressive multiple sequence alignment method has been greatly improved for the alignment of divergent protein sequences. Firstly, individual weights are assigned to each sequence in a partial alignment in order to down-weight near-duplicate sequences and up-weight the most divergent ones. Secondly, amino acid substitution matrices are varied at different alignment stages according to the divergence of the sequences to be aligned. Thirdly, residue-specific gap penalties and locally reduced gap penalties in hydrophilic regions encourage new gaps in potential loop regions rather than regular secondary structure. Fourthly, positions in early alignments where gaps have been opened receive locally reduced gap penalties to encourage the opening up of new gaps at these positions. These modifications are incorporated into a new program, CLUSTAL W which is freely available.     

Characterization of a putative clone for the 67-kilodalton elastin/laminin receptor suggests that it encodes a cytoplasmic protein rather than a cell surface receptor

The 67-kDa elastin binding protein shares many immunological and structural properties with the high-affinity 67-kDa tumor cell laminin receptor. Taking advantage of these similarities, we have screened a bovine cDNA library with a partial cDNA probe for the laminin receptor and have isolated and characterized a cDNA clone of 1038 bp that hybridizes to a single-size mRNA of 1.3 kb. The clone encodes a protein with a predicted molecular weight of 33K that lacks an N-terminal leader sequence, shows no posttranslational processing when translated in vitro in the presence of microsomes, and does not bind to elastin affinity columns. Although the bovine clone is nearly identical with clones encoding human and mouse proteins proported to be 67-kDa laminin receptor, physical and functional characteristics of the encoded protein suggest that it is a cytoplasmic protein that does not bind elastin. This finding calls into question the earlier conclusion that the clone encodes the 67-kDa receptor.     

Quantity rather than quality in teratospermic males: a histomorphometric and flow cytometric evaluation of spermatogenesis in the domestic cat (Felis catus)

Teratozoospermia (ejaculation of <40% morphologically normal sperm) commonly occurs within the Felidae, including certain domestic cats, but the cellular and molecular mechanisms that give rise to this phenomenon remain unknown. This study quantified spermatogenesis to identify differential dysfunctions in teratospermic versus normospermic (>60% normal sperm/ejaculate) domestic cats. Sperm used were from electroejaculates and cauda epididymides. Testes from 10 normo- and 10 teratospermic males were obtained by castration and then evaluated by histomorphometry, flow cytometry, and testicular testosterone enzyme immunoassay. Some morphometric traits (tubular diameter, epithelium height, interstitial area, number of Leydig cells, and blood vessels per cross-section) as well as testicular testosterone concentrations were similar between groups, but testicular volume was greater in teratospermic males. Stage frequencies differed also between both cat populations, suggesting possible dysfunctions in spermiation. Quantification of cell populations in most frequent stages revealed more spermatogenic cells and fewer Sertoli cells per tubule cross-section as well as per tissue unit in teratospermic donors. Hence, the ratio of spermatogenic cells per Sertoli cell was elevated in the teratospermic cat. DNA flow cytometry confirmed higher total spermatogenic and meiotic transformations in teratospermic males. In summary, compared with normospermic counterparts, teratospermic cats have a higher sperm output achieved by more sperm-producing tissue, more germ cells per Sertoli cell, and reduced germ cell loss during spermatogenesis. Gains in sperm quantity are produced at the expense of sperm quality.     

Performance evaluation of a new algorithm for the detection of remote homologs with sequence comparison

A detailed analysis of the performance of hybrid, a new sequence alignment algorithm developed by Yu and coworkers that combines Smith Waterman local dynamic programming with a local version of the maximum-likelihood approach, was made to access the applicability of this algorithm to the detection of distant homologs by sequence comparison. We analyzed the statistics of hybrid with a set of nonhomologous protein sequences from the SCOP database and found that the statistics of the scores from hybrid algorithm follows an Extreme Value Distribution with lambda approximately 1, as previously shown by Yu et al. for the case of artificially generated sequences. Local dynamic programming was compared to the hybrid algorithm by using two different test data sets of distant homologs from the PFAM and COGs protein sequence databases. The studies were made with several score functions in current use including OPTIMA, a new score function originally developed to detect remote homologs with the Smith Waterman algorithm. We found OPTIMA to be the best score function for both both dynamic programming and the hybrid algorithms. The ability of dynamic programming to discriminate between homologs and nonhomologs in the two sets of distantly related sequences is slightly better than that of hybrid algorithm. The advantage of producing accurate score statistics with only a few simulations may overcome the small differences in performance and make this new algorithm suitable for detection of homologs in conjunction with a wide range of score functions and gap penalties.     

