Initial Folding Research Articles

The role of chaperone proteins in the aryl hydrocarbon receptor core complex

The aryl hydrocarbon receptor (AhR) exists in the absence of a ligand as a tetrameric complex composed of a 95–105 kDa ligand binding subunit, a dimer of hsp90, and the immunophilin-like X-associated protein 2 (XAP2). XAP2 has a highly conserved carboxy terminal tetratricopeptide repeat domain that is required for both hsp90 and AhR binding. Hsp 90 appears to be involved in the initial folding of newly synthesized AhR, stabilization of ligand binding conformation of the receptor, and inhibition of constitutive dimerization with ARNT. XAP2 is capable of stabilizing the AhR, as well as enhancing cytoplasmic localization of the receptor. XAP2 binds to both the AhR and hsp90 in the receptor complex, and is capable of independently binding to both hsp90 and the AhR. However, the exact functional role for XAP2 in the AhR complex remains to be fully established.

Protein folding by a quasi-static-like process: a first-order state transition.

In this paper we report that quasi-static-like processes, in which stable intermediates were introduced carefully and deliberately, may be used to reversibly unfold and refold purified native porcine growth hormone. Through circular dichroism (CD) and dynamic light scattering (DLS), we were able to study the secondary structure conformational changes, tertiary structure thermal stabilities, and the particle size distributions of both the intermediates and the final folded product. The CD data showed that the secondary structure was restored in the initial folding stage, whereas the tertiary structure within the protein was restored one step before the last folding stage, as elucidated by thermal stability experiments. DLS analysis suggested that the average hydrodynamic radii of the folding intermediates shrunk to nativelike size immediately after the first folding stage. Our data suggested that the denaturant-containing protein folding reaction is a first-order-like state transition process. This quasi-static-like process may be useful in the prevention of aggregate formation in protein purification and thus can be used in protein engineering to improve the overall yield from harvesting proteins.

Large Amplitude Folding in Finely Layered Viscoelastic Rock Structures

We analyze folding phenomena in finely layered viscoelastic rock. Fine is meant in the sense that the thickness of each layer is considerably smaller than characteristic structural dimensions. For this purpose we derive constitutive relations and apply a computational simulation scheme (a finite-element based particle advection scheme; see MORESI et al., 2001) suitable for problems involving very large deformations of layered viscous and viscoelastic rocks. An algorithm for the time integration of the governing equations as well as details of the finite-element implementation is also given. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered plate. The domain is compressed along the layer axis by prescribing velocities along the sides. First, for the viscous limit we consider the response to a series of harmonic perturbations of the director orientation. The Fourier spectra of the initial folding velocity are compared for different viscosity ratios. Turning to the nonlinear regime we analyze viscoelastic folding histories up to 40% shortening. The effect of layering manifests itself in that appreciable buckling instabilities are obtained at much lower viscosity ratios (1:10) as is required for the buckling of isotropic plates (1:500). The wavelength induced by the initial harmonic perturbation of the director orientation seems to be persistent. In the section of the parameter space considered here elasticity seems to delay or inhibit the occurrence of a second, larger wavelength. Finally, in a linear instability analysis we undertake a brief excursion into the potential role of couple stresses on the folding process. The linear instability analysis also provides insight into the expected modes of deformation at the onset of instability, and the different regimes of behavior one might expect to observe.

