Autonomously Folding Protein Fragments Reveal Differences in the Energy Landscapes of Homologous RNases H

An important approach to understanding how a protein sequence encodes its energy landscape is to compare proteins with different sequences that fold to the same general native structure. In this work, we compare E. coli and T. thermophilus homologs of the protein RNase H. Using protein fragments, we create equilibrium mimics of two different potential partially-folded intermediates (I_core and I_core+1) hypothesized to be present on the energy landscapes of these two proteins. We observe that both T. thermophilus RNase H (ttRNH) fragments are folded and have distinct stabilities, indicating that both regions are capable of autonomous folding and that both intermediates are present as local minima on the ttRNH energy landscape. In contrast, the two E. coli RNase H (ecRNH) fragments have very similar stabilities, suggesting that the presence of additional residues in the I_core+1 fragment does not affect the folding or structure as compared to I_core. NMR experiments provide additional evidence that only the I_core intermediate is populated by ecRNH. This is one of the biggest differences that has been observed between the energy landscapes of these two proteins. Additionally, we used a FRET experiment in the background of full-length ttRNH to specifically monitor the formation of the I_core+1 intermediate. We determine that the ttRNH I_core+1 intermediate is likely the intermediate populated prior to the rate-limiting barrier to global folding, in contrast to E. coli RNase H for which I_core is the folding intermediate. This result provides new insight into the nature of the rate-limiting barrier for the folding of RNase H.     

Multiple time scale backbone dynamics of homologous thermophilic and mesophilic ribonuclease HI enzymes

Backbone conformational fluctuations on multiple time scales in a cysteine-free Thermus thermophilus ribonuclease HI mutant (ttRNH(*)) are quantified using (15)N nuclear magnetic spin relaxation. Laboratory-frame relaxation data acquired at 310 K and at static magnetic field strengths of 11.7, 14.1 and 18.8 T are analysed using reduced spectral density mapping and model-free approaches. Chemical exchange line broadening is characterized using Hahn-echo transverse and multiple quantum relaxation data acquired over a temperature range of 290-320 K and at a static magnetic field strength of 14.1 T. Results for ttRNH(*) are compared to previously published data for a mesophilic homologue, Escherichia coli ribonuclease HI (ecRNH). Intramolecular conformational fluctuations on the picosecond-to-nanosecond time scale generally are similar for ttRNH(*) and ecRNH. beta-Strands 3 and 5 and the glycine-rich region are more rigid while the substrate-binding handle region and C-terminal tail are more flexible in ttRNH(*) than in ecRNH. Rigidity in the two beta-strands and the glycine-rich region, located along the periphery of the central beta-sheet, may be associated with the increased thermodynamic stability of the thermophilic enzyme. Chemical exchange line broadening, reflecting microsecond-to-millisecond time scale conformational changes, is more pronounced in ttRNH(*) than in ecRNH, particularly for residues in the handle and surrounding the catalytic site. The temperature dependence of chemical exchange show an increase of approximately 15 kJ/mol in the apparent activation energies for ttRNH(*) residues in the handle compared to ecRNH. Increased activation barriers, coupled with motion between alpha-helices B and C not present in ecRNH, may be associated with the reduced catalytic activity of the thermophilic enzyme at 310 K.     

Sequence effects of aminofluorene-modified DNA duplexes: thermodynamic and circular dichroism properties

Circular dichroism (CD) and UV-melting experiments were conducted with 16 oligodeoxynucleotides modified by the carcinogen 2-aminofluorene, whose sequence around the lesion was varied systematically [d(CTTCTNG[AF]NCCTC), N = G, A, C, T], to gain insight into the factors that determine the equilibrium between base-displaced stacked (S) and external B-type (B) duplex conformers. Differing stabilities among the duplexes can be attributed to different populations of S and B conformers. The AF modification always resulted in sequence-dependent thermal (T_m) and thermodynamic (−ΔG°) destabilization. The population of B-type conformers derived from eight selected duplexes (i.e. -AG*N- and -CG*N-) was inversely proportional to the −ΔG° and T_m values, which highlights the importance of carcinogen/base stacking in duplex stabilization even in the face of disrupted Watson–Crick base pairing in S-conformation. CD studies showed that the extent of the adduct-induced negative ellipticities in the 290–350 nm range is correlated linearly with −ΔG° and T_m, but inversely with the population of B-type conformations. Taken together, these results revealed a unique interplay between the extent of carcinogenic interaction with neighboring base pairs and the thermodynamic properties of the AF-modified duplexes. The sequence-dependent S/B heterogeneities have important implications in understanding how arylamine–DNA adducts are recognized in nucleotide excision repair.     