Thermodynamic and structural studies of cavity formation in proteins suggest that loss of packing interactions rather than the hydrophobic effect dominates the observed energetics

The hydrophobic effect is widely believed to be an important determinant of protein stability. However, it is difficult to obtain unambiguous experimental estimates of the contribution of the hydrophobic driving force to the overall free energy of folding. Thermodynamic and structural studies of large to small substitutions in proteins are the most direct method of measuring this contribution. We have substituted the buried residue Phe8 in RNase S with alanine, methionine, and norleucine. Binding thermodynamics and structures were characterized by titration calorimetry and crystallography, respectively. The crystal structures of the RNase S F8A, F8M, and F8Nle mutants indicate that the protein tolerates the changes without any main chain adjustments. The correlation of structural and thermodynamic parameters associated with large to small substitutions was analyzed for nine mutants of RNase S as well as 32 additional cavity-containing mutants of T4 lysozyme, human lysozyme, and barnase. Such substitutions were typically found to result in negligible changes in DeltaC(p)() and positive values of both DeltaDeltaH degrees and DeltaDeltaS of folding. Enthalpic effects were dominant, and the sign of DeltaDeltaS is the opposite of that expected from the hydrophobic effect. Values of DeltaDeltaG degrees and DeltaDeltaH degrees correlated better with changes in packing parameters such as residue depth or occluded surface than with the change in accessible surface area upon folding. These results suggest that the loss of packing interactions rather than the hydrophobic effect is a dominant contributor to the observed energetics for large to small substitutions. Hence, estimates of the magnitude of the hydrophobic driving force derived from earlier mutational studies are likely to be significantly in excess of the actual value.     

Cell-free synthesis of tryptophanase from Escherichia coli. Use of ribonucleic acid isolated from induced cells and a comparison of the product from a system employing ribosomes with that from one employing ribosomes and exogenous ribonucleic acid

1. Polyribosomes and RNA were isolated from cultures in which tryptophanase (EC 4.2.1.-) was induced. The polyribosomes were incubated under conditions of protein synthesis, in the presence of a radioactive amino acid and a post-ribosomal supernatant fraction obtained from repressed cells. The RNA preparations were incubated under conditions of protein synthesis in the presence of a radioactive amino acid and a supernatant fraction containing ribosomes from repressed cells. 2. The system was characterized and the synthesis of a radioactive protein with the same chromatographic properties as tryptophanase was demonstrated. This synthesis was shown to be time-dependent and required the presence of RNA from induced cultures, ribosomes and an energy supply; it was inhibited by chloramphenicol. 3. The maximum activity for the synthesis of this protein was found to be associated with 23S rRNA isolated from sucrose gradients. 4. The N-terminal amino acid of tryptophanase was labelled in the protein synthesized in this system but not in the protein synthesized by polyribosomes (without added RNA). Conversely, the C-terminal amino acid of tryptophanase was labelled in the polyribosome system but not in the RNA-containing system. 5. Tryptic digests of protein labelled in vitro were compared with those of tryptophanase. No labelled tryptic peptides were identified other than tryptophanase tryptic peptides. An analysis of the results implied that in the polyribosome system almost the complete tryptophanase subunit chain was labelled but that in the RNA-containing system these chains were incompletely synthesized. 6. Sucrose-gradient analysis of protein synthesized in the RNA-containing system suggested that it cannot be converted into structures with the same sedimentation properties as native tryptophanase. 7. The significance of these results for the assay of tryptophanase mRNA and for an understanding of the control of the translation of this mRNA in vivo is discussed.     

