RESUMO
BACKGROUND: Defects in BRCA1, BRCA2, and other members of the homologous recombination pathway have potential therapeutic relevance when used to support agents that introduce or exploit double-stranded DNA breaks. This study examines the association between homologous recombination defects and genomic patterns of loss of heterozygosity (LOH). METHODS: Ovarian tumours from two independent data sets were characterised for defects in BRCA1, BRCA2, and RAD51C, and LOH profiles were generated. Publically available data were downloaded for a third independent data set. The same analyses were performed on 57 cancer cell lines. RESULTS: Loss of heterozygosity regions of intermediate size were observed more frequently in tumours with defective BRCA1 or BRCA2 (P=10(-11)). The homologous recombination deficiency (HRD) score was defined as the number of these regions observed in a tumour sample. The association between HRD score and BRCA deficiency was validated in two independent ovarian cancer data sets (P=10(-5) and 10(-29)), and identified breast and pancreatic cell lines with BRCA defects. CONCLUSION: The HRD score appears capable of detecting homologous recombination defects regardless of aetiology or mechanism. This score could facilitate the use of PARP inhibitors and platinum in breast, ovarian, and other cancers.
Assuntos
Perda de Heterozigosidade , Neoplasias Epiteliais e Glandulares/genética , Neoplasias Ovarianas/genética , Reparo de DNA por Recombinação , Adulto , Idoso , Idoso de 80 Anos ou mais , Proteína BRCA1/genética , Proteína BRCA2/genética , Carcinoma Epitelial do Ovário , Linhagem Celular Tumoral , Estudos de Coortes , Quebras de DNA de Cadeia Dupla , Proteínas de Ligação a DNA/genética , Intervalo Livre de Doença , Feminino , Humanos , Pessoa de Meia-IdadeRESUMO
The HTR1A -1019C>G genotype was associated with major depression in the Utah population. Linkage analysis on Utah pedigrees with strong family histories of major depression including only cases with the HTR1A -1019G allele revealed a linkage peak on chromosome 10 (maximum HLOD=4.4). Sequencing of all known genes in the linkage region revealed disease-segregating single-nucleotide polymorphisms (SNPs) in LHPP. LHPP SNPs were also associated with major depression in both Utah and Ashkenazi populations. Consistent with the linkage evidence, LHPP associations depended on HTR1A genotype. Lhpp or a product of a collinear brain-specific transcript, therefore, may interact with Htr1a in the pathogenesis of major depression.
Assuntos
Transtorno Depressivo Maior/epidemiologia , Transtorno Depressivo Maior/genética , Ligação Genética , Pirofosfatase Inorgânica/genética , Receptor 5-HT1A de Serotonina/genética , Cromossomos Humanos Par 10 , Feminino , Genótipo , Humanos , Judeus/genética , Judeus/estatística & dados numéricos , Masculino , Linhagem , Polimorfismo de Nucleotídeo Único , Fatores de Risco , Utah/epidemiologiaRESUMO
We study the impact of disulfide bonds on protein stability and folding. Using lattice model simulations, we show that formation of a disulfide bond stabilizes a protein to an extent that depends on the distance along the chain between linked cysteine residues. However, the impact of disulfide bonds on folding kinetics varies broadly, from acceleration when disulfides are introduced in or close to the folding nucleus, to slowing when disulfides are introduced outside the nucleus. Having established the effect of disulfide bonds on stability, we study the correlation between the number of disulfide bonds and the composition of certain amino acid classes with the goal to use it as a statistical probe into factors that contribute to stability of proteins. We find that the number of disulfides is negatively correlated with aliphatic hydrophobic but not aromatic content. It is surprising that we observe a strong correlation of disulfide content with polar (Q,S,T,N) amino acid content and a strong negative correlation with charged (E,D,K,R) content. These findings provide insights into factors that determine protein stability and principles of protein design as well as possible relations of disulfide bonds and protein function.