Cold denaturation of monoclonal antibodies

The susceptibility of monoclonal antibodies (mAbs) to undergo cold denaturation remains unexplored. In this study, the phenomenon of cold denaturation was investigated for a mAb, mAb1, through thermodynamic and spectroscopic analyses. tryptophan fluorescence and circular dichroism (CD) spectra were recorded for the guanidine hydrochloride (GuHCl)-induced unfolding of mAb1 at pH 6.3 at temperatures ranging from −5 to 50°C. A three-state unfolding model incorporating the linear extrapolation method was fit to the fluorescence data to obtain an apparent free energy of unfolding, ΔG_u, at each temperature. CD studies revealed that mAb1 exhibited polyproline II helical structure at low temperatures and at high GuHCl concentrations. the Gibbs-Helmholtz expression fit to the ΔG_u versus temperature data from fluorescence gave a ΔC_p of 8.0 kcal mol⁻¹ K⁻¹, a maximum apparent stability of 23.7 kcal mol⁻¹ at 18°C, and an apparent cold denaturation temperature (T_CD) of −23°C. ΔG_u values for another mAb (mAb2) with a similar framework exhibited less stability at low temperatures, suggesting a depressed protein stability curve and a higher relative T_CD. Direct experimental evidence of the susceptibility of mAb1 and mAb2 to undergo cold denaturation in the absence of denaturant was confirmed at pH 2.5. thus, mAbs have a potential to undergo cold denaturation at storage temperatures near −20°C (pH 6.3), and this potential needs to be evaluated independently for individual mAbs.Key words: monoclonal antibodies, thermodynamic stability, cold denaturation, free energy, fluorescence     

Structural Characteristic of the Initial Unfolded State on Refolding Determines Catalytic Efficiency of the Folded Protein in Presence of Osmolytes

Osmolytes are low molecular weight organic molecules accumulated by organisms to assist proper protein folding, and to provide protection to the structural integrity of proteins under denaturing stress conditions. It is known that osmolyte-induced protein folding is brought by unfavorable interaction of osmolytes with the denatured/unfolded states. The interaction of osmolyte with the native state does not significantly contribute to the osmolyte-induced protein folding. We have therefore investigated if different denatured states of a protein (generated by different denaturing agents) interact differently with the osmolytes to induce protein folding. We observed that osmolyte-assisted refolding of protein obtained from heat-induced denatured state produces native molecules with higher enzyme activity than those initiated from GdmCl- or urea-induced denatured state indicating that the structural property of the initial denatured state during refolding by osmolytes determines the catalytic efficiency of the folded protein molecule. These conclusions have been reached from the systematic measurements of enzymatic kinetic parameters (K _m and k _cat), thermodynamic stability (T _m and ΔH _m) and secondary and tertiary structures of the folded native proteins obtained from refolding of various denatured states (due to heat-, urea- and GdmCl-induced denaturation) of RNase-A in the presence of various osmolytes.     

Development at Cold-Hardening Temperatures : The Structure and Composition of Purified Rye Light Harvesting Complex II