Comparative anatomy of a regulatory ribosomal protein

Ribosomal protein L4 is a crucial folding mediator and an important architectural component of the large ribosomal subunit. Furthermore, Escherichia coli L4 produced in excess of its rRNA binding sites downregulates the transcription and translation of its own S10 operon, encoding 11 ribosomal proteins. Genetic experiments and the crystal structure of Thermotoga maritima L4 had implicated separable regions on L4 in ribosome association and expression control while RNA competition experiments and the regulatory capacity of heterologous L4 had suggested an overlap of the protein sequences involved in the two functions. We report herein that contrary to other foreign bacterial L4 proteins, L4 from T. maritima only weakly controlled expression of the S10 operon in E. coli. Also, wildtype T. maritima L4 was more weakly associated with E. coli ribosomes than with the E. coli analog. Rational mutageneses were performed to try to increase the regulatory competence of T. maritima L4. The ribosome incorporation of the mutant proteins was also investigated. Two different deletions removing T. maritima-specific sequences had little effects on regulation although one did improve ribosome association. Interestingly, a set of multiple mutations, which rendered the region around helices α4 and α5 in T. maritima L4 more E. coli-like, had no influence on the incorporation of the protein into the large ribosomal subunit but considerably improved its regulatory potential. Therefore, the area around helices α4 and α5, which is critical for the initial folding steps of the large subunit, is also a central element of autogenous control, presumably by contacting the S10 mRNA leader. Ribosome association is compounded at later stages of assembly by additional rRNA contacts through L4 areas which do not participate in regulation. Similarly, sequences outside the α4/α5 region aid expression control.

Metal injection molding: 3D modeling of nonisothermal filling

AbstractA three‐dimensional transient finite element flow analysis code that includes inertia and free surface modeling is used to predict uniform (axisymmetric) and nonuniform (nonaxisymmetric) filling patterns in a thick‐walled tool with a diaphragm gate. The simulation for a metal injection molding compound, which is strongly influenced by thermal effects, predicted several observed flow patterns: initial annular free surface flow (jetting), bypass and folding flow to form surface defects, and the transition from uniform (axisymmetric) flow to nonuniform (nonaxisymmetric flow) with increasing fill time and lower temperatures. Simulations of filling through a thicker diaphragm gate showed jetting and the associated problems were eliminated. Simulations also demonstrate the effects of filling time, mold temperature, inertia, yield stress, and wall slip on filling patterns, particularly the processing conditions that separate regions of uniform and nonuniform flow.

Protein unfolding: rigidity lost.

We relate the unfolding of a protein to its loss of structural stability or rigidity. Rigidity and flexibility are well defined concepts in mathematics and physics, with a body of theorems and algorithms that have been applied successfully to materials, allowing the constraints in a network to be related to its deformability. Here we simulate the weakening or dilution of the noncovalent bonds during protein unfolding, and identify the emergence of flexible regions as unfolding proceeds. The transition state is determined from the inflection point in the change in the number of independent bond-rotational degrees of freedom (floppy modes) of the protein as its mean atomic coordination decreases. The first derivative of the fraction of floppy modes as a function of mean coordination is similar to the fraction-folded curve for a protein as a function of denaturant concentration or temperature. The second derivative, a specific heat-like quantity, shows a peak around a mean coordination of <r> = 2.41 for the 26 diverse proteins we have studied. As the protein denatures, it loses rigidity at the transition state, proceeds to a state where just the initial folding core remains stable, then becomes entirely denatured or flexible. This universal behavior for proteins of diverse architecture, including monomers and oligomers, is analogous to the rigid to floppy phase transition in network glasses. This approach provides a unifying view of the phase transitions of proteins and glasses, and identifies the mean coordination as the relevant structural variable, or reaction coordinate, along the unfolding pathway.

The intestinal fatty acid binding protein: the role of turns in fast and slow folding processes.

The intestinal fatty acid binding protein is one of a family of proteins that are composed of two beta-sheets surrounding a large interior cavity into which the ligand binds. Glycine residues occur in many of the turns between adjacent antiparallel beta-strands. In previous work, the effect of replacing these glycine residues with valine has been examined with stopped flow instrumentation using intrinsic tryptophan fluorescence spectroscopy [Kim and Frieden (1998) Protein Sci. 7, 1821-1828]. To resolve the burst phase missing in the stopped flow measurements, these valine mutants have been reexamined with sub-millisecond continuous flow instrumentation. Some of the glycine residues have also been replaced with proline, and the folding reactions of these proline mutants have been compared with those of their valine counterparts. In all cases, the stability of the protein is decreased, but some turns appear to be more critical for final structure stabilization than others. Surprisingly, the rate constants observed for all the mutants measured by sub-millisecond continuous flow methods are quite similar (1400-3000 s(-1)), and in all the mutants, there is a shift in the fluorescence emission maximum from that of the unfolded protein to lower wavelengths, suggesting some collapse of the unfolded state within 200 micros. In contrast to the rate constants observed for the initial folding events measured by the sub-millisecond continuous flow method, the rate constants for the slower phase observed in the stopped flow instrument vary widely for the different mutants. The latter step appears to be related to side chain stabilization rather than secondary structure formation. It is also shown that the ligand binds tightly only to the native protein and not to any intermediate forms.

