Integration of multiscale entropy and BASED scale of electroencephalography after adrenocorticotropic hormone therapy predict relapse of infantile spasms

BACKGROUND

Even though adrenocorticotropic hormone (ACTH) demonstrated powerful efficacy in the initially successful treatment of infantile spasms (IS), nearly half of patients have experienced a relapse. We sought to investigate whether features of electroencephalogram (EEG) predict relapse in those IS patients without structural brain abnormalities.

METHODS

We retrospectively reviewed data from children with IS who achieved initial response after ACTH treatment, along with EEG recorded within the last two days of treatment. The recurrence of epileptic spasms following treatment was tracked for 12 months. Subjects were categorized as either non-relapse or relapse groups. General clinical and EEG recordings were collected, burden of amplitudes and epileptiform discharges (BASED) score and multiscale entropy (MSE) were carefully explored for cross-group comparisons.

RESULTS

Forty-one patients were enrolled in the study, of which 26 (63.4%) experienced a relapse. The BASED score was significantly higher in the relapse group. MSE in the non-relapse group was significantly lower than the relapse group in the γ band but higher in the lower frequency range (δ, θ, α). Sensitivity and specificity were 85.71% and 92.31%, respectively, when combining MSE in the δ/γ frequency of the occipital region, plus BASED score were used to distinguish relapse from non-relapse groups.

CONCLUSIONS

BASED score and MSE of EEG after ACTH treatment could be used to predict relapse for IS patients without brain structural abnormalities. Patients with BASED score ≥ 3, MSE increased in higher frequency, and decreased in lower frequency had a high risk of relapse.

[Mechanical circulatory support combined with immunomodulation treatment for patients with fulminant myocarditis: a single-center real-world study]

Objective: To investigate the relationship between the mechanical circulatory support (MCS) combined with immunomodulation and the prognosis of patients with fulminant myocarditis. Methods: This is a retrospective study. A total of 88 patients with fulminant myocarditis admitted to Dongguan Kanghua hospital from Aug. 2008 to Dec. 2020 were included. Medical histories, results of laboratory tests, treatment regimens and clinical outcomes of these patients during their hospitalization were collected from the medical record system. According to the treatment methods, the patients were divided into MCS+immunomodulation group (38 cases), MCS group (20 cases) and traditional treatment group (30 cases). Patients in the MCS+immunomodulation group received intra-aortic balloon pump (IABP) or IABP combined with extracorporeal membrane oxygenation (ECMO) and immunoglobulin or glucocorticoid. Patients in the MCS group only received mechanical circulatory support. Patients in the traditional treatment group received neither mechanical circulatory support nor immunomodulatory therapy, and only used vasoactive drugs and cardiotonic drugs. The in-hospital mortality and length of stay were compared among the three groups. Results: A total of 88 patients with fulminant myocarditis aged (35.0±10.8) years were included, and there were 46 males (52.3%). The mortality of MCS+immunomodulation group (7.9% (3/38) vs. 56.7% (17/30), P=0.001 2) and MCS group (30.0% (6/20) vs. 56.7% (17/30), P=0.002 8) were lower than that of traditional treatment group. Compared with the MCS group, the in-hospital mortality in the MCS+immunomodulation group was lower (P=0.005 4). The most common cause of death was multiple organ dysfunction syndrome (MODS). The constituent ratios of death in MCS+immunomodulation group, MCS group and traditional treatment group were 3/3, 4/6 and 12/17, respectively. The incidence of MODS in the MCS group (20% (4/20)) and the traditional treatment group (40% (12/30)) was significantly higher than that in the MCS+immunomodulation group (7.9% (3/38)) (both P<0.01). In discharged patients, the hospitalization time of MCS+immunomodulation group was shorter than that of traditional treatment group ((13.4±5.5)d vs. (18.5±7.4)d, P<0.05) and MCS group ((13.4±5.5)d vs. (16.9±8.5)d, P<0.05). Conclusion: MCS combined with immunomodulatory therapy is associated with lower in-hospital mortality and shorter hospital stay in patients with fulminant myocarditis.

Overexpression of miR-101-2 in donor cells improves the early development of Holstein cow somatic cell nuclear transfer embryos

Accumulating studies have suggested that microRNA play a part in regulating multiple cellular processes, such as cell proliferation, apoptosis, the cell cycle, and embryo development. This study explored the effects of miR-101-2 on donor cell physiological status and the development of Holstein cow somatic cell nuclear transfer (SCNT) embryos in vitro. Holstein cow bovine fetal fibroblasts (BFF) overexpressing miR-101-2 were used as donor cells to perform SCNT; then, cleavage rate, blastocyst rate, inner cell mass-to-trophectoderm ratio, and the expression of some development- and apoptosis-related genes in different groups were analyzed. The miR-101-2 suppressed the expression of inhibitor of growth protein 3 (ING3) at mRNA and protein levels, expedited cell proliferation, and decreased apoptosis in BFF, suggesting that ING3, a target gene of miR-101-2, is a potential player in this process. Moreover, by utilizing donor cells overexpressing miR-101-2, the development of bovine SCNT embryos in vitro was significantly enhanced; the apoptotic rate in SCNT blastocysts was reduced, and the inner cell mass-to-trophectoderm ratio and SOX2, POU5F1, and BCL2L1 expression significantly increased, whereas BAX and ING3 expression decreased. Collectively, these findings suggest that miR-101-2 promotes BFF proliferation and vitality, reduces their apoptosis, and improves the early development of SCNT embryos.

Protective effects of trehalose on frozen-thawed ovarian granulosa cells of cattle

In this study, trehalose was investigated for its cryoprotective effects on ovarian granulosa cells (bGCs) of cattle. Five concentrations of trehalose at 0, 0.2, 0.4, 0.6 and 0.8 mol/L were added to the cryopreservation medium of bGCs, and the effects on the quality of frozen-thawed bGCs were assessed. The results indicate that the use of cryopreservation medium containing 0.2 and 0.4 mol/L of trehalose resulted in a greater rate of bGC viability compared to those of other groups (P<0.05). Culturing with trehalose at 0.2 and 0.4 mol/L increased 17β- estradiol (E₂)and decreased progesterone (P₄)production (P < 0.05) in post-thawed bGCs. Compared with the control group, the intracellular Ca²⁺ concentrations of frozen-thawed bGCs were less in all treatment groups (P<0.05), and the least Ca²⁺ concentration was observed in the group containing 0.4 mol/L trehalose. The plasma membrane potentials of frozen-thawed bGCs were greater in the groups with 0.2 and 0.4 mol/L trehalose, and the group treated with 0.4 mol/L trehalose had the greatest membrane potential in comparison to other groups (P < 0.05). The relative abundance of the CYP19 mRNA in frozen-thawed bGCs was greater in the groups containing 0.2, 0.4 and 0.6 mol/L trehalose, and relative abundances of FSHR and BCL2 mRNA were greater in the group of bGCs treated with 0.2 mol/L trehalose (P<0.05). Trehalose treatment at 0.4, 0.6 and 0.8 mol/L had an inhibitory effect on BAX gene transcription in frozen-thawed bGCs (P<0.05). In summary, trehalose exhibited a greater cryoprotective effect on bGCs than basic cryopreservation medium.

