Shape anisotropy of a single random-walk polymer

Random walks have been used to describe a wide variety of systems ranging from cell colonies to polymers. Sixty-five years ago, Kuhn [Kuhn, W. (1934) Kolloid-Z. 68, 2–11] made the prediction, backed later by computer simulations, that the overall shape of a random-walk polymer is aspherical, yet no experimental work has directly tested Kuhn's general idea and subsequent computer simulations. By using fluorescence microscopy, we monitored the conformation of individual, long, random-walk polymers (fluorescently labeled DNA molecules) at equilibrium. We found that a polymer most frequently adopts highly extended, nonfractal structures with a strongly anisotropic shape. The ensemble-average ratio of the lengths of the long and short axes of the best-fit ellipse of the polymer was much larger than unity.

Evidence for nonrandom hydrophobicity structures in protein chains.

The question of whether proteins originate from random sequences of amino acids is addressed. A statistical analysis is performed in terms of blocked and random walk values formed by binary hydrophobic assignments of the amino acids along the protein chains. Theoretical expectations of these variables from random distributions of hydrophobicities are compared with those obtained from functional proteins. The results, which are based upon proteins in the SWISS-PROT data base, convincingly show that the amino acid sequences in proteins differ from what is expected from random sequences in a statistically significant way. By performing Fourier transforms on the random walks, one obtains additional evidence for nonrandomness of the distributions. We have also analyzed results from a synthetic model containing only two amino acid types, hydrophobic and hydrophilic. With reasonable criteria on good folding properties in terms of thermodynamical and kinetic behavior, sequences that fold well are isolated. Performing the same statistical analysis on the sequences that fold well indicates similar deviations from randomness as for the functional proteins. The deviations from randomness can be interpreted as originating from anticorrelations in terms of an Ising spin model for the hydrophobicities. Our results, which differ from some previous investigations using other methods, might have impact on how permissive with respect to sequence specificity protein folding process is-only sequences with nonrandom hydrophobicity distributions fold well. Other distributions give rise to energy landscapes with poor folding properties and hence did not survive the evolution.

A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Charge transfer and transport in DNA

We explore charge migration in DNA, advancing two distinct mechanisms of charge separation in a donor (d)–bridge ({Bj})–acceptor (a) system, where {Bj} = B1,B2, … , BN are the N-specific adjacent bases of B-DNA: (i) two-center unistep superexchange induced charge transfer, d*{Bj}a → d∓{Bj}a±, and (ii) multistep charge transport involves charge injection from d* (or d+) to {Bj}, charge hopping within {Bj}, and charge trapping by a. For off-resonance coupling, mechanism i prevails with the charge separation rate and yield exhibiting an exponential dependence ∝ exp(−βR) on the d-a distance (R). Resonance coupling results in mechanism ii with the charge separation lifetime τ ∝ Nη and yield Y ≃ (1 + δ̄ Nη)−1 exhibiting a weak (algebraic) N and distance dependence. The power parameter η is determined by charge hopping random walk. Energetic control of the charge migration mechanism is exerted by the energetics of the ion pair state d∓B1±B2 … BNa relative to the electronically excited donor doorway state d*B1B2 … BNa. The realization of charge separation via superexchange or hopping is determined by the base sequence within the bridge. Our energetic–dynamic relations, in conjunction with the energetic data for d*/d− and for B/B+, determine the realization of the two distinct mechanisms in different hole donor systems, establishing the conditions for “chemistry at a distance” after charge transport in DNA. The energetic control of the charge migration mechanisms attained by the sequence specificity of the bridge is universal for large molecular-scale systems, for proteins, and for DNA.

Torsional directed walks, entropic elasticity, and DNA twist stiffness

DNA and other biopolymers differ from classical polymers because of their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the “torsional directed walk.” Motivated by a recent experiment on single lambda-DNA molecules [Strick, T. R., Allemand, J.-F., Bensimon, D., Bensimon, A. & Croquette, V. (1996) Science 271, 1835–1837], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C = 120 nm and D = 50 nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.