The inbreeding effective number and the effective number of alleles in a population that varies in size

Consider a population that does not change in size. If it is assumed that there are an infinite number of possible neutral alleles at a locus and u is the probability that a particular gene mutates to some other gene in one generation, the effective number of alleles n_e is computed to be 4N_eu + 1, where N_e is the inbreeding effective population number. It is assumed in this paper that the number of individuals in a monoecious population, or the numbers of males and females in a dioecious population, are states in a finite irreducible Markov chain. In general it is impossible to obtain a single value of n_e. In some cases where the computation of n_e is possible, the results are as follows. When the population is monoecious, N_e is the reciprocal of the asymptotic average, over population sizes, of the probabilities that two gametes uniting to form an individual came from the same individual one generation earlier. In dioecious populations, N_e is the reciprocal of the long-run average of the probabilities that two homologous genes in separate individuals of one generation came from the same individual one generation earlier. Special cases are discussed.     

'Candidatus Liberibacter europaeus' sp. nov. that is associated with and transmitted by the psyllid Cacopsylla pyri apparently behaves as an endophyte rather than a pathogen

'Candidatus Liberibacter spp.' cause serious plant diseases. 'Candidatus Liberibacter asiaticus', 'Ca. L. americanus' and 'Ca. L. africanus' are the aetiological agents of citrus greening (Huanglongbing) in Asia, America and Africa. 'Candidatus Liberibacter solanacearum' causes diseases in Solanaceae in America and New Zealand. All four species are vectored by psyllid insects of different genera. Here, we show that the pear psyllid pest Cacopsylla pyri (L.) hosts a novel liberibacter species that we named 'Ca. Liberibacter europaeus'. It can bloom to high titres in the psyllid host, with more than 10(9) 16S rRNA gene copies per individual. Fluorescent in situ hybridization experiments showed that 'Ca. L. europaeus' is present in the host midgut lumen, salivary glands and Malpighian tubules. 'Candidatus L. europaeus' has a relatively high prevalence (> 51%) in C. pyri from different areas in the Piedmont and Valle d'Aosta regions in Italy and can be transmitted to pear plants in experimental transmission trials. However, even though high titres of the bacterium (more than 10(8) 16S rRNA gene copies g(-1) of pear plant tissue) could be detected, in the pear tissues no specific disease symptoms could be observed in the infected plants over a 6-month period. Despite liberibacters representing potential quarantine organisms, 'Ca. L. europaeus', first described in Italy and Europe, apparently behaves as an endophyte rather than a pathogen.     

Logging leaves a fingerprint on the number,size, spatial configuration and geometry of tropical forest canopy gaps

Recent advances in remote sensing such as airborne laser scanning have revolutionized our ability to accurately map forest canopy gaps, with huge implications for tracking forest dynamics at scale. However, few studies have explored how canopy gaps vary among forests at different successional stages following disturbances, such as those caused by logging. Moreover, most studies have focused exclusively on the size distribution of gaps, ignoring other key features such as their spatial distribution and shape. Here, we test a series of hypotheses about how the number, size, spatial configuration, and geometry of gaps vary across a logging disturbance gradient in Malaysian Borneo. As predicted, we found that recently logged forests had much higher gap fraction compared to old-growth forests, a result of having both a greater total number of gaps and a higher proportion of large gaps. Regrowing forests, on the other hand, fell at the opposite end of the spectrum, being characterized by both fewer and smaller gaps compared to nearby old-growth forests. Across all successional stages gaps were found to be spatially clustered. However, logging significantly diluted the degree of spatial aggregation and led to the formation of gaps with much more complex geometries. Our results showcase how logging and subsequent regrowth substantially alter not just the number and size of gaps in a forest, but also their spatial arrangement and shape. Linking these emergent patterns to their underlying processes is key to better understanding the impacts of human disturbance on the structure and function of tropical forests.     

Excitation properties of the squid axon membrane and model systems with current stimulation. Statistical evaluation and comparison.

