Reconciling observations of sequence-specific conformational propensities with the generic polymeric behavior of denatured proteins

Radii of gyration of denatured proteins vary with chain length and are insensitive to details of amino acid sequence. Observations of sequence independence in polymeric properties conflict with results from spectroscopic experiments, which suggest the presence of sequence-specific residual structure in denatured states. Can we reconcile the two apparently conflicting sets of observations? To answer this question, we need knowledge of the ensemble of conformations accessible to proteins in good solvents. The excluded-volume limit provides an ideal mimic of polymers in good solvents. Therefore, we attempt to solve the "reconciliation problem" by simulating conformational ensembles accessible to peptides and proteins in the excluded-volume limit. Analysis of these ensembles for a variety of polypeptide sequences leads to results that are consistent with experimental observations of sequence-specific conformational preferences in short peptides and the scaling behavior of polymeric quantities for denatured proteins. Reconciliation in the excluded-volume limit comes about due to a tug of war between two factors, namely, minimization of steric overlap and the competing effects of conformational entropy. Minimization of steric overlap promotes chain stretching and leads to experimentally observed sequence-dependent preferences for locally extended segments such as polyproline II helices, beta-strands, and very short stretches of alpha-helix. Conformational entropy opposes chain stretching, and the calculated persistence length for sequence-dependent conformational preferences is less than five amino acids. This estimate does not vary with amino acid sequence. The short persistence lengths lead directly to experimental observations of generic sequence-independent behavior of radii of gyration for denatured proteins.     

Scale dependency in the functional form of the distance decay relationship

We examine a novel mathematical approach which posits that the decay of similarity in community composition with increasing distance (aka distance decay) can be modeled as the sum of individual species joint‐probability vs distance relationships. Our model, supported by analyses of these curves from three datasets (North American breeding birds, North American taiga plants, and tropical forest trees), suggest that when sampling grain is large enough to avoid absences due to stochastic sampling effects, and/or sampling extent is large enough to generate species turnover through the deterministic crossing of environmental and/or geographical range limits, species joint‐probability over increasing distance will generally exhibit exponential decay. However, at small scales where occurrence is driven more by stochastic sampling effects, species joint‐probability curves exhibit a power‐law decay form. Lacking a theoretical prediction of how individual species joint‐probability relationships combine to generate community distance decay, we also performed a meta‐analysis of 26 ecological and 4 human‐system datasets, using non‐linear regression to mean and quantile non‐linear regression at tau = 0.95 for linear, exponential, and power‐law decay forms. These analyses demonstrate that the functional form of community distance decay – as shown by comparison of AIC ranks – is largely determined by observational scale, with power law decay prevailing within domains where the species pool remains constant, while exponential decay prevails at larger scales over which the species pool varies, paralleling the patterns predicted in our mathematical approach.     

Dynamic models of infectious diseases as regulators of population sizes

Five SIRS epidemiological models for populations of varying size are considered. The incidences of infection are given by mass action terms involving the number of infectives and either the number of susceptibles or the fraction of the population which is susceptible. When the population dynamics are immigration and deaths, thresholds are found which determine whether the disease dies out or approaches an endemic equilibrium. When the population dynamics are unbalanced births and deaths proportional to the population size, thresholds are found which determine whether the disease dies out or remains endemic and whether the population declines to zero, remains finite or grows exponentially. In these models the persistence of the disease and disease-related deaths can reduce the asymptotic population size or change the asymptotic behavior from exponential growth to exponential decay or approach to an equilibrium population size.Research supported by Centers for Disease Control contract 200-87-0515. Support services provided at the University of Iowa Center for Advanced Studies     

The fluorescence decay of tryptophan residues in native and denatured proteins.