Guanidine hydrochloride blocks a critical step in the propagation of the prion-like determinant [PSI+] of Saccharomyces cerevisiae

The cytoplasmic heritable determinant [PSI+] of the yeast Saccharomyces cerevisiae reflects the prion-like properties of the chromosome-encoded protein Sup35p. This protein is known to be an essential eukaryote polypeptide release factor, namely eRF3. In a [PSI+] background, the prion conformer of Sup35p forms large oligomers, which results in the intracellular depletion of functional release factor and hence inefficient translation termination. We have investigated the process by which the [PSI+] determinant can be efficiently eliminated from strains, by growth in the presence of the protein denaturant guanidine hydrochloride (GuHCl). Strains are “cured” of [PSI+] by millimolar concentrations of GuHCl, well below that normally required for protein denaturation. Here we provide evidence indicating that the elimination of the [PSI+] determinant is not derived from the direct dissolution of self-replicating [PSI+] seeds by GuHCl. Although GuHCl does elicit a moderate stress response, the elimination of [PSI+] is not enhanced by stress, and furthermore, exhibits an absolute requirement for continued cell division. We propose that GuHCl inhibits a critical event in the propagation of the prion conformer and demonstrate that the kinetics of curing by GuHCl fit a random segregation model whereby the heritable [PSI+] element is diluted from a culture, after the total inhibition of prion replication by GuHCl.

Anterograde flow of cargo across the Golgi stack potentially mediated via bidirectional “percolating” COPI vesicles

How do secretory proteins and other cargo targeted to post-Golgi locations traverse the Golgi stack? We report immunoelectron microscopy experiments establishing that a Golgi-restricted SNARE, GOS 28, is present in the same population of COPI vesicles as anterograde cargo marked by vesicular stomatitis virus glycoprotein, but is excluded from the COPI vesicles containing retrograde-targeted cargo (marked by KDEL receptor). We also report that GOS 28 and its partnering t-SNARE heavy chain, syntaxin 5, reside together in every cisterna of the stack. Taken together, these data raise the possibility that the anterograde cargo-laden COPI vesicles, retained locally by means of tethers, are inherently capable of fusing with neighboring cisternae on either side. If so, quanta of exported proteins would transit the stack in GOS 28–COPI vesicles via a bidirectional random walk, entering at the cis face and leaving at the trans face and percolating up and down the stack in between. Percolating vesicles carrying both post-Golgi cargo and Golgi residents up and down the stack would reconcile disparate observations on Golgi transport in cells and in cell-free systems.

Least activation path for protein folding: investigation of staphylococcal nuclease folding by stopped-flow circular dichroism.

Is the pathway of protein folding determined by the relative stability of folding intermediates, or by the relative height of the activation barriers leading to these intermediates? This is a fundamental question for resolving the Levinthal paradox, which stated that protein folding by a random search mechanism would require a time too long to be plausible. To answer this question, we have studied the guanidinium chloride (GdmCl)-induced folding/unfolding of staphylococcal nuclease [(SNase, formerly EC 3.1.4.7; now called microbial nuclease or endonuclease, EC 3.1.31.1] by stopped-flow circular dichroism (CD) and differential scanning microcalorimetry (DSC). The data show that while the equilibrium transition is a quasi-two-state process, kinetics in the 2-ms to 500-s time range are triphasic. Data support the sequential mechanism for SNase folding: U3 <--> U2 <--> U1 <--> N0, where U1, U2, and U3 are substates of the unfolded protein and N0 is the native state. Analysis of the relative population of the U1, U2, and U3 species in 2.0 M GdmCl gives delta-G values for the U3 --> U2 reaction of +0.1 kcal/mol and for the U2 --> U1 reaction of -0.49 kcal/mol. The delta-G value for the U1 --> N0 reaction is calculated to be -4.5 kcal/mol from DSC data. The activation energy, enthalpy, and entropy for each kinetic step are also determined. These results allow us to make the following four conclusions. (i) Although the U1, U2, and U3 states are nearly isoenergetic, no random walk occurs among them during the folding. The pathway of folding is unique and sequential. In other words, the relative stability of the folding intermediates does not dictate the folding pathway. Instead, the folding is a descent toward the global free-energy minimum of the native state via the least activation path in the vast energy landscape. Barrier avoidance leads the way, and barrier height limits the rate. Thus, the Levinthal paradox is not applicable to the protein-folding problem. (ii) The main folding reaction (U1 --> N0), in which the peptide chain acquires most of its free energy (via van der Waals' contacts, hydrogen bonding, and electrostatic interactions), is a highly concerted process. These energy-acquiring events take place in a single kinetic phase. (iii) U1 appears to be a compact unfolded species; the rate of conversion of U2 to U1 depends on the viscosity of solution. (iv) All four relaxation times reported here depend on GdmCl concentrations: it is likely that none involve the cis/trans isomerization of prolines. Finally, a mechanism is presented in which formation of sheet-like chain conformations and a hydrophobic condensation event precede the main-chain folding reaction.

A modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).

The kinesin walk: a dynamic model with elastically coupled heads.

Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. In this paper we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads that show all of these properties. The analytic and numerical treatment of our model results in a very good fit to the experimental data and practically has no free parameters. Changing the values of the parameters in the restricted range allowed by the related experimental estimates has almost no effect on the shape of the curves and results mainly in a variation of the zero load velocity that can be directly fitted to the measured data. In addition, the model is consistent with the measured pathway of the kinesin ATPase.

Broken symmetry and critical transport properties of random metals

Recent experimental data on the conductivity σ+(T), T → 0, on the metallic side of the metal–insulator transition in ideally random (neutron transmutation-doped) 70Ge:Ga have shown that σ+(0) ∝ (N − Nc)μ with μ = ½, confirming earlier ultra-low-temperature results for Si:P. This value is inconsistent with theoretical predictions based on diffusive classical scaling models, but it can be understood by a quantum-directed percolative filamentary amplitude model in which electronic basis states exist which have a well-defined momentum parallel but not normal to the applied electric field. The model, which is based on a new kind of broken symmetry, also explains the anomalous sign reversal of the derivative of the temperature dependence in the critical regime.

Conformational influences of glycosylation of a peptide: A possible model for the effect of glycosylation on the rate of protein folding

Improved strategies for synthesis make it possible to expand the range of glycopeptides available for detailed conformational studies. The glycopeptide 1 was synthesized using a new solid phase synthesis of carbohydrates and a convergent coupling to peptide followed by deprotection. Its conformational properties were subjected to NMR analysis and compared with a control peptide 2 prepared by conventional solid phase methods. Whereas peptide 2 fails to manifest any appreciable secondary structure, the glycopeptide 1 does show considerable conformational bias suggestive of an equilibrium between an ordered and a random state. The implications of this ordering effect for the larger issue of protein folding are considered.

Identification of fission yeast nuclear markers using random polypeptide fusions with green fluorescent protein

We describe a method for identifying genes encoding proteins with stereospecific intracellular localizations in the fission yeast Schizosaccharomyces pombe. Yeast are transformed with a gene library in which S. pombe genomic sequences are fused to the gene encoding the Aequorea victoria green fluorescent protein (GFP), and intracellular localizations are subsequently identified by rapid fluorescence screening in vivo. In a model application of these methods to the fission yeast nucleus, we have identified several novel genes whose products are found in specific nuclear regions, including chromatin, the nucleolus, and the mitotic spindle, and sequence similarities between some of these genes and previously identified genes encoding nuclear proteins have validated the approach. These methods will be useful in identifying additional components of the S. pombe nucleus, and further extensions of this approach should also be applicable to a more comprehensive identification of the elements of intracellular architecture in fission yeast.

An equilibrium statistical model for the spreading phase of open-ocean convection

A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading phase of open-ocean convection. The theory depends only on bulk conserved quantities such as energy, circulation, and the range of values of potential vorticity in each layer. The simplest theory is formulated for a uniform cooling event over the entire basin that triggers a homogeneous random distribution of convective towers. For a small Rossby deformation radius typical for open-ocean convection sites, the most probable states that arise from this theory strongly resemble the saturated baroclinic states of the spreading phase of convection, with a stabilizing barotropic rim current and localized temperature anomaly.

Direct conversion of an oligopeptide from a β-sheet to an α-helix: A model for amyloid formation

A 16-amino acid oligopeptide forms a stable β-sheet structure in water. In physiological solutions it is able to self-assemble to form a macroscopic matrix that stains with Congo red. On raising the temperature of the aqueous solution above 70°C, an abrupt structural transition occurs in the CD spectra from a β-sheet to a stable α-helix without a detectable random-coil intermediate. With cooling, it retained the α-helical form and took several weeks at room temperature to partially return to the β-sheet form. Slow formation of the stable β-sheet structure thus shows kinetic irreversibility. Such a formation of very stable β-sheet structures is found in the amyloid of a number of neurological diseases. This oligopeptide could be a model system for studying the protein conformational changes that occurs in scrapie or Alzheimer disease. The abrupt and direct conversion from a β-sheet to an α-helix may also be found in other processes, such as protein folding and protein–protein interaction. Furthermore, such drastic structure changes may also be exploited in biomaterials designed as sensors to detect environmental changes.