Assuntos
Biologia Computacional , Simulação por Computador , Dissulfetos/metabolismo , Dobramento de Proteína , Proteínas/química , Proteínas/metabolismo , Aminoácidos/análise , Cisteína/metabolismo , Bases de Dados Factuais , Dissulfetos/química , Cinética , Estatística como Assunto , Temperatura , TermodinâmicaRESUMO
To address the question of how the geometry of a protein's native conformation affects its folding and stability, we studied three model 36-mers on a cubic lattice. The native structure of one of these model 36-mers consisted mostly of local contacts, while that of a second consisted mostly of non-local contacts. The third native structure had a typical compact native conformation, and served as our reference. For each protein, the amino acid sequence was designed to have a pronounced energy minimum at its native conformation. We observed dramatic differences in folding, dependent on the presence or absence of non-local contacts. For the proteins with a typical large number of non-local contacts, the folding transition was all-or-none, whereas for the one with mostly local contacts, it was not. Although the maximum rate of folding was similar for all three proteins, we found that under conditions at which each native conformation was stable, the structure with mostly non-local contacts folded two orders of magnitude faster than the one with mostly local contacts. The statistical analysis of protein structure agrees fully with the implications of the theory. We discuss the importance of cooperativity in protein folding for its stability.
Assuntos
Dobramento de Proteína , Proteínas/química , Termodinâmica , Sequência de Aminoácidos , Simulação por Computador , Cinética , Modelos Químicos , Dados de Sequência Molecular , Conformação ProteicaRESUMO
INTRODUCTION: Interpretation of results from mutation screening of tumour suppressor genes known to harbour high risk susceptibility mutations, such as APC, BRCA1, BRCA2, MLH1, MSH2, TP53, and PTEN, is becoming an increasingly important part of clinical practice. Interpretation of truncating mutations, gene rearrangements, and obvious splice junction mutations, is generally straightforward. However, classification of missense variants often presents a difficult problem. From a series of 20,000 full sequence tests of BRCA1 carried out at Myriad Genetic Laboratories, a total of 314 different missense changes and eight in-frame deletions were observed. Before this study, only 21 of these missense changes were classified as deleterious or suspected deleterious and 14 as neutral or of little clinical significance. METHODS: We have used a combination of a multiple sequence alignment of orthologous BRCA1 sequences and a measure of the chemical difference between the amino acids present at individual residues in the sequence alignment to classify missense variants and in-frame deletions detected during mutation screening of BRCA1. RESULTS: In the present analysis we were able to classify an additional 50 missense variants and two in-frame deletions as probably deleterious and 92 missense variants as probably neutral. Thus we have tentatively classified about 50% of the unclassified missense variants observed during clinical testing of BRCA1. DISCUSSION: An internal test of the analysis is consistent with our classification of the variants designated probably deleterious; however, we must stress that this classification is tentative and does not have sufficient independent confirmation to serve as a clinically applicable stand alone method.
Assuntos
Proteína BRCA1/genética , Genes BRCA1 , Variação Genética/genética , Mutação de Sentido Incorreto/genética , Sequência de Aminoácidos/genética , Animais , Proteína BRCA1/classificação , Galinhas/genética , Sequência Conservada/genética , DNA/classificação , DNA/genética , Cães , Evolução Molecular , Proteínas de Peixes/genética , Predisposição Genética para Doença/classificação , Predisposição Genética para Doença/genética , Humanos , Camundongos , Modelos Genéticos , Dados de Sequência Molecular , Pan troglodytes/genética , Alinhamento de Sequência/métodos , Alinhamento de Sequência/estatística & dados numéricos , Análise de Sequência de DNA/estatística & dados numéricos , Takifugu/genética , Proteínas de Xenopus/genéticaRESUMO
By means of Monte Carlo simulation, we investigated the equilibrium between folded and unfolded states of lattice model proteins. The amino acid sequences were designed to have pronounced energy minimum target conformations of different length and shape. For short fully compact (36-mer) proteins, the all-or-none transition from the unfolded state to the native state was observed. This was not always the case for longer proteins. Among 12 designed sequences with the native structure of a fully compact 48-mer, a simple all-or-none transition was observed in only three cases. For the other nine sequences, three states of behavior-the native, denatured, and intermediate states-were found. The contiguous part of the native structure (domain) was conserved in the intermediate state, whereas the remaining part was completely unfolded and structureless. These parts melted separately from each other.