The space-clamped squid axon membrane and two versions of the Hodgkin-Huxley model (the original, and a strongly adapting version) are subjected to a first order dynamic analysis. Stable, repetitive firing is induced by phase-locking nerve impulses to sinusoidal currents. The entrained impulses are then pulse position modulated by additional, small amplitude perturbation sinusoidal currents with respect to which the frequencies response of impulse density functions are measured. (Impulse density is defined as the number of impulses per unit time of an ensemble of membranes with each membrane subject to the same stimulus). Two categories of dynamic response are observed: one shows clear indications of a corner frequency, the other has the corner frequency obscured by dynamics associated with first order conductance perturbations in the interspike interval. The axon membrane responds with first order perturbations whereas the unmodified Hodgkin-Huxley model does not. Quantitative dynamic signatures suggest that the relaxation times of axonal recovery excitation variables are twice as long as those of the corresponding model variables. A number of other quantitative differences between axon and models, including the values of threshold stimuli are also observed.     

Renaming restoration: conceptualizing and justifying the activity as a restoration of lost moral value rather than a return to a previous state

A significant percentage of contemporary restoration work, while informed by history, aims for a novel state rather than an exact simulacrum of any particular historical state. However, the lay definition of “restoration” is to return something to its original state, and this influences public perceptions—and perhaps perceptions inside the field—about what the goals of restoration are. Relying on history to justify the proposed end state of a restoration project is problematic because of climate change, knowledge gaps, and the fact that ecosystems are dynamic and have no single historical state. Restorationists should be open to discussing whether the name of their field is inaccurate and considering alternatives. The process productively forces them to think about, articulate, and justify their values. One possible outcome of this process is a redefinition of “restoration” to mean a restoration of moral value rather than a restoration of a historical state. Restorationists will need to be comfortable talking about choices, intentions, values, and justifications in a world where historical fidelity no longer reigns supreme.     

A comparison of approaches to estimate the inbreeding coefficient and pairwise relatedness using genomic and pedigree data in a sheep population

Genome-wide SNP data provide a powerful tool to estimate pairwise relatedness among individuals and individual inbreeding coefficient. The aim of this study was to compare methods for estimating the two parameters in a Finnsheep population based on genome-wide SNPs and genealogies, separately. This study included ninety-nine Finnsheep in Finland that differed in coat colours (white, black, brown, grey, and black/white spotted) and were from a large pedigree comprising 319 119 animals. All the individuals were genotyped with the Illumina Ovine SNP50K BeadChip by the International Sheep Genomics Consortium. We identified three genetic subpopulations that corresponded approximately with the coat colours (grey, white, and black and brown) of the sheep. We detected a significant subdivision among the colour types (F _ST = 5.4%, P<0.05). We applied robust algorithms for the genomic estimation of individual inbreeding (F _SNP) and pairwise relatedness (Φ _SNP) as implemented in the programs KING and PLINK, respectively. Estimates of the two parameters from pedigrees (F _PED and Φ _PED) were computed using the RelaX2 program. Values of the two parameters estimated from genomic and genealogical data were mostly consistent, in particular for the highly inbred animals (e.g. inbreeding coefficient F>0.0625) and pairs of closely related animals (e.g. the full- or half-sibs). Nevertheless, we also detected differences in the two parameters between the approaches, particularly with respect to the grey Finnsheep. This could be due to the smaller sample size and relative incompleteness of the pedigree for them.We conclude that the genome-wide genomic data will provide useful information on a per sample or pairwise-samples basis in cases of complex genealogies or in the absence of genealogical data.     

Fluoxetine counteracts the cognitive and cellular effects of 5-fluorouracil in the rat hippocampus by a mechanism of prevention rather than recovery