Early evolution of an extensional monocline by a propagating normal fault: 3D analysis from combined field study and numerical modeling

The Nopolo structure is located along the eastern margin of the Baja California peninsula and formed during the early stages (12–6 Ma) of development of the Gulf of California. The Nopolo structure is an ∼15-km-long series of two NW-striking, extensional monoclines produced by the upward propagation of normal faults. Where normal faults reach the surface, the footwall contains undisturbed, gently dipping strata, whereas the hanging wall is a highly deformed zone that contains fractured and faulted steep to subvertical strata. Long, narrow grabens with moderate to steep east-dipping strata are present in the hanging wall of the main normal faults. Initial monoclinal folding over blind normal faults produced a minimum of ∼300 m of structural relief. Once the faults propagated to the surface, they offset the monoclines ∼20–30 m before faulting ceased. We use an elastic dislocation model to invert fault geometry from bedding orientations around the Nopolo structure. The data are best matched by a listric normal fault that soles out at ∼5 km depth. The model suggests that the tip line of the fault was located ∼1 km below the surface prior to the breaching of the monocline. Because the offset along the main normal faults is minimal (∼20 m), the Nopolo structure is a unique example of an extensional faulted monocline and monocline system where faulting ended soon after the monoclines were breached and offset.

Refolding of β-lactoglobulin studied by stopped-flow circular dichroism at subzero temperatures

Refolding of bovine β-lactoglobulin was studied by stopped-flow circular dichroism at subzero temperatures. In ethylene glycol 45%–buffer 55% at −15°C, the isomerization rate from the kinetic intermediate rich in α-helix to the native state is approximately 300-fold slower than that at 4°C in the absence of ethylene glycol, whereas the initial folding is completed within the dead time of the stopped-flow apparatus (10 ms). At −28°C, we observed at least three phases; the fastest process, accompanied by an increase of α-helix content, is completed within the dead time of the stopped-flow apparatus (10 ms), the second phase, accompanied by an increase of α-helix content with the rate of 2 s −1, and the third phase, accompanied by a decrease of α-helix content. This last phase, corresponding to the isomerization process at −15°C described above, was so slow that we could not monitor any changes within 4 h. Based on the findings above, we propose that rapid α-helix formation and their concurrent collapse are common even in proteins rich in β-structure in their native forms.

Reversible interruption of Giardia lamblia cyst wall protein transport in a novel regulated secretory pathway

To survive in the environment and infect a new host, Giardia lamblia secretes an extracellular cyst wall using a poorly understood pathway. The two cyst wall proteins (CWPs) form disulphide-bonded heterodimers and are exported via novel encystation-specific secretory vesicles (ESVs). Exposure of eukaryotic cells to dithiothreitol (DTT) blocks the formation of disulphide bonds in nascent proteins that accumulate in the endoplasmic reticulum (ER) and induces an unfolded protein response (UPR). Proteins that have exited the ER are not susceptible. Exposure to DTT inhibits ESV formation by > 85%. Addition of DTT to encysting cells causes rapid (t1/2 < 10 min), reversible disappearance of ESVs, correlated with reduction of CWPs to monomers and reformation of CWP oligomers upon removal of DTT. Neither CWPs nor ESVs are affected by mercaptoethanesulphonic acid, a strong reducing agent that does not penetrate cells. DTT does not inhibit the overall protein secretory pathway, and recovery does not require new protein synthesis. We found evidence of protein disulphide isomerases in the ESV and the surface of encysting cells, in which they may catalyse initial CWP folding and recovery from DTT. This is the first suggestion of non-CWP proteins in ESVs and of enzymes on the giardial surface. DTT treatment did not stimulate a UPR, suggesting that Giardia may have diverged before the advent of this conserved form of ER quality control.

Molecular pathogenesis of a disease: structural consequences of aspartylglucosaminuria mutations.