Light harvesting complex II (LHCII) was purified from cold-hardened (RH) and nonhardened winter rye (RNH) (Secale cereale L. cv Puma) employing a modified procedure of JJ Burke, CL Ditto, CJ Arntzen (Arch Biochem Biophys 187: 252-263). Triton X-100 solubilization of thylakoid membranes followed by three successive precipitations with 100 mm KCl and 10 mm MgCl₂ resulted in yields of up to 25% on a chlorophyll (Chl) basis and a purity of 90 to 95%, based on polypeptide analysis within 4 hours. Polypeptide and pigment analyses, 77 K fluorescence emission and room temperature absorption spectra indicate the LHCII obtained by this modified method is comparable to LHCII obtained by other published methods. Comparison of purified RH and RNH LHCII indicated no significant differences with respect to polypeptide, amino acid, Chl, and carotenoid compositions as well as no differences in lipid content. However, RH LHCII differed from RNH LHCII specifically with respect to the fatty acid composition of phosphatidyldiacylglycerol only. RH LHCII exhibited a 54% lower trans-Δ³-hexadecenoic acid level associated with PG and a 60% lower oligomeric LHCII:monomeric LHCII (LHCII₁:LHCII₃) than RNH LHCII. Both RH and RNH LHCII exhibited a 5-fold enrichment in PG specifically. Complete removal of PG by enzymic hydrolysis resulted in a significant reduction in the oligomeric content of both RH and RNH LHCII such that LHCII₁:LHCII₃ of RH and RNH LHCII preparations were the same. This confirms that this specific compositional change accounts for the structural differences between RH and RNH LCHII observed in situ and in vitro.     

Thermodynamics of DNA target site recognition by homing endonucleases

The thermodynamic profiles of target site recognition have been surveyed for homing endonucleases from various structural families. Similar to DNA-binding proteins that recognize shorter target sites, homing endonucleases display a narrow range of binding free energies and affinities, mediated by structural interactions that balance the magnitude of enthalpic and entropic forces. While the balance of ΔH and TΔS are not strongly correlated with the overall extent of DNA bending, unfavorable ΔH_binding is associated with unstacking of individual base steps in the target site. The effects of deleterious basepair substitutions in the optimal target sites of two LAGLIDADG homing endonucleases, and the subsequent effect of redesigning one of those endonucleases to accommodate that DNA sequence change, were also measured. The substitution of base-specific hydrogen bonds in a wild-type endonuclease/DNA complex with hydrophobic van der Waals contacts in a redesigned complex reduced the ability to discriminate between sites, due to nonspecific ΔS_binding.     

How long is too long? Effects of loop size on G-quadruplex stability

We compared here 80 different sequences containing four tracts of three guanines with loops of variable length (between 1 and 15 bases for unmodified sequences, up to 30 for fluorescently labeled oligonucleotides). All sequences were capable of forming stable quadruplexes, with T_m above physiological temperature in most cases. Unsurprisingly, the melting temperature was systematically lower in sodium than in potassium but the difference between both ionic conditions varied between 1 and >39°C (average difference: 18.3°C). Depending on the sequence context, and especially for G4 sequences involving two very short loops, the third one may be very long without compromising the stability of the quadruplex. A strong inverse correlation between total loop length and T_m was found in K⁺: each added base leads to a 2°C drop in T_m or ∼0.3 kcal/mol loss in ΔG°. The trend was less clear in Na⁺, with a longer than expected optimal loop length (up to 5 nt). This study will therefore extend the sequence repertoire of quadruplex-prone sequences, arguing for a modification of the widely used consensus (maximal loop size of 7 bases).     

The First Identification of Carbohydrate Binding Modules Specific to Chitosan

Two carbohydrate binding modules (DD1 and DD2) belonging to CBM32 are located at the C terminus of a chitosanase from Paenibacillus sp. IK-5. We produced three proteins, DD1, DD2, and tandem DD1/DD2 (DD1+DD2), and characterized their binding ability. Transition temperature of thermal unfolding (T_m) of each protein was elevated by the addition of cello-, laminari-, chitin-, or chitosan-hexamer (GlcN)₆. The T_m elevation (ΔT_m) in DD1 was the highest (10.3 °C) upon the addition of (GlcN)₆ and was markedly higher than that in DD2 (1.0 °C). A synergistic effect was observed (ΔT_m = 13.6 °C), when (GlcN)₆ was added to DD1+DD2. From isothermal titration calorimetry experiments, affinities to DD1 were not clearly dependent upon chain length of (GlcN)_n; ΔG_r° values were −7.8 (n = 6), −7.6 (n = 5), −7.6 (n = 4), −7.6 (n = 3), and −7.1 (n = 2) kcal/mol, and the value was not obtained for GlcN due to the lowest affinity. DD2 bound (GlcN)_n with the lower affinities (ΔG_r° = −5.0 (n = 3) ∼ −5.2 (n = 6) kcal/mol). Isothermal titration calorimetry profiles obtained for DD1+DD2 exhibited a better fit when the two-site model was used for analysis and provided greater affinities to (GlcN)₆ for individual DD1 and DD2 sites (ΔG_r° = −8.6 and −6.4 kcal/mol, respectively). From NMR titration experiments, (GlcN)_n (n = 2∼6) were found to bind to loops extruded from the core β-sandwich of individual DD1 and DD2, and the interaction sites were similar to each other. Taken together, DD1+DD2 is specific to chitosan, and individual modules synergistically interact with at least two GlcN units, facilitating chitosan hydrolysis.     