[Establishment and evaluation of a new method for determining hemodynamics of pulmonary hypertension rats]

Objective: By evaluating the hemodynamic parameters such as cardiac output (CO), right ventricular pressure (RVP), pulmonary artery pressure (PAP) and total pulmonary resistance index (TPRI) in pulmonary hypertension rat model, we established a more comprehensive hemodynamic evaluation system, which objectively evaluated the severity of disease and exercise tolerance in rats with pulmonary hypertension. Methods: SD rats were randomly divided into a control group and a model group with 5 rats in each group. The model group was intraperitoneally injected with SU5416 (20 mg/kg) and placed in an oxygen chamber at a 10% oxygen concentration for 21 days and then placed in a normoxic environment for 14 days. After modeling, rats were anesthetized and mechanically ventilated. The operator cut the skin along the right paraxial line, detached and ligated the intercostal artery, and then cut off the 3 and 4 ribs, exposing the heart and freeing aortic root about 0.2 cm. The flowmeter probe was set in the dissected aortic segment, and real-time recording time, blood flow waveforms, cardiac output were calculated accordingly. Then the needle attached to the baroreceptor was inserted into the right ventricle and the system acquired the right ventricular time-pressure waveform. After the waveform stabilized for about 30 seconds, the end of the cannula was sent to the pulmonary artery trunk through the entrance of the pulmonary artery to record the time-pressure curve of the pulmonary artery. Results: RVSP, PASP, PADP and mPAP in the model group were significantly higher than those of the control group [ RVSP(23.4±5.4) mmHg, 1 mmHg=0.133 kPa vs (56.4±13.0) mmHg, PASP (22.8±4.4) mmHg vs (58.5±14.9) mmHg, PADP (9.7±1.9) mmHg vs (30.3±7.0) mmHg, mPAP (14.1±2.7) mmHg vs (41.9±8.0) mmHg, all P<0.05 ]. Compared with the control group, the cardiac index in the model group was significantly lower [ CI (0.54±0.08) ml·min(-1)·g(-1) vs (0.40±0.09) ml·min(-1)·g(-1,) P=0.02 ]. Furthermore, compared with the control group, pulmonary vascular resistance index was significantly increased in the model group[PVRI (0.27±0.03) mmHg·ml(-1)·min(-1)·kg(-1) vs (0.06±0.01) mmHg·ml(-1)·min(-1)·kg(-1,) P<0.05]. The pathological results also showed that the middle part of pulmonary arterioles in the model group had muscular hypertrophy and muscular pulmonary arterioles, and even plexiform lesions. Conclusion: In this study, we established a new method that simultaneously determined several hemodynamic parameters such as RVSP, PASP, PADP, CO, CI and PVRI, which provided a more comprehensive assessment of hemodynamic changes in pulmonary hypertension rat models.

Fisetin Exerts Antioxidant and Neuroprotective Effects in Multiple Mutant hSOD1 Models of Amyotrophic Lateral Sclerosis by Activating ERK

Oxidative stress exhibits a central role in the course of amyotrophic lateral sclerosis (ALS), a progressive neurodegenerative disease commonly found to include a copper/zinc superoxide dismutase (SOD1) gene mutation. Fisetin, a natural antioxidant, has shown benefits in varied neurodegenerative diseases. The possible effect of fisetin in ALS has not been clarified as of yet. We investigated whether fisetin affected mutant hSOD1 ALS models. Three different hSOD1-related mutant models were used: Drosophila expressing mutant hSOD1^G85R, hSOD1^G93A NSC34 cells, and transgenic mice. Fisetin treatment provided neuroprotection as demonstrated by an improved survival rate, attenuated motor impairment, reduced ROS damage and regulated redox homeostasis compared with those in controls. Furthermore, fisetin increased the expression of phosphorylated ERK and upregulated antioxidant factors, which were reversed by MEK/ERK inhibition. Finally, fisetin reduced the levels of both mutant and wild-type hSOD1 in vivo and in vitro, as well as the levels of detergent-insoluble hSOD1 proteins. The results indicate that fisetin protects cells from ROS damage and improves the pathological behaviors caused by oxidative stress in disease models related to SOD1 gene mutations probably by activating ERK, thereby providing a potential treatment for ALS.

[Primary culture and functional identification of distal pulmonary artery smooth muscle cells in mice]

Objective: To establish a method of isolation and primary culture of mice distal pulmonary artery smooth muscle cells (PASMCs) and identify the functional properties. Methods: PASMCs were harvested from the distal pulmonary artery (PA) tissue of mice by enzymatic digestion of collagenaseⅠand papain; and the growth characteristics were observed under inverted microscope and identified by Immunofluorescence technique. Effects on the intracellular calcium ion concentration of distal PASMCs were detected by Fura-2-AM fluorescent probe tracer under a fluorescence microscope in Krebs solution containing clopiazonic acid (CPA) and nifedipin (Nif). Results: PASMCs density reached approximately to 80% in a typical valley-peak-like shape after 6 days. Cell α-smooth muscle actin (α-SMA) immunofluorescence identified that 95% of the cultured cells were PASMCs. More than 95% PASMCs responded well to calcium-potassium Krebs solution (potassium ion concentration of 60 mmol/L) and showed a rapid increase in basal [Ca(2+) ](i) after 1 minute's perfusion (Δ[Ca(2+) ](i)>50), which demonstrated that the voltage-dependent calcium channels (VDCC) of distal PASMCs were in good function; after the perfusion of calcium Krebs, calcium-free/calcium-Krebs containing CPA and Nif, distal PASMCs showed two typical peaks, indicated the full function of store-operated calcium channel (SOCC) in distal PASMCs. Conclusion: This experiment successfully established a stable and reliable mice distal PASMCs model and the study of pulmonary vascular diseases could benefit from its higher purity and better functional condition.