5-Fluorouracil (5-FU) is a cytostatic drug associated with chemotherapy-induced cognitive impairments that many cancer patients experience after treatment. Previous work in rodents has shown that 5-FU reduces hippocampal cell proliferation, a possible mechanism for the observed cognitive impairment, and that both effects can be reversed by co-administration of the antidepressant, fluoxetine. In the present study we investigate the optimum time for administration of fluoxetine to reverse or prevent the cognitive and cellular effects of 5-FU. Male Lister-hooded rats received 5 injections of 5-FU (25 mg/kg, i.p.) over 2 weeks. Some rats were co-administered with fluoxetine (10 mg/kg/day, in drinking water) for 3 weeks before and during (preventative) or after (recovery) 5-FU treatment or both time periods (throughout). Spatial memory was tested using the novel location recognition (NLR) test and proliferation and survival of hippocampal cells was quantified using immunohistochemistry. 5-FU-treated rats showed cognitive impairment in the NLR task and a reduction in cell proliferation and survival in the subgranular zone of the dentate gyrus, compared to saline treated controls. These impairments were still seen for rats administered fluoxetine after 5-FU treatment, but were not present when fluoxetine was administered both before and during 5-FU treatment. The results demonstrate that fluoxetine is able to prevent but not reverse the cognitive and cellular effects of 5-FU. This provides information on the mechanism by which fluoxetine acts to protect against 5-FU and indicates when it would be beneficial to administer the antidepressant to cancer patients.     

Crystal structure and NMR studies of the apo SH2 domains of ZAP-70: two bikes rather than a tandem

The protein kinase ZAP-70 is involved in T-cell activation, and interacts with tyrosine-phosphorylated peptide sequences known as immunoreceptor tyrosine activation motifs (ITAMs), which are present in three of the subunits of the T-cell receptor. We have studied the tandem SH2 (tSH2) domains of ZAP-70, by both X-ray and NMR. Here, we present the crystal structure of the apoprotein, i.e., the tSH2 domain in the absence of ITAM. Comparison with the previously reported complex structure reveals that binding to the ITAM peptide induces surprisingly large movements between the two SH2 domains and within the actual binding sites. The conformation of the ITAM-free protein is partly governed by a hydrophobic cluster between the linker region and the C-terminal SH2 domain. Our data suggest that the two SH2 domains are able to undergo large interdomain movements. The proposed relative flexibility of the SH2 domains is further supported by the finding that no NMR signals could be detected for the two helices connecting the SH2 domains; these are likely to be broadened beyond detection due to conformational exchange. It is likely that this conformational reorientation induced by ITAM binding is the main signaling event activating the kinase domain in ZAP-70. Another NMR observation was that the N-terminal SH2 domain could bind tetrapeptides derived from the ITAM sequence, apparently without the need to interact with the C-terminal domain. In contrast, the C-terminal domain has little affinity for tetrapeptides. The opposite situation is true for binding to plain phosphotyrosine, where the C-terminal domain has a higher affinity. Distinct features in the crystal structure, showing the interdependence of both domains, explain these binding data.     

Reevaluation of the cox1 group I intron in Araceae and angiosperms indicates a history dominated by loss rather than horizontal transfer

The origin and modes of transmission of introns remain matters of much debate. Previous studies of the group I intron in the angiosperm cox1 gene inferred frequent angiosperm-to-angiosperm horizontal transmission of the intron from apparent incongruence between intron phylogenies and angiosperm phylogenies, patchy distribution of the intron among angiosperms, and differences between cox1 exonic coconversion tracts (the first 22 nt downstream of where the intron inserted). We analyzed the cox1 gene in 179 angiosperms, 110 of them containing the intron (intron(+)) and 69 lacking it (intron(-)). Our taxon sampling in Araceae is especially dense to test hypotheses about vertical and horizontal intron transmission put forward by Cho and Palmer (1999. Multiple acquisitions via horizontal transfer of a group I intron in the mitochondrial coxl gene during evolution of the Araceae family. Mol Biol Evol. 16:1155-1165). Maximum likelihood trees of Araceae cox1 introns, and also of all angiosperm cox1 introns, are largely congruent with known phylogenetic relationships in these taxa. The exceptions can be explained by low signal in the intron and long-branch attraction among a few taxa with high mitochondrial substitution rates. Analysis of the 179 coconversion tracts reveals 20 types of tracts (11 of them only found in single species, all involving silent substitutions). The distribution of these tracts on the angiosperm phylogeny shows a common ancestral type, characterizing most intron(+) and some intron(-) angiosperms, and several derivative tract types arising from gradual back mutation of the coconverted nucleotides. Molecular clock dating of small intron(+) and intron(-) sister clades suggests that coconversion tracts have persisted for 70 Myr in Araceae, whose cox1 sequences evolve comparatively slowly. Sequence similarity among the 110 introns ranges from 91% to identical, whereas putative homologs from fungi are highly different, but sampling in fungi is still sparse. Together, these results suggest that the cox1 intron entered angiosperms once, has largely or entirely been transmitted vertically, and has been lost numerous times, with coconversion tract footprints providing unreliable signal of former intron presence.     