The fluorescence decay kinetics at different ranges of the emission spectrum is reported for 17 proteins. Out of eight proteins containing a single tryptophan residue per molecule, seven proteins display multiexponential decay kinetics, suggesting that variability in protein structure may exist for most proteins. Tryptophan residues whose fluorescence spectrum is red shifted may have lifetimes longer than 7 ns. Such long lifetimes have not been detected in any of the denatured proteins studied, indicating that in native proteins the tryptophans having a red-shifted spectrum are affected by the tertiary structure of the protein. The fluorescence decay kinetics of ten denatured proteins studied obey multiexponential decay functions. It is therefore concluded that the tryptophan residues in denatured proteins can be grouped in two classes. The first characterized by a relatively long lifetime of about 4 ns and the second has a short lifetime of about 1.5 ns. The emission spectrum of the group which is characterized by the longer lifetime is red shifted relative to the emission spectrum of the group characterized by the shorter lifetime. A comparison of the decay data with the quantum yield of the proteins raises the possibility that a subgroup of the tryptophan residues is fully quenched. It is noteworthy that despite this heterogeneity in the environment of tryptophan residues in each denatured protein, almost the same decay kinetics has been obtained for all the denatured proteins studied in spite of the vastly different primary structures. It is therefore concluded that each tryptophan residue interacts in a more-or-less random manner with other groups on the polypeptide chain, and that on the average the different tryptophan residues in denatured proteins have a similar type of environment.     

Statistical analyses support power law distributions found in neuronal avalanches

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the power law, and (iii) comparison of the power law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling ("finite size" effect). This scale-free dynamics suggests the power law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to -1.5, which is in line with previous reports. Finally, the power law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the power law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the power law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.     

Dynamic regimes and correlated structural dynamics in native and denatured alpha-lactalbumin

Understanding the mechanisms of protein folding requires knowledge of both the energy landscape and the structural dynamics of a protein. We report a neutron-scattering study of the nanosecond and picosecond dynamics of native and the denatured alpha-lactalbumin. The quasielastic scattering intensity shows that there are alpha-helical structure and tertiary-like side-chain interactions fluctuating on sub-nanosecond time-scales under extremely denaturing conditions and even in the absence of disulfide bonds. Based on the length-scale dependence of the decay rate of the measured correlation functions, the nanosecond dynamics of the native and the variously denatured proteins have three dynamic regimes. When 0.051.0 A(-1) is a regime that displays the local dynamic behavior of individual residues, Gamma proportional to Q(1.8+/-0.3). The picosecond time-scale dynamics shows that the potential barrier to side-chain proton jump motion is reduced in the molten globule and in the denatured proteins when compared to that of the native protein. Our results provide a dynamic view of the native-like topology established in the early stages of protein folding.     

Effects of excluded volume upon protein stability in covalently cross-linked proteins with variable linker lengths

To explore the effects of molecular crowding and excluded volume upon protein stability, we used a series of cross-linking reagents with nine different single-cysteine mutants of staphylococcal nuclease to make covalently linked dimers. These cross-linkers ranged in length from 10.5 to 21.3 A, compelling separations which would normally be found only in the most concentrated protein solutions. The stabilities of the dimeric proteins and monomeric controls were determined by guanidine hydrochloride and thermal denaturation. Dimers with short linkers tend to exhibit pronounced three-state denaturation behavior, as opposed to the two-state behavior of the monomeric controls. Increasing linker length leads to less pronounced three-state behavior. The three-state behavior is interpreted in a three-state model where cross-linked native protein dimer, N-N, interconverts in a two-state transition with a dimer where one protein subunit is denatured, N-D. The remaining native protein in turn can denature in another two-state transition to a state, D-D, in which both tethered proteins are denatured. Three-state behavior is best explained by excluded volume effects in the denatured state. For many dimers, linkers longer than 17 A removed most three-state character. This sets a limit on the flexibility and size of the denatured state. Notably, in contradiction to theoretical predictions, these cross-linked dimers were not stabilized. The failure of these predictions is possibly due to neglect of the alteration in hydrophobic exposure that accompanies any significant reduction in the conformational space of the denatured state.     