Chronopharmacokinetics of puerarin in diabetic rats

Puerarin injection has been widely used for clinic treatment of diabetes recently. To assess the relationship between the administration time of puerarin and the blood concentration of puerarin as well as its pharmacokinetic parameters, the diabetic rat model was used in current study. The rats were randomly divided into morning and evening groups according to the administration time. After the puerarin injection, blood glucose was tested in order to know whether the efficiency of puerarin was influenced by its concentration and pharmacokinetic parameters. Our results show that the average concentration of puerarin in the evening group is significantly higher than that in the morning group. The numbers of t_1/2α, t_1/2β, CL and AUC_(0-∞) are significantly different between the morning and evening groups. The blood glucose level in the evening group was lower than that in the morning group. The speed of its onset is higher and the blood glucose level declines much more significantly in the evening group. These findings suggest that the concentration and pharmacokinetic parameters of puerarin affect its efficiency in diabetic rats. Therefore, it might be better to give puerarin in evening than in the morning for the mellitus treatment.

The significance of fragile histidine triad protein as a molecular prognostic marker of bladder urothelial carcinoma

OBJECTIVES

The role and clinical significance of fragile histidine triad (FHIT) gene in the pathogenesis of bladder urothelial carcinoma (UC) and the potential of Fhit protein as a prognostic biomarker for UC were investigated.

METHODS

FHIT expression was determined according to semiquantitative immunohistochemical staining for Fhit protein levels in normal bladder and bladder UC tissues. Associations between FHIT expression, clinicopathological features and survival were evaluated.

RESULTS

This study evaluated 42 cases of normal bladder and 125 cases of bladder UC; bladder UC cases had a median follow-up of 53.5 months. Immuno histochemistry showed that 95.2% of normal cases and 47.2% of bladder UC cases, respectively, were positive for Fhit protein; this difference was statistically significant. There was a significant association between negative FHIT expression in bladder UC and advanced tumour stage, high pathological grade, large tumour size, tumour recurrence and reduced survival time, but no association with age, gender, tumour number or tumour shape.

CONCLUSIONS

The FHIT gene may have an important role in the pathogenesis of bladder UC and was expressed at lower levels in bladder UC compared with normal bladder tissue. Using Fhit protein as a biomarker could provide important information about patient prognosis.

A novel method to calculate the G+C content of genomic DNA sequences

The base composition of a DNA fragment or genome is usually measured by the proportion of A+T or G+C in the sequence. The G+C content along genomic sequences is usually calculated using an overlapping or non-overlapping sliding window method. The result and accuracy of such an approach depends on the size of the window and the moving distance adopted. In this paper, a novel windowless technique to calculate the G+C content of genomic sequences is proposed. By this method, the G+C content can be calculated at different "resolution". In an extreme case, the G+C content may be computed at a specific point, rather than in a window of finite size. This is particularly useful to analyze the fine variation of base composition along genomic sequences. As the first example, the variation of G+C content along each of 16 yeast chromosomes is analyzed. The G+C-rich regions with length larger than 5 kb sequences are detected and listed in details. It is found that each chromosome consists of several G+C-rich and G+C-poor regions alternatively, i.e., a mosaic structure. Another example is to analyze the G+C content for each of the two chromosomes of the Vibrio cholerae genome. Based on the variations of the G+C content in each chromosome, it is shown that some fragments in the Vibrio cholerae genome may have been transferred from other species. Especially, the position and size of the large integron island on the smaller chromosome was precisely predicted. This method would be a useful tool for analyzing genomic sequences.

Magic nucleus 132Sn and its one-neutron-hole neighbor 131Sn

Prompt and delayed gamma-ray cascades in doubly magic 132Sn and its neighbor 131Sn have been studied at Gammasphere using a 248Cm fission source. Isotopic assignments of unknown gamma rays were based on coincidences with known transitions in A = 112-116 Pd fission partners. The yrast level spectra of both tin nuclei are interpreted using empirical nucleon-nucleon interactions from the 132Sn and 208Pb regions. Results include identification of the (nuf(7/2)h(-1)(11/2))9(+) aligned state in 132Sn and of extensive (nuf(7/2)h(-2)(11/2)), (nuf(7/2)d(-1)(3/2)h(-1)(11/2)) and (nuh(-1)(11/2)x3(-)) multiplets in 131Sn. The previously reported beta(-) decay of an unusual 131In high-spin isomer to levels in 131Sn is also elucidated.

Identification of protein-coding genes in the genome of Vibrio cholerae with more than 98% accuracy using occurrence frequencies of single nucleotides

The published sequence of the Vibrio cholerae genome indicates that, in addition to the genes that encode proteins of known and unknown function, there are 1577 ORFs identified as conserved hypothetical or hypothetical gene candidates. Because the annotation is not 100% accurate, it is not known which of the 1577 ORFs are true protein-coding genes. In this paper, an algorithm based on the Z curve method, with sensitivity, specificity and accuracy greater than 98%, is used to solve this problem. Twenty-fold cross-validation tests show that the accuracy of the algorithm is 98.8%. A detailed discussion of the mechanism of the algorithm is also presented. It was found that 172 of the 1577 ORFs are unlikely to be protein-coding genes. The number of protein-coding genes in the V. cholerae genome was re-estimated and found to be approximately 3716. This result should be of use in microarray analysis of gene expression in the genome, because the cost of preparing chips may be somewhat decreased. A computer program was written to calculate a coding score called VCZ for gene identification in the genome. Coding/noncoding is simply determined by VCZ > 0/VCZ < 0. The program is freely available on request for academic use.

A refined accuracy index to evaluate algorithms of protein secondary structure prediction

Nowadays even a 1% increase of the accuracy for the secondary structure prediction is considered remarkable progress. In this case, we have to consider the reasonableness of the accuracy index Q3, which is used widely. A refined accuracy index, called Q8, is proposed to evaluate algorithms of secondary structure prediction. It is shown that Q8 is superior to the widely used index Q3 in that the former carries more information of the predictive accuracy matrix than does the latter. Therefore, algorithms are evaluated more objectively by Q8 than Q3. Based on 396 nonhomologous proteins, five currently available algorithms of secondary structure prediction were evaluated and compared using the new index Q8. Of the five algorithms, PHD turned out to be the unique algorithm, with Q8 accuracy better than 70%. It is suggested that Q3 should be replaced by Q8 in evaluating secondary structure prediction in future studies.