A deficiency of functional aspartylglucosaminidase (AGA) causes a lysosomal storage disease, aspartylglucosaminuria (AGU). The recessively inherited disease is enriched in the Finnish population, where 98% of AGU alleles contain one founder mutation, AGU(Fin). Elsewhere in the world, we and others have described 18 different sporadic AGU mutations. Many of these are predicted to interfere with the complex intracellular maturation and processing of the AGA polypeptide. Proper initial folding of AGA in the endoplasmic reticulum (ER) is dependent on intramolecular disulfide bridge formation and dimerization of two precursor polypeptides. The subsequent activation of AGA occurs autocatalytically in the ER and the protein is transported via the Golgi to the lysosomal compartment using the mannose-6-phosphate receptor pathway. Here we use the three-dimensional structure of AGA to predict structural consequences of AGU mutations, including six novel mutations, and make an effort to characterize every known disease mutation by dissecting the effect of mutations on intracellular stability, maturation, transport and the activity of AGA. Most mutations are substitutions replacing the original amino acid with a bulkier residue. Mutations of the dimer interface prevent dimerization in the ER, whereas active site mutations not only destroy the activity but also affect maturation of the precursor. Depending on their effects on the AGA polypeptide the mutations can be categorized as mild, moderate or severe. These data contribute to the expanding body of knowledge pertaining to molecular pathogenesis of AGU.

Recent insights on RNA folding mechanisms from catalytic RNA.

Methods for probing RNA structure in real time have revealed that initial folding steps are complete in less than a second. Refolding of large catalytic RNAs in vitro often results in long-lived intermediates that reach the native structure very slowly. These kinetically trapped intermediates arise from alternative secondary structures that form early in the folding process. In cells, proteins modulate the outcome of RNA folding reactions by stabilizing specific conformations or by accelerating refolding of misfolded intermediates. At the same time, competition between metastable conformations provides a means for regulating the biological activity of transcripts.

A method for the improvement of threading-based protein models

A new method for the homology-based modeling of protein three-dimensional structures is proposed and evaluated. The alignment of a query sequence to a structural template produced by threading algorithms usually produces low-resolution molecular models. The proposed method attempts to improve these models. In the first stage, a high-coordination lattice approximation of the query protein fold is built by suitable tracking of the incomplete alignment of the structural template and connection of the alignment gaps. These initial lattice folds are very similar to the structures resulting from standard molecular modeling protocols. Then, a Monte Carlo simulated annealing procedure is used to refine the initial structure. The process is controlled by the model's internal force field and a set of loosely defined restraints that keep the lattice chain in the vicinity of the template conformation. The internal force field consists of several knowledge-based statistical potentials that are enhanced by a proper analysis of multiple sequence alignments. The template restraints are implemented such that the model chain can slide along the template structure or even ignore a substantial fraction of the initial alignment. The resulting lattice models are, in most cases, closer (sometimes much closer) to the target structure than the initial threading-based models. All atom models could easily be built from the lattice chains. The method is illustrated on 12 examples of target/template pairs whose initial threading alignments are of varying quality. Possible applications of the proposed method for use in protein function annotation are briefly discussed.

Folding dynamics of the B1 domain of protein G explored by ultrarapid mixing.

For many proteins, compact conformations are known to accumulate in advance of the rate-limiting step in folding. To understand the nature and significance of these early conformational events, we employed ultrarapid mixing methods to fully characterize the kinetics of folding of the 57-residue B1 domain of protein G. Continuous-flow fluorescence measurements exhibit a major exponential phase on the submillisecond time scale (600-700 micros), which is followed by a slower phase with a denaturant-dependent time constant (2-30 ms) observable by conventional stopped-flow measurements. The combined kinetic traces quantitatively account for the total change in Trp 43 fluorescence upon folding, including the previously unresolved 'burst phase' signal. The denaturant dependence of the two rate constants and their relative amplitudes are fully consistent with a three-state mechanism, U right harpoon over left harpoon I right harpoon over left harpoon N, where I is a productive intermediate with native-like fluorescence properties. The relatively slow rate and exponential time course of the initial folding phase indicates that a substantial free energy barrier is encountered during chain condensation, resulting in a partially organized ensemble of states distinct from the initial unfolded conformations.