Toward an accurate theoretical framework for describing ensembles for proteins under strongly denaturing conditions

Our focus is on an appropriate theoretical framework for describing highly denatured proteins. In high concentrations of denaturants, proteins behave like polymers in a good solvent and ensembles for denatured proteins can be modeled by ignoring all interactions except excluded volume (EV) effects. To assay conformational preferences of highly denatured proteins, we quantify a variety of properties for EV-limit ensembles of 23 two-state proteins. We find that modeled denatured proteins can be best described as follows. Average shapes are consistent with prolate ellipsoids. Ensembles are characterized by large correlated fluctuations. Sequence-specific conformational preferences are restricted to local length scales that span five to nine residues. Beyond local length scales, chain properties follow well-defined power laws that are expected for generic polymers in the EV limit. The average available volume is filled inefficiently, and cavities of all sizes are found within the interiors of denatured proteins. All properties characterized from simulated ensembles match predictions from rigorous field theories. We use our results to resolve between conflicting proposals for structure in ensembles for highly denatured states.     

Collagen and keratin polypeptide models for assessing the natural and artificial protein decay of organic materials

Among the materials constituting the natural and cultural heritage, organic materials of proteinaceous origin as bone (collagen), parchment and woolen textiles (keratin) are the most susceptible to damage and decay because of their exposure to air pollution, inappropriate values of ambient temperature, humidity and light. Aiming at contributing to the development of a reliable and reproducible immunoassay for the evaluation of collagen and keratin decay, three polypeptide models of these proteins were designed, synthesized and studied. Polypeptide [Pro‐Ser(OBzl)‐Gly]_n incorporates the typical motif Pro‐X‐Gly of collagen; polypeptide [Pro‐Cys(Acm)‐Gly]_n is a model of the C‐terminal domain of type I keratin, corresponding to the repeating unit Pro‐Cys‐X of keratin, while polypeptide Ac‐YRSGGGFGYRSGGGFGYRS‐βAla‐NH₂ encloses the characteristic repeating sequence GGGFGYRS of the N‐terminal part of Type II keratin. These polypeptides may be considered as simplified models that mimic fragments of collagen and keratin resulting from artificial and natural ageing or decay. It is concluded that high recognition of anti‐polypeptide antibodies, produced after immunizations, by the bone, parchment and textile samples is indicative of high deterioration, while high anti‐collagen or anti‐keratin recognition is indicative of low deterioration. Copyright © 2016 European Peptide Society and John Wiley & Sons, Ltd.     

Local dynamics in biological macromolecules

The diffusive approach in the optimized Rouse-Zimm approximation to segment relaxation in the nanosecond time domain (ORZLD) is extended to consider chains of nonequivalent units as occurring in biological macromolecules. The correlation times for second-order time correlation functions of each virtual bond on the chain are calculated for some homopolypeptides, and random and regular copolypeptides. The expected correlation times for biological macromolecules organized in multiple domains are discussed via a simple model of the ORZLD hierarchy. Dynamic bond correlation times are compared with static local persistence lengths.     

Distinguishing foldable proteins from nonfolders: When and how do they differ?

When a denatured polypeptide is put into refolding conditions, it undergoes conformational changes on a variety of times scales. We set out here to distinguish the fast events that promote productive folding from other processes that may be generic to any non-folding polypeptide. We have apply an ab initio folding algorithm to model the folding of various proteins and their compositionally identical, random-sequence analogues. In the earliest stages, proteins and their scrambled-sequence counterparts undergo indistinguishable reductions in the extent to which they explore conformation space. For both polypeptides, an early contraction occurs but does not involve the formation of a distinct intermediate. Following this phase, however, the naturally-occurring sequences are distinguished by an increase in the formation of three-body correlations wherein a hydrophobic group desolvates and protects an intra-molecular hydrogen bond. These correlations are manifested in a mild but measurable reduction of the accessible configuration space beyond that of the random-sequence peptides, and portend the folding to the native structure. Hence, early events reflect a generic response of the denatured ensemble to a change in solvent condition, but the wild-type sequence develops additional correlations as its structure evolves that can reveal the protein's foldability.     