Analysis of the codon usage pattern in the Vibrio cholerae genome

The codon usage in the Vibrio cholerae genome is analyzed in this paper. Although there are much more genes on the chromosome 1 than on chromosome 2, the codon usage patterns of genes on the two chromosomes are quite similar, indicating that the two chromosomes may have coexisted in the same cell for a very long history. Unlike the base frequency pattern observed in other genomes, the G+C content at the third codon position of the V. cholerae genome varies in a rather small interval. The most notable feature of codon usage of V. cholerae genome is that there is a fraction of genes show significant bias in base choice at the second codon position. The 2,006 known genes can be classified into two clusters according to the base frequencies at this position. The smaller cluster contains 227 genes, most of which code for proteins involved in transport and binding functions. The encoding products of these genes have significant bias in amino acids composition as compared with other genes. The codon usage patterns for the 1,836 function unknown ORFs are also analyzed, which is useful to study their functions.

Prediction of the subcellular location of prokaryotic proteins based on the hydrophobicity index of amino acids

An algorithm of predicting the subcellular location of prokaryotic proteins is proposed in this paper. In addition to the amino acid composition, the auto-correlation functions based on the hydrophobicity profile of amino acids along the primary sequence of the query protein have been used. Consequently, the best predictive accuracy to date has been achieved. Of the 997 prokaryotic proteins in the database used here, 688 cytoplasmic, 107 extracellular and 202 periplasmic proteins, the overall predictive accuracies are as high as 97.7 and 90.4% in the resubstitution and jackknife tests, respectively, using the hydrophilicity value of Hopp and Woods. The underlying mechanism of the improvement is also discussed. This work would be useful for a systematic analysis of the great amounts of prokaryotic genome sequences. The computer programs used in this paper are available on request via email.

A new approach to predict the helix/strand content of globular proteins

An improved multiple linear regression method has been proposed to predict the content of alpha-helix and beta-strand of a globular protein based on its primary sequence and structural class. The amino acid composition and the auto-correlation functions derived from the hydrophobicity profile of the primary sequence have been taken into account. However, only the compositions of a part of the amino acids and a part of the auto-correlation functions are selected as the regression terms, which lead to the least prediction error. The resubstitution test shows that the average absolute errors are 0.052 and 0.047 with the standard deviations 0.050 and 0.047 for the prediction of helix/strand content, respectively. A rigorous cross-validation test, the jackknife test shows that the average absolute errors are 0.058 and 0.053 with the standard deviations 0.057 and 0.053 for the prediction of helix/strand content, respectively. Both tests indicate the self-consistency and the extrapolating effectiveness of the new method. The high prediction accuracy means that the method is suitable for practical applications.

Recognition of protein coding genes in the yeast genome at better than 95% accuracy based on the Z curve

The Z curve is a three-dimensional space curve constituting the unique representation of a given DNA sequence in the sense that each can be uniquely reconstructed from the other. Based on the Z curve, a new protein coding gene-finding algorithm specific for the yeast genome at better than 95% accuracy has been proposed. Six cross-validation tests were performed to confirm the above accuracy. Using the new algorithm, the number of protein coding genes in the yeast genome is re-estimated. The estimate is based on the assumption that the unknown genes have similar statistical properties to the known genes. It is found that the number of protein coding genes in the 16 yeast chromosomes is </=5645, significantly smaller than the 5800-6000 which is widely accepted, and much larger than the 4800 estimated by another group recently. The mitochondrial genes were not included into the above estimate. A codingness index called the YZ score (YZ OE [0,1]) is proposed to recognize protein coding genes in the yeast genome. Among the ORFs annotated in the MIPS (Munich Information Centre for Protein Sequences) database, those recognized as non-coding by the present algorithm are listed in this paper in detail. The criterion for a coding or non-coding ORF is simply decided by YZ > 0.5 or YZ < 0.5, respectively. The YZ scores for all the ORFs annotated in the MIPS database have been calculated and are available on request by sending e-mail to the corresponding author.

Phase transitions above the Yrast line in 154Dy

Spectra of the E2 quasicontinuum gamma rays feeding different spin regions of the 154Dy yrast line have been extracted. These are compared with corresponding theoretical spectra obtained by numerical simulations based on temperature-dependent Hartree-Fock theory, with thermal shape fluctuations. In this manner, different regions of the spin-energy plane can be examined. The results support the predictions of a smeared-out phase transition at high spin above the yrast line.

S curve, a graphic representation of protein secondary structure sequence and its applications

A secondary structure sequence is a symbolic string composed of three kinds of letters, indicating the helix, strand, and coil (including turns), respectively. A graphic representation for this abstract symbolic sequence is proposed here, called the S curve. The S curve is the unique representation for a given secondary structure sequence in the sense that the sequence and the S curve can be uniquely determined from the other. Therefore, the S curve contains all the information that the secondary structure sequence contains. Different geometrical properties of the S curve are studied in details, which reflect the basic characteristics of the secondary structure sequences. The S curves are used to display, analyze, and compare the secondary structure sequences. Detailed application examples are presented. One advantage of the S curve methodology is that the main patterns of a given secondary structure sequence can be grasped quickly in a perceivable form. This is particularly useful in the cases in which longer sequences are involved and structures of proteins are unknown.

Prediction of membrane protein types based on the hydrophobic index of amino acids

A new algorithm to predict the types of membrane proteins is proposed. Besides the amino acid composition of the query protein, the information within the amino acid sequence is taken into account. A formulation of the autocorrelation functions based on the hydrophobicity index of the 20 amino acids is adopted. The overall predictive accuracy is remarkably increased for the database of 2054 membrane proteins studied here. An improvement of about 13% in the resubstitution test and 8% in the jackknife test is achieved compared with those of algorithms based merely on the amino acid composition. Consequently, overall predictive accuracy is as high as 94% and 82% for the resubstitution and jackknife tests, respectively, for the prediction of the five types. Since the proposed algorithm is based on more parameters than those in the amino acid composition approach, the predictive accuracy would be further increased for a larger and more class-balanced database. The present algorithm should be useful in the determination of the types and functions of new membrane proteins. The computer program is available on request.