An inserted Gly residue fine tunes dynamics between mesophilic and thermophilic ribonucleases H

Dynamic processes are inherent properties of proteins and are crucial for a wide range of biological functions. To address how changes in protein sequence and structure affect dynamic processes, a quantitative comparison of microsecond-to-microsecond time scale conformational changes, measured by solution NMR spectroscopy, within homologous mesophilic and thermophilic ribonuclease H (RNase H) enzymes is presented. Kinetic transitions between the observed major state (high population) and alternate (low population) conformational state(s) of the substrate-binding handle region in RNase H from the mesophile Escherichia coli (ecRNH) and thermophile Thermus thermophilus (ttRNH) occur with similar kinetic exchange rate constants, but the difference in stability between exchanging conformers is smaller in ttRNH compared to ecRNH. The altered thermodynamic equilibrium between kinetically exchanging conformers in the thermophile is recapitulated in ecRNH by the insertion of a Gly residue within a putative hinge between alpha-helices B and C. This Gly insertion is conserved among thermophilic RNases H, and allows the formation of additional intrahelical hydrogen bonds. A Gly residue inserted between alpha-helices B and C appears to relieve unfavorable interactions in the transition state and alternate conformer(s) and represents an important adaptation to adjust conformational changes within RNase H for activity at high temperatures.     

Optimal design of parallel triplex forming oligonucleotides containing Twisted Intercalating Nucleic Acids—TINA

Twisted intercalating nucleic acid (TINA) is a novel intercalator and stabilizer of Hoogsteen type parallel triplex formations (PT). Specific design rules for position of TINA in triplex forming oligonucleotides (TFOs) have not previously been presented. We describe a complete collection of easy and robust design rules based upon more than 2500 melting points (T_m) determined by FRET. To increase the sensitivity of PT, multiple TINAs should be placed with at least 3 nt in-between or preferable one TINA for each half helixturn and/or whole helixturn. We find that ΔT_m of base mismatches on PT is remarkably high (between 7.4 and 15.2°C) compared to antiparallel duplexes (between 3.8 and 9.4°C). The specificity of PT by ΔT_m increases when shorter TFOs and higher pH are chosen. To increase ΔTms, base mismatches should be placed in the center of the TFO and when feasible, A, C or T to G base mismatches should be avoided. Base mismatches can be neutralized by intercalation of a TINA on each side of the base mismatch and masked by a TINA intercalating direct 3′ (preferable) or 5′ of it. We predict that TINA stabilized PT will improve the sensitivity and specificity of DNA based clinical diagnostic assays.     

Molecular-Level Thermodynamic Switch Controls Chemical Equilibrium in Sequence-Specific Hydrophobic Interaction of 35 Dipeptide Pairs

Applying the Planck-Benzinger methodology, the sequence-specific hydrophobic interactions of 35 dipeptide pairs were examined over a temperature range of 273–333 K, based on data reported by Nemethy and Scheraga in 1962. The hydrophobic interaction in these sequence-specific dipeptide pairs is highly similar in its thermodynamic behavior to that of other biological systems. The results imply that the negative Gibbs free energy change minimum at a well-defined stable temperature, T_s, where the bound unavailable energy, TΔS^o = 0, has its origin in the sequence-specific hydrophobic interactions, are highly dependent on details of molecular structure. Each case confirms the existence of a thermodynamic molecular switch wherein a change of sign in ΔCp^o(T)_reaction (change in specific heat capacity of reaction at constant pressure) leads to true negative minimum in the Gibbs free energy change of reaction, ΔG^o(T)_reaction, and hence a maximum in the related equilibrium constant, K_eq. Indeed, all interacting biological systems examined to date by Chun using the Planck-Benzinger methodology have shown such a thermodynamic switch at the molecular level, suggesting its existence may be universal.     