Nicotinic acetylcholine receptors (nAChRs) at zebrafish red and white muscle show different properties during development

Nicotinic acetylcholine receptors (nAChRs) are highly expressed at the vertebrate neuromuscular junction (NMJ) where they are required for muscle activation. Understanding the factors that underlie NMJ development is critical for a full understanding of muscle function. In this study we performed whole cell and outside‐out patch clamp recordings, and single‐cell RT‐qPCR from zebrafish red and white muscle to examine the properties of nAChRs during the first 5 days of development. In red fibers miniature endplate currents (mEPCs) exhibit single exponential time courses at 1.5 days postfertilization (dpf) and double exponential time courses from 2 dpf onwards. In white fibers, mEPCs decay relatively slowly, with a single exponential component at 1.5 dpf. By 2 and 3 dpf, mEPC kinetics speed up, and decay with a double exponential component, and by 4 dpf the exponential decay reverts back to a single component. Single channel recordings confirm the presence of two main conductance classes of nAChRs (～45 pS and ～65 pS) in red fibers with multiple time courses. Two main conductance classes are also present in white fibers (～55 pS and ～73 pS), but they exhibit shorter mean open times by 5 dpf compared with red muscle. RT‐qPCR of mRNA for nicotinic receptor subunits supports a switch from γ to ε subunits in white fibers but not in red. Our findings provide a developmental profile of mEPC properties from red and white fibers in embryonic and larval zebrafish, and reveal previously unknown differences between the NMJs of these muscle fibers.© 2015 Wiley Periodicals, Inc. Develop Neurobiol 76: 916–936, 2016     

Non-random-coil behavior as a consequence of extensive PPII structure in the denatured state

Unfolded proteins may contain a native or nonnative residual structure, which has important implications for the thermodynamics and kinetics of folding, as well as for misfolding and aggregation diseases. However, it has been universally accepted that residual structure should not affect the global size scaling of the denatured chain, which obeys the statistics of random coil polymers. Here we use a single-molecule optical technique—fluorescence correlation spectroscopy—to probe the denatured state of a set of repeat proteins containing an increasing number of identical domains, from 2 to 20. The availability of this set allows us to obtain the scaling law for the unfolded state of these proteins, which turns out to be unusually compact, strongly deviating from random coil statistics. The origin of this unexpected behavior is traced to the presence of an extensive nonnative polyproline II helical structure, which we localize to specific segments of the polypeptide chain. We show that the experimentally observed effects of polyproline II on the size scaling of the denatured state can be well-described by simple polymer models. Our findings suggest a hitherto unforeseen potential of nonnative structure to induce significant compaction of denatured proteins, significantly affecting folding pathways and kinetics.     

Age invariant of Gompertz function and exponential decay of populations commensuration with CLOV experiments

The exponential decay law of populations is further examined on the basis of new observations of Japanese and Swedish cohorts. It is shown that the populations decrease exponentially at higher ages in accordance with the theoretical prediction, which confirms the previous conclusion. The theory is applied to recent experiments on Mediterranean fruit flies by Carey et al., (1992, Science, 258, 457-460), the results showing that the exponential decay law holds in sufficient approximation. All the evidences accumulated so far suggest that the decay law is a general theorem. On the basis of this information, we derive a general expression that estimates the limit age as a function of population. The predicted curve is in excellent agreement with the observed limit ages in Japan.     