A graphic approach to evaluate algorithms of secondary structure prediction

Algorithms of secondary structure prediction have undergone the developments of nearly 30 years. However, the problem of how to appropriately evaluate and compare algorithms has not yet completely solved. A graphic method to evaluate algorithms of secondary structure prediction has been proposed here. Traditionally, the performance of an algorithm is evaluated by a number, i.e., accuracy of various definitions. Instead of a number, we use a graph to completely evaluate an algorithm, in which the mapping points are distributed in a three-dimensional space. Each point represents the predictive result of the secondary structure of a protein. Because the distribution of mapping points in the 3D space generally contains more information than a number or a set of numbers, it is expected that algorithms may be evaluated and compared by the proposed graphic method more objectively. Based on the point distribution, six evaluation parameters are proposed, which describe the overall performance of the algorithm evaluated. Furthermore, the graphic method is simple and intuitive. As an example of application, two advanced algorithms, i.e., the PHD and NNpredict methods, are evaluated and compared. It is shown that there is still much room for further improvement for both algorithms. It is pointed out that the accuracy for predicting either the alpha-helix or beta-strand in proteins with higher alpha-helix or beta-strand content, respectively, should be greatly improved for both algorithms.

A quadratic discriminant analysis of protein structure classification based on the Helix/Strand content

Based on the 210 non-homologous proteins (domains) classified manually by Michie et al. (J. Mol. Biol. 262, 168-185, 1996), a new structure classification criterion of globular proteins relying on the content of helix/strand has been proposed, using a quadratic discriminant method. Each protein is classified into one of the three classes, i.e. those of alpha class, beta class and alphabeta class (including alpha/beta and alpha+beta classes). According to the new structure classification criterion, of the 210 proteins in the training set, 207 are correctly classified and thus the accuracy is 207/210=98.57%. Multiple cross-validation tests are performed. The jackknife test shows that of the 210 proteins 207 are correctly classified with an accuracy of 98.57%. To test the method further, of 3577 proteins (domains) extracted from SCOP, 91.39% of them are correctly reclassified by the new classification criterion. On average, the accuracy of the new criterion is about 8 percentage points higher than that of the criterion proposed by Nakashima et al. (J. Biochem. 99, 153-162, 1986). Our result shows that the classification based solely on structures is basically consistent with that combining both structural and evolutionary information. Further complete automated classification scheme should consider both structures and evolutionary relationship. The methodology presented provides an appropriate mathematical format to reach this goal.

Prediction of protein (domain) structural classes based on amino-acid index

A protein (domain) is usually classified into one of the following four structural classes: all-alpha, all-beta, alpha/beta and alpha + beta. In this paper, a new formulation is proposed to predict the structural class of a protein (domain) from its primary sequence. Instead of the amino-acid composition used widely in the previous structural class prediction work, the auto-correlation functions based on the profile of amino-acid index along the primary sequence of the query protein (domain) are used for the structural class prediction. Consequently, the overall predictive accuracy is remarkably improved. For the same training database consisting of 359 proteins (domains) and the same component-coupled algorithm [Chou, K.C. & Maggiora, G.M. (1998) Protein Eng. 11, 523-538], the overall predictive accuracy of the new method for the jackknife test is 5-7% higher than the accuracy based only on the amino-acid composition. The overall predictive accuracy finally obtained for the jackknife test is as high as 90.5%, implying that a significant improvement has been achieved by making full use of the information contained in the primary sequence for the class prediction. This improvement depends on the size of the training database, the auto-correlation functions selected and the amino-acid index used. We have found that the amino-acid index proposed by Oobatake and Ooi, i.e. the average nonbonded energy per residue, leads to the optimal predictive result in the case for the database sets studied in this paper. This study may be considered as an alternative step towards making the structural class prediction more practical.

Skewed distribution of protein secondary structure contents over the conformational triangle

A conformational triangle method is presented to analyze the secondary structure contents of 1028 structurally known proteins in the non-redundant data set of the recent 25% PDB_SELECT. The secondary structure contents of each protein are mapped on to a point in the triangle. It was found that the distribution of the 1028 points is strongly skewed in the triangle and about 42% of the whole area is empty, which is called the forbidden area. The detailed border between the allowable and forbidden areas was calculated. The possible explanation of the skewed distribution is discussed. The distributions of the mapping points for enzymes and non-enzymes in this non-redundant data set are compared. It was found that a necessary rather than a sufficient condition for an enzyme molecule is that its coil content must be >/=0.223. It is hoped that the skewed distribution observed here could be used to test the secondary structure and threading predictions.

A new criterion to classify globular proteins based on their secondary structure contents

MOTIVATION

With the enlargement of protein structure databases, it is hoped that a method to classify proteins automatically will be developed. Although the classification criterion proposed by Nakashima et al. ( J. Biochem., 1986, 99, 153-162) was widely used in the literature, it leads to some inconsistencies with the classification databases currently available in the class assignment of protein structures. To improve their work, a new classification criterion is proposed relying on statistical analysis of the secondary structure contents of more than 200 proteins with well-known structural classes. The Fisher linear discriminant algorithm is used to derive the new classification criterion.

RESULTS

Three cross-validation tests are performed to evaluate the new criterion. In the jackknife test, of the 210 proteins used to derive the criterion, 206 are correctly classified with an accuracy of 98.10%. Of the 16 proteins of purely intermediate structure (i.e. structures lying near borderlines between two classes) in the first test set, 15 are correctly classified with an accuracy of 93.75%. For the second test set which consists of 200 proteins selected randomly from SCOP, a testing accuracy of 94.00% is obtained. For comparison, the criterion of Nakashima et al. is also used to classify the 210, 16 and 200 proteins, respectively. Consequently, accuracies of 94.76%, 62.50% and 91.50% are obtained, respectively. On average, the accuracy of the new classification criterion is 4% higher than that of Nakashima et al.

AVAILABILITY

The program is available on request from the first author.

CONTACT

ctzhang@tju.edu.cn

A new quantitative criterion to distinguish between alpha/beta and alpha+beta proteins (domains)

According to the statistical analysis, it is shown that the differences of the content of alpha-helix and beta-strand between alpha/beta and alpha+beta proteins are of statistical significance. Based on the secondary structure content and the percentage of parallel or anti-parallel strands, any mixed alphabeta protein can be represented by a point in a three-dimensional prism. The distribution of the mapping points for 79 mixed alphabeta proteins (domains), of which 26 are class alpha/beta and 53 are class alpha+beta, shows that the two kinds of points are situated at distinct regions roughly. A new quantitative criterion based on the Fisher discriminant algorithm is proposed to distinguish between the alpha/beta and alpha+beta proteins (domains). Of the 79 proteins 77 are correctly classified (97.5%). As a stringent cross-validation test, the jackknife test shows that of the 79 proteins 77 are correctly classified. The jackknife test accuracy is still 97.5%. These figures indicate the self-consistence and the extrapolating effectiveness of the new quantitative criterion. Applying the new criterion to reclassify the alpha/beta and alpha+beta proteins (domains) in SCOP is also discussed. It is hoped that the new quantitative criterion will be useful for the development of protein classification databases.