Improved nearest-neighbor parameters for the stability of RNA/DNA hybrids under a physiological condition

The stability of Watson–Crick paired RNA/DNA hybrids is important for designing optimal oligonucleotides for ASO (Antisense Oligonucleotide) and CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats)–Cas9 techniques. Previous nearest-neighbour (NN) parameters for predicting hybrid stability in a 1 M NaCl solution, however, may not be applicable for predicting stability at salt concentrations closer to physiological condition (e.g. ∼100 mM Na⁺ or K⁺ in the presence or absence of Mg²⁺). Herein, we report measured thermodynamic parameters of 38 RNA/DNA hybrids at 100 mM NaCl and derive new NN parameters to predict duplex stability. Predicted ΔG°₃₇ and T_m values based on the established NN parameters agreed well with the measured values with 2.9% and 1.1°C deviations, respectively. The new results can also be used to make precise predictions for duplexes formed in 100 mM KCl or 100 mM NaCl in the presence of 1 mM Mg²⁺, which can mimic an intracellular and extracellular salt condition, respectively. Comparisons of the predicted thermodynamic parameters with published data using ASO and CRISPR–Cas9 may allow designing shorter oligonucleotides for these techniques that will diminish the probability of non-specific binding and also improve the efficiency of target gene regulation.     

Determination of the secondary structure of group II bulge loops using the fluorescent probe 2-aminopurine

Eleven RNA hairpins containing 2-aminopurine (2-AP) in either base-paired or single nucleotide bulge loop positions were optically melted in 1 M NaCl; and, the thermodynamic parameters ΔH°, ΔS°, ΔG°₃₇, and T_M for each hairpin were determined. Substitution of 2-AP for an A (adenosine) at a bulge position (where either the 2-AP or A is the bulge) in the stem of a hairpin, does not affect the stability of the hairpin. For group II bulge loops such as AA/U, where there is ambiguity as to which of the A residues is paired with the U, hairpins with 2-AP substituted for either the 5′ or 3′ position in the hairpin stem have similar stability. Fluorescent melts were performed to monitor the environment of the 2-AP. When the 2-AP was located distal to the hairpin loop on either the 5′ or 3′ side of the hairpin stem, the change in fluorescent intensity upon heating was indicative of an unpaired nucleotide. A database of phylogenetically determined RNA secondary structures was examined to explore the presence of naturally occurring bulge loops embedded within a hairpin stem. The distribution of bulge loops is discussed and related to the stability of hairpin structures.     

Ancestral Sequence Reconstruction of a Cytochrome P450 Family Involved in Chemical Defense Reveals the Functional Evolution of a Promiscuous,Xenobiotic-Metabolizing Enzyme in Vertebrates

The cytochrome P450 family 1 enzymes (CYP1s) are a diverse family of hemoprotein monooxygenases, which metabolize many xenobiotics including numerous environmental carcinogens. However, their historical function and evolution remain largely unstudied. Here we investigate CYP1 evolution via the reconstruction and characterization of the vertebrate CYP1 ancestors. Younger ancestors and extant forms generally demonstrated higher activity toward typical CYP1 xenobiotic and steroid substrates than older ancestors, suggesting significant diversification away from the original CYP1 function. Caffeine metabolism appears to be a recently evolved trait of the CYP1A subfamily, observed in the mammalian CYP1A lineage, and may parallel the recent evolution of caffeine synthesis in multiple separate plant species. Likewise, the aryl hydrocarbon receptor agonist, 6-formylindolo[3,2-b]carbazole (FICZ) was metabolized to a greater extent by certain younger ancestors and extant forms, suggesting that activity toward FICZ increased in specific CYP1 evolutionary branches, a process that may have occurred in parallel to the exploitation of land where UV-exposure was higher than in aquatic environments. As observed with previous reconstructions of P450 enzymes, thermostability correlated with evolutionary age; the oldest ancestor was up to 35 °C more thermostable than the extant forms, with a ¹⁰T₅₀ (temperature at which 50% of the hemoprotein remains intact after 10 min) of 71 °C. This robustness may have facilitated evolutionary diversification of the CYP1s by buffering the destabilizing effects of mutations that conferred novel functions, a phenomenon which may also be useful in exploiting the catalytic versatility of these ancestral enzymes for commercial application as biocatalysts.     

