Basic principles for costing and accounting for folding paper box manufacturers

https://egrove.olemiss.edu/aicpa_guides/2415/thumbnail.jp

Evolutionary Dynamics and Optimization: Neutral Networks as Model-Landscapes for RNA Secondary-Structure Folding-Landscapes

We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure $s$). By interpreting the secondary structure as biological information we can formulate the so called Error Threshold of Shapes as an extension of Eigen's et al. concept of an error threshold in the single peak landscape. Analogue to the approach of Derrida & Peliti for a of the population on the neutral network. On the one hand this model of a single shape landscape allows the derivation of analytical results, on the other hand the concept gives rise to study various scenarios by means of simulations, e.g. the interaction of two different networks. It turns out that the intersection of two sets of compatible sequences (with respect to the pair of secondary structures) plays a key role in the search for ''fitter'' secondary structures.Comment: 20 pages, uuencoded compressed postscript-file, Proc. of ECAL '95 conference, to appear., email: chris @ imb-jena.d

Bacterial Hsp70 resolves misfolded states and accelerates productive folding of a multi-domain protein

The ATP-dependent Hsp70 chaperones (DnaK in E. coli) mediate protein folding in cooperation with J proteins and nucleotide exchange factors (E. coli DnaJ and GrpE, respectively). The Hsp70 system prevents protein aggregation and increases folding yields. Whether it also enhances the rate of folding remains unclear. Here we show that DnaK/DnaJ/GrpE accelerate the folding of the multi-domain protein firefly luciferase (FLuc) 20-fold over the rate of spontaneous folding measured in the absence of aggregation. Analysis by single-pair FRET and hydrogen/deuterium exchange identified inter-domain misfolding as the cause of slow folding. DnaK binding expands the misfolded region and thereby resolves the kinetically-trapped intermediates, with folding occurring upon GrpE-mediated release. In each round of release DnaK commits a fraction of FLuc to fast folding, circumventing misfolding. We suggest that by resolving misfolding and accelerating productive folding, the bacterial Hsp70 system can maintain proteins in their native states under otherwise denaturing stress conditions. The Hsp70 system prevents protein aggregation and increases folding yields, but it is unknown whether it also enhances the rate of folding. Here the authors combine refolding assays, FRET and hydrogen/deuterium exchange-mass spectrometry measurements to study the folding of firefly luciferase and find that the bacterial Hsp70 actively promotes the folding of this multi-domain protein

Cooperativity and the origins of rapid, single-exponential kinetics in protein folding

The folding of naturally occurring, single domain proteins is usually well-described as a simple, single exponential process lacking significant trapped states. Here we further explore the hypothesis that the smooth energy landscape this implies, and the rapid kinetics it engenders, arises due to the extraordinary thermodynamic cooperativity of protein folding. Studying Miyazawa-Jernigan lattice polymers we find that, even under conditions where the folding energy landscape is relatively optimized (designed sequences folding at their temperature of maximum folding rate), the folding of protein-like heteropolymers is accelerated when their thermodynamic cooperativity enhanced by enhancing the non-additivity of their energy potentials. At lower temperatures, where kinetic traps presumably play a more significant role in defining folding rates, we observe still greater cooperativity-induced acceleration. Consistent with these observations, we find that the folding kinetics of our computational models more closely approximate single-exponential behavior as their cooperativity approaches optimal levels. These observations suggest that the rapid folding of naturally occurring proteins is, at least in part, consequences of their remarkably cooperative folding

Pathways to folding, nucleation events and native geometry

We perform extensive Monte Carlo simulations of a lattice model and the Go potential to investigate the existence of folding pathways at the level of contact cluster formation for two native structures with markedly different geometries. Our analysis of folding pathways revealed a common underlying folding mechanism, based on nucleation phenomena, for both protein models. However, folding to the more complex geometry (i.e. that with more non-local contacts) is driven by a folding nucleus whose geometric traits more closely resemble those of the native fold. For this geometry folding is clearly a more cooperative process.Comment: Accepted in J. Chem. Phy

Encoding folding paths of RNA switches

RNA co-transcriptional folding has long been suspected to play an active role in helping proper native folding of ribozymes and structured regulatory motifs in mRNA untranslated regions. Yet, the underlying mechanisms and coding requirements for efficient co-transcriptional folding remain unclear. Traditional approaches have intrinsic limitations to dissect RNA folding paths, as they rely on sequence mutations or circular permutations that typically perturb both RNA folding paths and equilibrium structures. Here, we show that exploiting sequence symmetries instead of mutations can circumvent this problem by essentially decoupling folding paths from equilibrium structures of designed RNA sequences. Using bistable RNA switches with symmetrical helices conserved under sequence reversal, we demonstrate experimentally that native and transiently formed helices can guide efficient co-transcriptional folding into either long-lived structure of these RNA switches. Their folding path is controlled by the order of helix nucleations and subsequent exchanges during transcription, and may also be redirected by transient antisense interactions. Hence, transient intra- and intermolecular base pair interactions can effectively regulate the folding of nascent RNA molecules into different native structures, provided limited coding requirements, as discussed from an information theory perspective. This constitutive coupling between RNA synthesis and RNA folding regulation may have enabled the early emergence of autonomous RNA-based regulation networks.Comment: 9 pages, 6 figure

Folding of a single domain protein entering the endoplasmic reticulum precedes disulfide formation

The relationship between protein synthesis, folding and disulfide formation within the endoplasmic reticulum (ER) is poorly understood. Previous studies have suggested pre-existing disulfide links are absolutely required to allow protein folding and, conversely, that protein folding occurs prior to disulfide formation. To address the question of what happens first within the ER; that is, protein folding or disulfide formation, we studied folding events at the early stages of polypeptide chain translocation into the mammalian ER using stalled translation intermediates. Our results demonstrate that polypeptide folding can occur without complete domain translocation. Protein disulfide isomerase (PDI) interacts with these early intermediates, but disulfide formation does not occur unless the entire sequence of the protein domain is translocated. This is the first evidence that folding of the polypeptide chain precedes disulfide formation within a cellular context and highlights key differences between protein folding in the ER and refolding of purified proteins

Protein Photo-folding and Quantum Folding Theory

The rates of protein folding with photon absorption or emission and the cross section of photon -protein inelastic scattering are calculated from the quantum folding theory by use of standard field-theoretical method. All these protein photo-folding processes are compared with common protein folding without interaction of photons (nonradiative folding). It is demonstrated that there exists a common factor (thermo-averaged overlap integral of vibration wave function, TAOI) for protein folding and protein photo-folding. Based on this finding it is predicted that: 1) the stimulated photo-folding rates show the same temperature dependence as protein folding; 2) the spectral line of electronic transition is broadened to a band which includes abundant vibration spectrum without and with conformational transition and the width of the vibration spectral line is largely reduced; 3) the resonance fluorescence cross section changes with temperature obeying the same law (Luo-Lu's law). The particular form of the folding rate - temperature relation and the abundant spectral structure imply the existence of a set of quantum oscillators in the transition process and these oscillators are mainly of torsion type of low frequency, imply the quantum tunneling between protein conformations does exist in folding and photo-folding processes and the tunneling is rooted deeply in the coherent motion of the conformational-electronic system.Comment: 17 pages, 1 figur