Prediction of the helix/strand content of globular proteins based on their primary sequences

An improved multiple linear regression method has been proposed to predict the content of alpha-helix and beta-strand of a globular protein based on its primary sequence. The amino acid composition and the auto-correlation functions based on the hydrophobicity profile of the primary sequence have been taken into account in the algorithm. The resubstitution test shows that the average absolute errors are 0.077 and 0.073 with the standard deviations 0.059 and 0.057 for the prediction of the content of alpha-helix and beta-strand, respectively. A stringent cross-validation test, i.e., the jackknife test, shows that the average absolute errors are 0.087 and 0.081 with the standard deviations 0.067 and 0.065 for the prediction of the content of alpha-helix and beta-strand, respectively. Both tests indicate the self-consistency and the extrapolating effectiveness of the new algorithm. This greatly improves on previous results (Eisenhaber,F., Imperiale,F., Argos,P. and Frommel,C., 1996, Proteins, 25, 157-168). Compared with other methods currently available, our method has the merits of simplicity and ease-of-use as well as a higher prediction accuracy. The only input of the method is the primary sequence of the query protein to be predicted. The program is available on request via e-mail: ctzhang@tju.edu.cn.

A new fourier transform approach for protein coding measure based on the format of the Z curve

MOTIVATION

At the core of most protein gene-finding algorithms are the coding measures used to make a decision on coding/non-coding. Of the protein coding measures, the Fourier measure is one of the most important. However, due to the limited length of the windows usually used, the accuracy of the measure is not satisfactory. This paper is devoted to improving the accuracy by lengthening the sequence to amplify the periodicity of 3 in the coding regions.

RESULTS

A new algorithm is presented called the lengthen-shuffle Fourier transform algorithm. For the same window length, the percentage accuracy of the new algorithm is 6-7% higher than that of the ordinary Fourier transform algorithm. The resulting percentage accuracy (average of specificity and sensitivity) of the new measure is 84.9% for the window length 162 bp.

AVAILABILITY

The program is available on request fromC.-T. Zhang.

CONTACT

ctzhang@tju.edu.cn

A novel approach to distinguish between intron-containing and intronless genes based on the format of Z curves

A novel method to distinguish between intron-containing and intronless DNA sequences has been proposed, based on different statistic behaviors between them. In this method, DNA sequences are first represented as Z curves. Three exponents alpha, beta and gamma for each given sequence are calculated based on the format of the Z curve for the DNA sequence. A three-dimensional space is spanned by the three exponents. Each DNA sequence may be represented by a point in this space. One hundred intronless and intron-containing genes, respectively, were selected randomly from the GenBank or EMBL database. It is shown that the 200 points are roughly distributed in different regions. The best separating plane to separate the two regions is obtained by using Fisher's discriminant algorithm. For any given sequence to be discriminated, calculate three exponents alpha, beta and gamma, corresponding to a point in the three-dimensional space. If the point is situated at the upper region of the separating plane, the sequence is discriminated as an intronless one; otherwise, the sequence is an intron-containing one. A test of the method for the sequences in an independent test set shows that the discriminant accuracy reaches as high as 89.0%.

Prediction of the secondary structure contents of globular proteins based on three structural classes

The prediction of the secondary structural contents (those of alpha-helix and beta-strand) of a globular protein is of great use in the prediction of protein structure. In this paper, a new prediction algorithm has been proposed based on Chou's database [Chou (1995), Proteins 21, 319-344]. The new algorithm is an improved multiple linear regression method, taking into account the nonlinear and coupling terms of the frequencies of different amino acids and the length of the protein. The prediction is also based on the structural classes of proteins, but instead of four classes, only three classes are considered, the alpha class, beta class, and the mixed alpha+beta and alpha/beta class or simply the alphabeta class. Thus the ambiguity that usually occurs between alpha+beta proteins and alpha/beta proteins is eliminated. A resubstitution examination for the algorithm shows that the average absolute errors are 0.040 and 0.035 for the prediction of alpha-helix content and beta-strand content, respectively. An examination of cross-validation, the jackknife analysis, shows that the average absolute errors are 0.051 and 0.045 for the prediction of alpha-helix content and beta-strand content, respectively. Both examinations indicate the self-consistency and the extrapolating effectiveness of the new algorithm. Compared with other methods, ours has the merits of simplicity and convenience for use, as well as high prediction accuracy. By incorporating the prediction of the structural classes, the only input of our method is the amino acid composition and the length of the protein to be predicted.

Prediction and classification of domain structural classes

Can the coupling effect among different amino acid components be used to improve the prediction of protein structural classes? The answer is yes according to the study by Chou and Zhang (Crit. Rev. Biochem. Mol. Biol. 30:275-349, 1995), but a completely opposite conclusion was drawn by Eisenhaber et al. when using a different dataset constructed by themselves (Proteins 25:169-179, 1996). To resolve such a perplexing problem, predictions were performed by various approaches for the datasets from an objective database, the SCOP database (Murzin, Brenner, Hubbard, and Chothia. J. Mol. Biol. 247:536-540, 1995). According to SCOP, the classification of structural classes for protein domains is based on the evolutionary relationship and on the principles that govern the 3D structure of proteins, and hence is more natural and reliable. The results from both resubstitution tests and jackknife tests indicate that the overall rates of correct prediction by the algorithm incorporated with the coupling effect among different amino acid components are significantly higher than those by the algorithms without using such an effect. It is elucidated through an analysis that the main reasons for Eisenhaber et al. to have reached an opposite conclusion are the result of (1) misusing the component-coupled algorithm, and (2) using a conceptually incorrect rule to classify protein structural classes. The formulation and analysis presented in this article are conducive to clarify these problems, helping correctly to apply the prediction algorithm and interpret the results.