Bacterial Porin Disrupts Mitochondrial Membrane Potential and Sensitizes Host Cells to Apoptosis

The bacterial PorB porin, an ATP-binding β-barrel protein of pathogenic Neisseria gonorrhoeae, triggers host cell apoptosis by an unknown mechanism. PorB is targeted to and imported by host cell mitochondria, causing the breakdown of the mitochondrial membrane potential (ΔΨ_m). Here, we show that PorB induces the condensation of the mitochondrial matrix and the loss of cristae structures, sensitizing cells to the induction of apoptosis via signaling pathways activated by BH3-only proteins. PorB is imported into mitochondria through the general translocase TOM but, unexpectedly, is not recognized by the SAM sorting machinery, usually required for the assembly of β-barrel proteins in the mitochondrial outer membrane. PorB integrates into the mitochondrial inner membrane, leading to the breakdown of ΔΨ_m. The PorB channel is regulated by nucleotides and an isogenic PorB mutant defective in ATP-binding failed to induce ΔΨ_m loss and apoptosis, demonstrating that dissipation of ΔΨ_m is a requirement for cell death caused by neisserial infection.     

Monitoring Rates and Heterogeneity of High-Pressure Germination of Bacillus Spores by Phase-Contrast Microscopy of Individual Spores

Germination of Bacillus spores with a high pressure (HP) of ∼150 MPa is via activation of spores'' germinant receptors (GRs). The HP germination of multiple individual Bacillus subtilis spores in a diamond anvil cell (DAC) was monitored with phase-contrast microscopy. Major conclusions were that (i) >95% of wild-type spores germinated in 40 min in a DAC at ∼150 MPa and 37°C but individual spores'' germination kinetics were heterogeneous; (ii) individual spores'' HP germination kinetic parameters were similar to those of nutrient-triggered germination with a variable lag time (T_lag) prior to a period of the rapid release (ΔT_release) of the spores'' dipicolinic acid in a 1:1 chelate with Ca²⁺ (CaDPA); (iii) spore germination at 50 MPa had longer average T_lag values than that at ∼150 MPa, but the ΔT_release values at the two pressures were identical and HPs of <10 MPa did not induce germination; (iv) B. subtilis spores that lacked the cortex-lytic enzyme CwlJ and that were germinated with an HP of 150 MPa exhibited average ΔT_release values ∼15-fold longer than those for wild-type spores, but the two types of spores exhibited similar average T_lag values; and (v) the germination of wild-type spores given a ≥30-s 140-MPa HP pulse followed by a constant pressure of 1 MPa was the same as that of spores exposed to a constant pressure of 140 MPa that was continued for ≥35 min; (vi) however, after short 150-MPa HP pulses and incubation at 0.1 MPa (ambient pressure), spore germination stopped 5 to 10 min after the HP was released. These results suggest that an HP of ∼150 MPa for ≤30 s is sufficient to fully activate spores'' GRs, which remain activated at 1 MPa but can deactivate at ambient pressure.     

Adaptive basis of geographic variation: genetic,phenotypic and environmental differences among beach mouse populations