Assuntos
Modelos Químicos , Conformação Proteica , Dobramento de Proteína , Proteínas/química , Sequência de Aminoácidos , Simulação por Computador , Modelos Moleculares , Dados de Sequência Molecular , Método de Monte Carlo , TemperaturaRESUMO
A pragmatic approach that balances the benefit of a whole-genome association (WGA) experiment against the cost of individual genotyping is to use pooled genomic DNA samples. We aimed to determine the feasibility of this approach in a WGA scan in rheumatoid arthritis (RA) using the validated human leucocyte antigen (HLA) and PTPN22 associations as test loci. A total of 203 269 single-nucleotide polymorphisms (SNPs) on the Affymetrix 100K GeneChip and Illumina Infinium microarrays were examined. A new approach to the estimation of allele frequencies from Affymetrix hybridization intensities was developed involving weighting for quality signals from the probe quartets. SNPs were ranked by z-scores, combined from United Kingdom and New Zealand case-control cohorts. Within a 1.7 Mb HLA region, 33 of the 257 SNPs and at PTPN22, 21 of the 45 SNPs, were ranked within the top 100 associated SNPs genome wide. Within PTPN22, individual genotyping of SNP rs1343125 within MAGI3 confirmed association and provided some evidence for association independent of the PTPN22 620W variant (P=0.03). Our results emphasize the feasibility of using genomic DNA pooling for the detection of association with complex disease susceptibility alleles. The results also underscore the importance of the HLA and PTPN22 loci in RA aetiology.
Assuntos
Artrite Reumatoide/genética , Predisposição Genética para Doença , Genoma Humano , Genômica/métodos , Estudos de Casos e Controles , Estudos de Coortes , DNA/genética , Feminino , Antígenos HLA/genética , Humanos , Masculino , Análise de Sequência com Séries de Oligonucleotídeos , Polimorfismo de Nucleotídeo Único , Proteína Tirosina Fosfatase não Receptora Tipo 22 , Proteínas Tirosina Fosfatases/genéticaRESUMO
APAF1, encoding the protein apoptosis protease activating factor 1 (Apaf-1), has recently been established as a chromosome 12 gene conferring predisposition to major depression in humans. The molecular phenotypes of Apaf-1 variants were determined by in vitro reconstruction of the apoptosome complex in which Apaf-1 activates caspase 9 and thus initiates a cascade of proteolytic events leading to apoptotic destruction of the cell. Cellular phenotypes were measured using a yeast heterologous expression assay in which human Apaf-1 and other proteins necessary to constitute a functional apoptotic pathway were overexpressed. Apaf-1 variants encoded by APAF1 alleles that segregate with major depression in families linked to chromosome 12 shared a common gain-of-function phenotype in both assay systems. In contrast, other Apaf-1 variants showed neutral or loss-of-function phenotypes. The depression-associated alleles thus have a common phenotype that is distinct from that of non-associated variants. This result suggests an etiologic role for enhanced apoptosis in major depression.
Assuntos
Apoptose/genética , Transtorno Depressivo Maior/genética , Transtorno Depressivo Maior/patologia , Peptídeos e Proteínas de Sinalização Intracelular/genética , Proteínas/genética , Alelos , Fator Apoptótico 1 Ativador de Proteases , Predisposição Genética para Doença , Humanos , Fenótipo , Polimorfismo GenéticoRESUMO
Experimental and simulation studies show that small monomeric proteins fold in one kinetic step, which entails overcoming the free-energy barrier between the unfolded and the native protein through a transition state. Two models of transition state formation have been proposed: a 'nonspecific' one in which it depends on the formation of a sufficient number of native-like contacts regardless of what amino acids are involved, and a 'specific' one, in which it depends on formation of a specific subset of the native structure (a folding nucleus). The latter requires that some amino acids form most of their contacts in the transition state, whereas others only do so on reaching the native conformation. If so, mutations affecting the stability of the transition state nucleus should have a greater effect on the folding kinetics than mutations elsewhere, and the residues involved should be evolutionarily conserved. Lattice-model simulations and experiments suggest that such mutations exist. Here we present a method for determining the folding nucleus of a protein with known structure with two-state folding kinetics. This method is based on the alignment of many sequences designed to fold into the native conformation of a protein to identify the positions where amino acids are most conserved in designed sequences. The method is applied to chymotrypsin inhibitor 2 (CI2), a protein whose transition state has been previously studied by protein engineering. The involvement of residues in folding nucleus of CI2 is clearly correlated with their conservation in design, and the residues forming the nucleus are highly conserved in 23 natural sequences homologous to CI2.