Conformational dynamics of unfolded peptides as a function of chain length: a frequency domain fluorescence approach

The fluorescence emission decays of single-tryptophan-containing peptides of different chain lengths in their unfolded state were investigated in the frequency domain. The data were analyzed using different functions, i.e., exponential fit and probability-density functions of different shape. We found that unimodal Lorentzian distributions best describe the fluorescence decays. This finding agrees with the point of view, now broadly accepted, that rapid motions exist in polypeptides. As a consequence of this flexibility, a large variety of conformations, with an unequal perturbation of tryptophan in its excited state, is generated. The lifetime distribution center was independent of the length of the polypeptide chain but strongly related to the nature of the amino acid residues located in the proximity of the tryptophan in the primary structure. The full width at half maximum, W, of the lifetime distribution was found to be related to the length of unfolded polypeptide by the empirical logarithmic relationship W = 0.83 log n, where n indicates the number of residues. For short peptides, a single lifetime or a narrow range of lifetimes is observed because of the fast relaxation of the tryptophanyl environment. On peptide lengthening, the spectrum of conformations, which the peptide can assume, increases; this causes a complex fluorescence decay represented by a lifetime distribution. For long polypeptide chains, the motions of the regions far from tryptophan do not significantly perturb the chromophore environment.     

Mechanics and structure of titin oligomers explored with atomic force microscopy

Titin is a giant polypeptide that spans half of the striated muscle sarcomere and generates passive force upon stretch. To explore the elastic response and structure of single molecules and oligomers of titin, we carried out molecular force spectroscopy and atomic force microscopy (AFM) on purified full-length skeletal-muscle titin. From the force data, apparent persistence lengths as long as ∼1.5 nm were obtained for the single, unfolded titin molecule. Furthermore, data suggest that titin molecules may globally associate into oligomers which mechanically behave as independent wormlike chains (WLCs). Consistent with this, AFM of surface-adsorbed titin molecules revealed the presence of oligomers. Although oligomers may form globally via head-to-head association of titin, the constituent molecules otherwise appear independent from each other along their contour. Based on the global association but local independence of titin molecules, we discuss a mechanical model of the sarcomere in which titin molecules with different contour lengths, corresponding to different isoforms, are held in a lattice. The net force response of aligned titin molecules is determined by the persistence length of the tandemly arranged, different WLC components of the individual molecules, the ratio of their overall contour lengths, and by domain unfolding events. Biased domain unfolding in mechanically selected constituent molecules may serve as a compensatory mechanism for contour- and persistence-length differences. Variation in the ratio and contour length of the component chains may provide mechanisms for the fine-tuning of the sarcomeric passive force response.     

Time-resolved fluorescence and anisotropy decay of the tryptophan in adrenocorticotropin-(1-24)

The direct time-resolved fluorescence anisotropy of the single tryptophan residue in the polypeptide hormone adrenocorticotropin-(1-24) (ACTH) and the fluorescence decay kinetics of this residue (Trp-9) are reported. Two rotational correlation times are observed. One, occurring on the subnanosecond time scale, reflects the rotation of the indole ring, and the other, which extends into the nanosecond range, is dominated by the complex motions of the polypeptide chain. The fluorescence lifetimes of the single tryptophan in glucagon (Trp-25) and the 23-26 glucagon peptide were also measured. In all cases the fluorescence kinetics were satisfied by a double-exponential decay law. The fluorescence lifetimes of several tryptophan and indole derivatives and two tryptophan dipeptides were examined in order to interpret the kinetics. In close agreement with the findings of Szabo and Rayner [Szabo, A. G., & Rayner, D. M. (1980) J. Am. Chem. Soc. 102, 554-563], the tryptophan zwitterion exhibits emission wavelength dependent double-exponential decay kinetics. At 320 nm tau 1 = 3.2 ns and tau 2 = 0.8 ns, with alpha 1 = 0.7 and alpha 2 = 0.3. Above 380 nm only the 3.2-ns component is observed. By contrast the neutral derivative N-acetyltryptophanamide has a single exponential decay of 3.0 ns. The multiexponential decay kinetics of the polypeptides are discussed in terms of flexibility of the polypeptide chain and neighboring side-chain interactions.     