Seasonal and habitat differences affect the impact of food and predation on herbivores: a comparison between gaps and understory of a tropical forest

Herbivore populations are influenced by a combination of food availability and predator pressure, the relative contribution of which is hypothesized to vary across a productivity gradient. In tropical forests, treefall gaps are pockets of high productivity in the otherwise less productive forest understory. Thus, we hypothesize that higher light availability in gaps will increase plant resources, thereby decreasing resource limitation of herbivores relative to the understory. As a result, predators should regulate herbivore populations in gaps, whereas food should limit herbivores in the understory. We quantified potential food availability and compared arthropod herbivore and predator densities in large forest light gaps and in the intact understory in Panama. Plants, young leaves, herbivores and predators were significantly more abundant per ground area in gaps than in the understory. This pattern was similar when we focused on seven gap specialist plant species and 15 shade-tolerant species growing in gaps and understory. Consistent with the hypothesis, herbivory rates were higher in gaps than the understory. Per capita predation rates on artificial caterpillars indicated higher predation pressure in gaps in both the dry and late wet seasons. These diverse lines of evidence all suggest that herbivores experience higher predator pressure in gaps and more food limitation in the understory.     

Cytometric evidence that cervical intraepithelial neoplasia I and II are dysplasias rather than true neoplasias. An image analysis study of factors involved in the progression of cervical lesions.

Image analysis was performed on 40 Feulgen-stained histologic samples and 48 Feulgen-stained cytologic preparations representing normal squamous epithelium and all grades of cervical lesions (from mild dysplasia to invasive carcinoma) in order to characterize the evolutionary progressive changes in cervical epithelial proliferative disease toward malignancy. Quantitative studies included the analysis of proliferative features, differentiation features, nuclear morphology and DNA content. The data obtained on the histologic sections showed that the various features, to a different extent, detected a gradual increase in phenotypic cellular disarrangements related to the progression of the cervical lesions toward malignancy--that is, the modifications to nuclear area, perimeter, DNA content, percentage of nuclei with nucleoli, nuclear/cytoplasmic ratio and percentage of cells with no membrane positivity for soybean agglutinin lectin were progressively greater, moving from normal epithelium and mild dysplasia toward infiltrating carcinoma. In particular, all the morphologic and histochemical features appeared to parallel a diploid reduction and the appearance of aneuploidy. The simultaneous evaluation of proliferation- and differentiation-related features, together with those of nuclear DNA content, showed two main successive preneoplastic lesions: one characterized by an increase in cell turnover without alterations in its organization and another by a true neoplastic disorder. The data obtained on sequential cytologic examinations showed that individual cell changes are detectable and seem basically to be characterized by the appearance of clusters of cells with somatic characteristics not observed in previous cytologic checks. From the results of our study, the cervical intraepithelial neoplasia (CIN) concept appears to be inaccurate. In fact, only CIN III (severe dysplasia/carcinoma in situ) lesions have the morphologic and proliferative alterations of true neoplasia. In contrast, CIN I and some cases of CIN II lesions lack these characteristics and seem to be properly classified as dysplasia, thus avoiding the term neoplasia, implicit in CIN. Moreover, the multivariate study of data sets of features related to the progressive somatic changes, both in histologically and cytologically studied cases, allows us to detect the steps of progression; they are marked by the appearance of cell clusters with qualitatively different phenotypic characters when compared to the cell populations from which they presumably arise. These results seem to provide a further argument against the CIN theory, which stresses the concept that progression is related only to a gradual numerical increase in an initially established phenotype with the characteristics of malignancy.