Assuntos
Sequência Conservada , Dobramento de Proteína , Sequência de Aminoácidos , Quimotripsina/antagonistas & inibidores , Cinética , Dados de Sequência Molecular , Método de Monte Carlo , Peptídeos/química , Proteínas de Plantas , Alinhamento de Sequência , Inibidores de Serina Proteinase/químicaRESUMO
BACKGROUND: The role of intermediates in protein folding has been a matter of great controversy. Although it was widely believed that intermediates play a key role in minimizing the search problem associated with the Levinthal paradox, experimental evidence has been accumulating that small proteins fold fast without any detectable intermediates. RESULTS: We study the thermodynamics and kinetics of folding using a simple lattice model. Two folding sequences obtained by the design procedure exhibit different folding scenarios. The first sequence folds fast to the native state and does not exhibit any populated intermediates during folding. In contrast, the second sequence folds much slower, often being trapped in misfolded low-energy conformations. However, a small fraction of folding molecules for the second sequence fold on a fast track avoiding misfolded traps. In equilibrium at the same temperature the second sequence has a highly populated intermediate with structure similar to that of the kinetics intermediate. CONCLUSIONS: Our analysis suggests that intermediates may often destabilize native conformations and derail the folding process leading it to traps. Less-optimized sequences fold via parallel pathways involving misfolded intermediates. A better designed sequence is more stable in the native state and folds fast without intermediates in a two-state process.
Assuntos
Modelos Químicos , Dobramento de Proteína , Sequência de Aminoácidos , Desenho de Fármacos , Estabilidade de Medicamentos , Cinética , Dados de Sequência Molecular , Estrutura Molecular , Conformação Proteica , Proteínas/química , TermodinâmicaRESUMO
BACKGROUND: A number of approaches to design stable and fast-folding sequences for model polypeptide chains have been based on the premise that optimization of the relative energy of the native conformation (or Z-score) is sufficient to yield stable and fast-folding sequences. Although this approach has been successful, for longer chains it often yielded sequences that failed to fold cooperatively, instead having multidomain folding behavior. RESULTS: We show that one of the factors determining single-domain or multidomain folding behavior is the dispersion of energies of native contacts. So, we study folding of sequences optimized to have the same native conformation as a global energy minimum but having different dispersion of native contact energies. Our results suggest that under conditions at which native conformation is stable, the best-folding proteins are those that have smaller heterogeneity of native contact energies. For them, the folding transition is all-or-none. On the other hand, proteins with greater heterogeneity of native contact energies have more gradual multidomain folding transition and fold into stable native conformation much slower than those proteins with small dispersion of native contact energies.
Assuntos
Desenho de Fármacos , Dobramento de Proteína , Proteínas/química , Sequência de Aminoácidos , Estabilidade de Medicamentos , Cinética , Modelos Químicos , Dados de Sequência Molecular , Conformação Proteica , TermodinâmicaRESUMO
We propose an algorithm providing sequences of model proteins with rapid folding into a given target (native) conformation. This algorithm is applied to a chain of 27 residues on a cubic lattice. It generates sequences with folding 2 orders of magnitude faster than that of the practically random starting sequence. Thermodynamic analysis shows that the increase in speed is matched by an increase in stability: the evolved sequences are much more stable in their native conformation than the initial random sequence. The unfolding temperature for evolved sequences is slightly higher than the simulation temperature, bearing direct correspondence to the relatively low stability of real proteins.
Assuntos
Peptídeos/química , Dobramento de Proteína , Algoritmos , Cinética , Método de Monte Carlo , TermodinâmicaRESUMO
Folding of the lattice model of proteins is studied using Monte Carlo simulation. The amino acid sequence is designed to have a pronounced energy minimum for a given target (native) conformation. Our simulations reveal two possible scenarios. When the overall attraction between residues dominates, we find that folding to the native conformation is preceded by a rapid collapse into a burst intermediate which is a compact but structureless globule. Then, after a much longer time, an all-or-none transition from the globule to the native conformation occurs. In contrast, when the overall attraction is not strong, we do not observe a burst collapse stage. Instead, we find an all-or-none transition directly from the coil to the native conformation. Both scenarios yield comparable rates of folding. On the basis of these findings we discuss the role of intermediates in thermodynamics and kinetics of protein folding.