A symmetrical theory of DNA sequences and its applications

A unified symmetrical theory of DNA sequences has been established based on the basic symmetry of the DNA bases. It is shown that the symmetry of DNA sequences is inherently related to that of a cube and its inscribed regular tetrahedron. A DNA group is defined as a particular alternating group of order 4, in which the permuted objects are four bases. The symmetry of DNA sequences is described by the DNA group which is isomorphic to the tetrahedral group. The matrix representation for the DNA group has been obtained, and used to establish the relationships between the transforms of bases and the rotations of the tetrahedron. It is found that any DNA sequence can be uniquely described by three independent distributions, i.e., the distributions of the bases of purine/pyrimidine, of amino group/keto group and of strong/weak hydrogen bonds along the sequence. The three distributions are invariant in some sense under the transforms of the DNA group, indicating that the three distributions are inherent for the sequence. The mathematical format of the theory lays a foundation for further development. The applications of the theory to analyse some DNA sequences are presented.

Relations of the numbers of protein sequences, families and folds

The relations among the numbers of protein sequences, families and folds have been studied theoretically. It is found that the number of families is related to the natural logarithm of the number of sequences. The logarithmic relation should not be changed regardless of what value of the homology threshold is applied in the protein sequence comparison routines. To study the relation between the numbers of families and folds, the degenerate degree of a fold has been introduced. The degenerate degree of a fold is the number of protein families which adopt the same fold. The distribution of the degenerate degrees of folds has been found to be very likely exponential. Based on the distribution, the average degenerate degree d is calculated. The number of folds is simply equal to that of families divided by the average degenerate degree of folds. It is shown that d is an increasing function of time. The current value of d is about 2. It will continue to increase and reach the value of at least 3.3 in some years. By using the above result, the numbers of protein folds for four species have been estimated. In particular, the number of folds for human proteins is estimated to be < or =5200.

Disposition of amphiphilic helices in heteropolar environments

It is known that alpha helices in globular proteins usually consist of two types of residues, hydrophobic and hydrophilic, with the number of each type being roughly equal. Except for many transmembrane helices, alpha-helices are generally amphiphilic to some degree. This is not entirely surprising because alpha-helices typically reside in heteropolar environments that arise from the polar aqueous solution that surrounds a protein and the apolar "hydrophobic core" located at its center. The packing of alpha-helices in such heteropolar environments is driven by the minimization of free energy brought about by placing hydrophobic sidechains into apolar environments and hydrophilic sidechains into polar environments. The interface between the two environments can be characterized by an interfacial plane, called the demarcation plane, that optimally separates the two classes of residues. The inclination angle omega between the axis of the helix and the demarcation plane provides a measure of the degree of amphiphilicity of an alpha-helix. For highly amphiphilic helices, omega approximately 0. The inclination angle provides a new measure of amphiphilicity that complements the hydrophobic moments of Eisenberg et al. Based on the simple physical model described above, an algorithm is developed for predicting the helix inclination angle. The calculated results show that the inclination angle for most alpha-helices extracted from globular proteins is less than 25 degrees in magnitude. This suggests that helices found in globular proteins tend to be reasonably amphiphilic with half their face dominated by hydrophobic residues and the other half by hydrophilic residues. A new two-dimensional representation that characterizes the disposition of hydrophobic and hydrophilic residues in alpha-helices, called a "wenxiang diagram," is presented. The wenxiang diagram can also be used as an important element to represent a protein molecule.

A vector projection method for predicting supersecondary motifs

For the 11 types of most frequently occurring supersecondary motifs, we used a new method--the vector projection method--to predict a protein's supersecondary structure. In a training set of peptides and a test set of peptides we obtained a satisfactory result, with a prediction accuracy of about 90%. The high prediction accuracy indicates that this method is reasonable for predicting the folding motifs of proteins. This work provides insight into the problem of predicting a protein's local structure accurately, and is of particular value in protein modeling, prediction, and molecule design.

Prediction of the secondary structure content of globular proteins based on structural classes

The prediction of the secondary structure content (alpha-helix and beta-strand content) of a globular protein may play an important complementary role in the prediction of the protein's structure. We propose a new prediction algorithm based on Chou's database [Chou (1995), Proteins Struct. Funct. Genet. 21, 319]. The new algorithm is an improved multiple linear regression method, taking the nonlinear and coupling terms of the frequencies of different amino acids into account. The prediction is also based on the structural classes of proteins. A resubstitution examination for the algorithm shows that the average errors are 0.040 and 0.033 for the prediction of alpha-helix content and beta-strand content, respectively. The examination of cross-validation, the jackknife analysis, shows that the average errors are 0.051 and 0.044 for the prediction of alpha-helix content and beta-strand content, respectively. Both examinations indicate the self-consistency and the extrapolative effectiveness of the new algorithm. Compared with the other methods available currently, our method has the merits of simplicity and convenience for use, as well as a high prediction accuracy. By incorporating the prediction of the structural classes, the only input of our method is the amino acid composition of the protein to be predicted.

Study on the isentropic equations of nucleotide sequences and their application

The tetrahedral representation of DNA sequences and its applications have been studied by many authors. In this paper we study the isentropic equations of DNA sequences and their application. First, the DNA sequence entropy is introduced, and the entropy current and divergence are defined. Second, the isentropic equations are deduced and the isentropic curves on the three coordinate planes are respectively drawn by a computer. Third, an analysis is given on the entropy distribution on the coordinate planes. Finally, we make use of the results to discuss the relationship of the fastest increasing directions of the entropy for the cytochrome c genes of seven species.

Do "antisense proteins" exist?

A DNA double helix consists of two complementary strands antiparallel with each other. One of them is the sense chain, while the other is an antisense chain which does not directly involve the protein-encoding process. The reason that an antisense chain cannot encode for a protein is generally attributed to the lack of certain preconditions such as a promotor and some necessary sequence segments. Suppose it were provided with all these preconditions, could an antisense chain encode for an "antisense protein"? To answer this question, an analysis has been performed based on the existing database. Nine proteins have been found that have a 100% sequence match with the hypothetical antisense proteins derived from the known Escherichia coli antisense chains.

An analysis of protein folding type prediction by seed-propagated sampling and jackknife test

In the development of methodology for statistical prediction of protein folding types, how to test the predicted results is a crucial problem. In addition to the resubstitution test in which the folding type of each protein from a training set is predicted based on the rules derived from the same set, cross-validation tests are needed. Among them, the single-test-set method seems to be least reliable due to the arbitrariness in selecting the test set. Although the leaving-one-out (or jackknife) test is more objective and hence more reliable, it may cause a severe information loss by leaving a protein in turn out of the training set when its size is not large enough. In order to overcome the above drawback, a seed-propagated sampling approach is proposed that can be used to generate any number of simulated proteins with a desired type based on a given training set database. There is no need to make any predetermined assumption about the statistical distribution function of the amino acid frequencies. Combined with the existing cross-validation methods, the new technique may provide a more objective estimation for various protein-folding-type prediction methods.