Mechanics and structure of titin oligomers explored with atomic force microscopy

Titin is a giant polypeptide that spans half of the striated muscle sarcomere and generates passive force upon stretch. To explore the elastic response and structure of single molecules and oligomers of titin, we carried out molecular force spectroscopy and atomic force microscopy (AFM) on purified full-length skeletal-muscle titin. From the force data, apparent persistence lengths as long as approximately 1.5 nm were obtained for the single, unfolded titin molecule. Furthermore, data suggest that titin molecules may globally associate into oligomers which mechanically behave as independent wormlike chains (WLCs). Consistent with this, AFM of surface-adsorbed titin molecules revealed the presence of oligomers. Although oligomers may form globally via head-to-head association of titin, the constituent molecules otherwise appear independent from each other along their contour. Based on the global association but local independence of titin molecules, we discuss a mechanical model of the sarcomere in which titin molecules with different contour lengths, corresponding to different isoforms, are held in a lattice. The net force response of aligned titin molecules is determined by the persistence length of the tandemly arranged, different WLC components of the individual molecules, the ratio of their overall contour lengths, and by domain unfolding events. Biased domain unfolding in mechanically selected constituent molecules may serve as a compensatory mechanism for contour- and persistence-length differences. Variation in the ratio and contour length of the component chains may provide mechanisms for the fine-tuning of the sarcomeric passive force response.     

Two-state expansion and collapse of a polypeptide

The initial phase of folding for many proteins is presumed to be the collapse of the polypeptide chain from expanded to compact, but still denatured, conformations. Theory and simulations suggest that this collapse may be a two-state transition, characterized by barrier-crossing kinetics, while the collapse of homopolymers is continuous and multi-phasic. We have used a laser temperature-jump with fluorescence spectroscopy to measure the complete time-course of the collapse of denatured cytochrome c with nanosecond time resolution. We find the process to be exponential in time and thermally activated, with an apparent activation energy approximately 9 k(B)T (after correction for solvent viscosity). These results indicate that polypeptide collapse is kinetically a two-state transition. Because of the observed free energy barrier, the time scale of polypeptide collapse is dramatically slower than is predicted by Langevin models for homopolymer collapse.     

Sequence analysis by additive scales: DNA structure for sequences and repeats of all lengths

MOTIVATION: DNA structure plays an important role in a variety of biological processes. Different di- and tri-nucleotide scales have been proposed to capture various aspects of DNA structure including base stacking energy, propeller twist angle, protein deformability, bendability, and position preference. Yet, a general framework for the computational analysis and prediction of DNA structure is still lacking. Such a framework should in particular address the following issues: (1) construction of sequences with extremal properties; (2) quantitative evaluation of sequences with respect to a given genomic background; (3) automatic extraction of extremal sequences and profiles from genomic databases; (4) distribution and asymptotic behavior as the length N of the sequences increases; and (5) complete analysis of correlations between scales. RESULTS: We develop a general framework for sequence analysis based on additive scales, structural or other, that addresses all these issues. We show how to construct extremal sequences and calibrate scores for automatic genomic and database extraction. We show that distributions rapidly converge to normality as Nincreases. Pairwise correlations between scales depend both on background distribution and sequence length and rapidly converge to an analytically predictable asymptotic value. For di- and tri-nucleotide scales, normal behavior and asymptotic correlation values are attained over a characteristic window length of about 10-15 bp. With a uniform background distribution, pairwise correlations between empirically-derived scales remain relatively small and roughly constant at all lengths, except for propeller twist and protein deformability which are positively correlated. There is a positive (resp. negative) correlation between dinucleotide base stacking (resp. propeller twist and protein deformability) and AT-content that increases in magnitude with length. The framework is applied to the analysis of various DNA tandem repeats. We derive exact expressions for counting the number of repeat unit classes at all lengths. Tandem repeats are likely to result from a variety of different mechanisms, a fraction of which is likely to depend on profiles characterized by extreme structural features.