Assuntos
Dobramento de Proteína , Sequência de Aminoácidos , Simulação por Computador , Cinética , Modelos Químicos , Dados de Sequência Molecular , Método de Monte Carlo , Conformação Proteica , Estrutura Secundária de Proteína , Proteínas/química , TermodinâmicaRESUMO
In this work, we discuss a possible origin of the first biopolymers with stable unique structures. We suggest that at the prebiotic stage of evolution, long organic polymers had to be compact to avoid hydrolysis and had to be soluble and thus must not be exceedingly hydrophobic. We present an algorithm that generates such sequences for model proteins. The evolved sequences turn out to have a stable unique structure, into which they quickly fold. This result illustrates the idea that the unique three-dimensional native structures of first biopolymers could have evolved as a side effect of nonspecific physicochemical factors acting at the prebiotic stage of evolution.
Assuntos
Algoritmos , Evolução Biológica , Origem da Vida , Peptídeos/química , Dobramento de Proteína , BiopolímerosRESUMO
We have studied the folding mechanism of lattice model 36-mer proteins. Using a simulated annealing procedure in sequence space, we have designed sequences to have sufficiently low energy in a given target conformation, which plays the role of the native structure in our study. The sequence design algorithm generated sequences for which the native structures is a pronounced global energy minimum. Then, designed sequences were subjected to lattice Monte Carlo simulations of folding. In each run, starting from a random coil conformation, the chain reached its native structure, which is indicative that the model proteins solve the Levinthal paradox. The folding mechanism involved nucleation growth. Formation of a specific nucleus, which is a particular pattern of contacts, is shown to be a necessary and sufficient condition for subsequent rapid folding to the native state. The nucleus represents a transition state of folding to the molten globule conformation. The search for the nucleus is a rate-limiting step of folding and corresponds to overcoming the major free energy barrier. We also observed a folding pathway that is the approach to the native state after nucleus formation; this stage takes about 1% of the simulation time. The nucleus is a spatially localized substructure of the native state having 8 out of 40 native contacts. However, monomers belonging to the nucleus are scattered along the sequence, so that several nucleus contacts are long-range while other are short-range. A folding nucleus was also found in a longer chain 80-mer, where it also constituted 20% of the native structure. The possible mechanism of folding of designed proteins, as well as the experimental implications of this study is discussed.
Assuntos
Modelos Moleculares , Dobramento de Proteína , Algoritmos , Sequência de Aminoácidos , Dados de Sequência Molecular , Conformação Proteica , TermodinâmicaRESUMO
This paper is a review of our previous work on the field of possible ways of prebiotic evolution. We propose an algorithm providing sequences of model proteins with rapid folding into a given native conformation. Thermodynamical analysis shows that the increase in speed is matched by an increase in stability: the evolved sequences are much more stable in their native conformation than the initial random sequence. We discuss a possible origin of the first biopolymers, having stable unique structure. We suggest that at the prebiotic stage of evolution, long organic polymers had to be compact in order to avoid hydrolysis and had to be soluble and thus must not be exceedingly hydrophobic. We present an algorithm that generates such sequences of model proteins. The evolved sequences turn out to have a stable unique structure, into which they quickly fold. This result illustrates the idea that the unique three-dimensional native structure of first biopolymers could have evolved as a side effect of a nonspecific physico-chemical factors acting at the prebiotic stage of evolution.
Assuntos
Evolução Biológica , Simulação por Computador , Origem da Vida , Algoritmos , Modelos Biológicos , Modelos Moleculares , Mutação , Conformação Proteica , Proteínas/química , Proteínas/genética , Distribuição Aleatória , Software , TermodinâmicaRESUMO
Sequences of fast-folding model proteins (48 residues long on a cubic lattice) were generated by an evolution-like selection toward fast folding. We find that fast-folding proteins exhibit a specific folding mechanism in which all transition state conformations share a smaller subset of common contacts (folding nucleus). Acceleration of folding was accompanied by dramatic strengthening of interactions in the folding nucleus whereas average energy of nonnucleus interactions remained largely unchanged. Furthermore, the residues involved in the nucleus are the most conserved ones within families of evolved sequences. Our results imply that for each protein structure there is a small number of conserved positions that are key determinants of fast folding into that structure. This conjecture was tested on two protein superfamilies: the first having the classical monophosphate binding fold (CMBF; 98 families) and the second having type-III repeat fold (47 families). For each superfamily, we discovered a few positions that exhibit very strong and statistically significant "conservatism of conservatism"-amino acids in those positions are conserved within every family whereas the actual types of amino acids varied from family to family. Those amino acids are in spatial contact with each other. The experimental data of Serrano and coworkers [Lopez-Hernandez, E. & Serrano, L. (1996) Fold. Des. (London) 1, 43-55]. for one of the proteins of the CMBF superfamily (CheY) show that residues identified this way indeed belong to the folding nucleus. Further analysis revealed deep connections between nucleation in CMBF proteins and their function.