An eigenvalue-eigenvector approach to predicting protein folding types

The accuracy of predicting protein folding types can be significantly enhanced by a recently developed algorithm in which the coupling effect among different amino acid components is taken into account [Chou and Zhang (1994) J. Biol. Chem. 269, 22014-22020]. However, in practical calculations using this powerful algorithm, one may sometimes face ill-conditioned matrices. To overcome such a difficulty, an effective eigenvalue-eigenvector approach is proposed. Furthermore, the new approach has been used to predict a recently constructed set of 76 proteins not included in the training set, and the accuracy of prediction is also much higher than those of other methods.

Monte Carlo simulation studies on the prediction of protein folding types from amino acid composition. II. Correlative effect

A number of methods to predicting the folding type of a protein based on its amino acid composition have been developed during the past few years. In order to perform an objective and fair comparison of different prediction methods, a Monte Carlo simulation method was proposed to calculate the asymptotic limit of the prediction accuracy [Zhang and Chou (1992), Biophys. J. 63, 1523-1529, referred to as simulation method I]. However, simulation method I was based on an oversimplified assumption, i.e., there are no correlations between the compositions of different amino acids. By taking into account such correlations, a new method, referred to as simulation method II, has been proposed to recalculate the objective accuracy of prediction for the least Euclidean distance method [Nakashima et al. (1986), J. Bochem. 99, 152-162] and the least Minkowski distance method [Chou (1989), Prediction in Protein Structure and the Principles of Protein Conformation, Plenum Press, New York, pp. 549-586], respectively. The results show that the prediction accuracy of the former is still better than that of the latter, as found by simulation method I; however, after incorporating the correlative effect, the objective prediction accuracies become lower for both methods. The reason for this phenomenon is discussed in detail. The simulation method and the idea developed in this paper can be applied to examine any other statistical prediction method, including the computer-simulated neural network method.

Predicting protein structural classes from amino acid composition: application of fuzzy clustering

Most globular proteins can be classified into one of four structural classes--all-alpha, all-beta, alpha + beta and alpha/beta--depending upon the type, amount and arrangement of secondary structures present. In this work a new method, based upon fuzzy clustering, is proposed for predicting the structural class of a protein from its amino acid composition. Here, each of the structural classes is described by a fuzzy cluster and each protein is characterized by its membership degree, a number between zero and one in each of the four clusters, with the constraint that the sum of the membership degrees equals unity. A given protein is then classified as belonging to that structural class corresponding to the fuzzy cluster with maximum membership degree. Calculation of membership degrees is carried out using the fuzzy c-means algorithm on a training set of 64 proteins. Results obtained for the training set show that the fuzzy clustering approach produces results comparable with or better than those obtained by other methods. A test set of 27 proteins also produced comparable results to those obtained with the training set. The success of the present preliminary work on protein structure class prediction suggests that further refinements of method may lead to improved predictions and this is currently being investigated.

A vector projection method for predicting the specificity of GalNAc-transferase

The specificity of UDP-GalNAc:polypeptide N-acetylgalactosaminytransferase (GalNAc-transferase) is consistent with the existence of an extended site composed of nine subsites, denoted by P4, P3, P2, P1, P0, P1', P2', P3', P4', where the acceptor at P0 is being either Ser or Thr. To predict whether a peptide will react with the enzyme to form a Ser- or Thr-conjugated glycopeptide, a vector projection method is proposed which uses a training set of amino acid sequences surrounding 90 Ser and 106 Thr O-glycosylation sites extracted from the National Biomedical Research Foundation Protein Database. The model postulates independent interactions of the 9 amino acid moieties with their respective binding sites. The high ratio of correct predictions vs. total predictions for the data in both the training and the testing sets indicates that the method is self-consistent and efficient. It provides a rapid means for predicting O-glycosylation and designing effective inhibitors of GalNAc-transferase.

Prediction of protein structural classes

A protein is usually classified into one of the following five structural classes: alpha, beta, alpha + beta, alpha/beta, and zeta (irregular). The structural class of a protein is correlated with its amino acid composition. However, given the amino acid composition of a protein, how may one predict its structural class? Various efforts have been made in addressing this problem. This review addresses the progress in this field, with the focus on the state of the art, which is featured by a novel prediction algorithm and a recently developed database. The novel algorithm is characterized by a covariance matrix that takes into account the coupling effect among different amino acid components of a protein. The new database was established based on the requirement that the classes should have (1) as many nonhomologous structures as possible, (2) good quality structure, and (3) typical or distinguishable features for each of the structural classes concerned. The very high success rate for both the training-set proteins and the testing-set proteins, which has been further validated by a simulated analysis and a jackknife analysis, indicates that it is possible to predict the structural class of a protein according to its amino acid composition if an ideal and complete database can be established. It also suggests that the overall fold of a protein is basically determined by its amino acid composition.

Predicting protein folding types by distance functions that make allowances for amino acid interactions

Given the amino acid composition of a protein, how may one predict its folding type? Although around this problem a number of methods have been proposed, none of them has taken into account the correlative effect among different amino acids, and hence the accuracy of prediction could not be improved to the extent that it should have. In view of this, a new method has been developed in which the similarity between two protein molecules is based on the scale of Mahalanobis distance rather than on the ordinary intuitive geometric distances, such as Minkowski's distance and Euclidian distance. By introducing the Mahalanobis distance, the correlative effect among different amino acids can be automatically incorporated. Predictions have been performed for 131 real proteins consisting of alpha, beta, alpha+beta, and alpha/beta proteins. The results indicate that the rates of correct prediction for both alpha and beta proteins are 100%, and those for alpha+beta and alpha/beta are 88.9 and 89.7%, respectively, with an average accuracy of 94.7%. Predictions have also been performed for 10,000 simulated proteins generated by Monte Carlo sampling for each of the above four folding types, yielding an average accuracy of 95.9%. The accuracy thus obtained for the simulated proteins can avoid the bias due to the limited number of testing proteins selected arbitrarily by different investigators and hence can be regarded as an objective accuracy. It is anticipated that a method with such a high objective accuracy should become a reliable tool in predicting the protein folding type and a useful tool for improving the prediction of secondary structure as well.