A major goal in evolutionary biology is to understand how and why populations differentiate, both genetically and phenotypically, as they invade a novel habitat. A classical example of adaptation is the pale colour of beach mice, relative to their dark mainland ancestors, which colonized the isolated sandy dunes and barrier islands on Florida''s Gulf Coast. However, much less is known about differentiation among the Gulf Coast beach mice, which comprise five subspecies linearly arrayed on Florida''s shoreline. Here, we test the role of selection in maintaining variation among these beach mouse subspecies at multiple levels—phenotype, genotype and the environments they inhabit. While all beach subspecies have light pelage, they differ significantly in colour pattern. These subspecies are also genetically distinct: pair-wise F_st-values range from 0.23 to 0.63 and levels of gene flow are low. However, we did not find a correlation between phenotypic and genetic distance. Instead, we find a significant association between the average ‘lightness’ of each subspecies and the brightness of the substrate it inhabits: the two most genetically divergent subspecies occupy the most similar habitats and have converged on phenotype, whereas the most genetically similar subspecies occupy the most different environments and have divergent phenotypes. Moreover, allelic variation at the pigmentation gene, Mc1r, is statistically correlated with these colour differences but not with variation at other genetic loci. Together, these results suggest that natural selection for camouflage—via changes in Mc1r allele frequency—contributes to pigment differentiation among beach mouse subspecies.     

Asymptotic Distributions of Coalescence Times and Ancestral Lineage Numbers for Populations with Temporally Varying Size

The distributions of coalescence times and ancestral lineage numbers play an essential role in coalescent modeling and ancestral inference. Both exact distributions of coalescence times and ancestral lineage numbers are expressed as the sum of alternating series, and the terms in the series become numerically intractable for large samples. More computationally attractive are their asymptotic distributions, which were derived in Griffiths (1984) for populations with constant size. In this article, we derive the asymptotic distributions of coalescence times and ancestral lineage numbers for populations with temporally varying size. For a sample of size n, denote by T_m the mth coalescent time, when m + 1 lineages coalesce into m lineages, and A_n(t) the number of ancestral lineages at time t back from the current generation. Similar to the results in Griffiths (1984), the number of ancestral lineages, A_n(t), and the coalescence times, T_m, are asymptotically normal, with the mean and variance of these distributions depending on the population size function, N(t). At the very early stage of the coalescent, when t → 0, the number of coalesced lineages n − A_n(t) follows a Poisson distribution, and as m → n, n(n ? 1)T_m/2N(0) follows a gamma distribution. We demonstrate the accuracy of the asymptotic approximations by comparing to both exact distributions and coalescent simulations. Several applications of the theoretical results are also shown: deriving statistics related to the properties of gene genealogies, such as the time to the most recent common ancestor (TMRCA) and the total branch length (TBL) of the genealogy, and deriving the allele frequency spectrum for large genealogies. With the advent of genomic-level sequencing data for large samples, the asymptotic distributions are expected to have wide applications in theoretical and methodological development for population genetic inference.     

Cooperative Unfolding of Residual Structure in Heat Denatured Proteins by Urea and Guanidinium Chloride

The denatured states of proteins have always attracted our attention due to the fact that the denatured state is the only experimentally achievable state of a protein, which can be taken as initial reference state for considering the in vitro folding and defining the native protein stability. It is known that heat and guanidinium chloride (GdmCl) give structurally different states of RNase-A, lysozyme, α-chymotrypsinogen A and α-lactalbumin. On the contrary, differential scanning calorimetric (DSC) and isothermal titration calorimetric measurements, reported in the literature, led to the conclusion that heat denatured and GdmCl denatured states are thermodynamically and structurally identical. In order to resolve this controversy, we have measured changes in the far-UV CD (circular dichroism) of these heat-denatured proteins on the addition of different concentrations of GdmCl. The observed sigmoidal curve of each protein was analyzed for Gibbs free energy change in the absence of the denaturant (ΔG ⁰ _X→D) associated with the process heat denatured (X) state ↔ GdmCl denatured (D) state. To confirm that this thermodynamic property represents the property of the protein alone and is not a manifestation of salvation effect, we measured urea-induced denaturation curves of these heat denatured proteins under the same experimental condition in which GdmCl-induced denaturation was carried out. In this paper we report that (a) heat denatured proteins contain secondary structure, and GdmCl (or urea) induces a cooperative transition between X and D states, (b) for each protein at a given pH and temperature, thermodynamic cycle connects quantities, ΔG ⁰ _N→X (native (N) state ↔ X state), ΔG ⁰ _X→D and ΔG ⁰ _N→D (N state ↔ D state), and (c) there is not a good enthalpy difference between X and D states, which is the reason for the absence of endothermic peak in DSC scan for the transition, X state ↔ D state.