Assuntos
Proteínas de Bactérias , Conformação Proteica , Dobramento de Proteína , Sítios de Ligação , Evolução Biológica , Simulação por Computador , Cinética , Proteínas de Membrana/ultraestrutura , Proteínas Quimiotáticas Aceptoras de Metil , Modelos Moleculares , Fosfatos/metabolismo , Mutação Puntual , Relação Estrutura-AtividadeRESUMO
BACKGROUND: Protein engineering has been used extensively to evaluate the properties of transition states in protein folding. Although the method has proved useful, its limitations and the details of interpretation of the obtained results remain largely unexplored. RESULTS: Lattice model simulations are used to test and verify the protein engineering analysis of the transition state in protein folding. It is shown that in some cases - but not always - this method is able to determine the transition state with reasonable accuracy. Limitations of protein engineering are revealed and analyzed. In particular, the change in non-native interactions as a result of mutations is shown to influence the results of the protein engineering analysis. Furthermore, the temperature dependencies of phi values (which are a measure of the participation of a residue in the transition state) and the character of the transition state ensemble are studied. It is shown that as a general trend phi values decrease when the temperature decreases, a finding consistent with recent experimental results. Our analysis suggests that this trend results primarily from the formation of some contacts (native and non-native) in the unfolded state at a lower temperature, when the barrier for folding is energetic. CONCLUSIONS: Our analysis helps to interpret the results of protein engineering and allows observed φ values to be directly related to structural features of the unfolded state, the transition state and the native state.
Assuntos
Simulação por Computador , Modelos Químicos , Engenharia de Proteínas/métodos , Dobramento de Proteína , Sequência de Aminoácidos , Previsões , Cinética , Dados de Sequência Molecular , Método de Monte Carlo , Conformação Proteica , TermodinâmicaRESUMO
This study focuses of the phenomenon of kinetic partitioning when a polypeptide chain has two ground-state conformations, one of which is kinetically more reachable than the other. We designed sequences for lattice model proteins with two different conformations of equal energy corresponding to the global energy minimum. Folding simulations revealed that one of these conformations was indeed much more kinetically accessible than the other. We found that the number and strength of local contacts in the ground-state conformation are the major factors that determine which conformation is reached faster; the greater the number of local contacts, the more kinetically reachable a conformation is. We present simple statistical-mechanical arguments to explain these findings. Our results may be relevant in explaining the phenomenology of such proteins as human plasminogen activator inhibitor-1 (PAI-1), photosystem II, and prions.
Assuntos
Simulação por Computador , Modelos Químicos , Príons/química , Dobramento de Proteína , Sequência de Aminoácidos , Humanos , Cinética , Dados de Sequência Molecular , Método de Monte Carlo , Peptídeos/química , Inibidor 1 de Ativador de Plasminogênio/química , Proteínas PrPC/química , Proteínas PrPSc/química , Conformação Proteica , TermodinâmicaRESUMO
The folding ability of a heteropolymer model for proteins subject to Monte Carlo dynamics on a simple cubic lattice is shown to be strongly correlated with the stability of the native state. We consider a number of estimates of the stability that can be determined without simulation, including the energy gap between the native state and the structurally dissimilar part of the spectrum (Z score) and, for sequences with fully compact native states, the gap in energy between the native and first excited fully compact states. These estimates are found to be more robust predictors of folding ability than a parameter sigma that requires simulation for its evaluation: sigma = 1 - Tf/Ttheta, where Tf is the temperature at which the fluctuation of an order parameter is at its maximum and Ttheta is the temperature at which the specific heat is at its maximum. We show that the interpretation of Ttheta as the collapse transition temperature is not correct in general and that the correlation between sigma and the folding ability arises from the fact that sigma is related to the energy gap (Z score).