Structures and mechanisms associated with development of a fold in the Cantabrian Zone thrust belt, NW Spain

A detailed history of progressive fold development based on mesostructural analysis is provided for a metre-scale fold in the Cantabrian fold and thrust belt of northwestern Spain. The well-exposed asymmetric syncline displays a wide variety of structures including extensional faults, thrusts, veins, tectonic stylolites, bedding plane faults, drag folds, and a main limb thrust that transects the entire fold. Important constraints on fold development are provided by the spatial distribution and style of deformation, angular relations, and cross-cutting relations among the structures. Fold mechanisms varied as a function of structural position; while the northwest limb was subjected to pure shear shortening in the form of contractional faults, the southeast limb was bent under tangential longitudinal strain, resulting in a combination of outer-arc extensional faulting in dolostones and simple shear along interbedded shales. Sequential development of the Bárzana fold consisted of; (i) initial flexural slip folding until the southeast limb attained a dip of 60°; (ii) a phase of pressure solution upon locking of bedding plane faults; (iii) shortening accommodated by bed-confined mesofaulting and the propagation of a limb thrust; (iv) unlocking of bedding plane faults and resumption of flexural slip; and (v) propagation of a new limb thrust due to offset of the main thrust by flexural slip. This study demonstrates that a number of very different mechanisms can operate during the course of fold development, and that folding processes and geometries are strongly dependent upon structural position, mechanical stratigraphy, and magnitude of tectonic shortening.

Studies of the Role of the Integrin EF-Hand, Ca2+-Binding Sites in Glycosylphosphatidylinositol-Specific Phospholipase D: Reduced Expression Following Mutagenesis of Residues Predicted to Bind Ca2+

Previous studies of glycosylphosphatidylinositol-specific phospholipase D (GPI-PLD) have demonstrated that GPI-PLD can bind Ca2+ions with high specificity (J.-Y. Li, K. Hollfelder, K.-S. Huang, and M. G. Low,J. Biol. Chem.269, 28063–28971, 1994). In this study the functional role of the bound Ca2+ions was evaluated. The enzymatic activity of purified GPI-PLD, which was depleted of divalent cations by pretreatment with EDTA, EGTA, or 1,10-phenanthroline, could be completely restored with Zn2+(and partially with Co2+), which indicates that Ca2+can be removed from the protein without affecting its enzymatic activity. This result suggested that Ca2+bound to GPI-PLD has a structural or regulatory role but is not required for GPI hydrolysis. To evaluate these possibilities we transfected COS cells with GPI-PLD mutants in which the predicted Ca2+-binding sites were either deleted completely or altered by single-residue substitution. All of the mutations showed substantial reductions in the amount of GPI-PLD secreted into the medium (0–6% of wild type). The data indicate that bound Ca2+plays an important role in the initial folding, intracellular transport, or secretion of GPI-PLD even though it has no discernible role in the mature, secreted protein.

The Cell Biology of the Prohormone Convertases PCI and PC2

Mature peptide hormones and neuropeptides are typically synthesized from much larger precursors and require several posttranslational processing steps--including proteolytic cleavage--for the formation of the bioactive species. The subtilisin-related proteolytic enzymes that accomplish neuroendocrine-specific cleavages are known as prohormone convertases 1 and 2 (PC1 and PC2). The cell biology of these proteases within the regulated secretory pathway of neuroendocrine cells is complex, and they are themselves initially synthesized as inactive precursor molecules. ProPC1 propeptide cleavage occurs rapidly in the endoplasmic reticulum, yet its major site of action on prohormones takes place later in the secretory pathway. PC1 undergoes an interesting carboxyl terminal processing event whose function appears to be to activate the enzyme. ProPC2, on the other hand, exhibits comparatively long initial folding times and exits the endoplasmic reticulum without propeptide cleavage, in association with the neuroendocrine-specific protein 7B2. Once the proPC2/7B2 complex arrives at the trans-Golgi network, 7B2 is internally cleaved into two domains, the 21-kDa fragment and a carboxy-terminal 31 residue peptide. PC2 propeptide removal occurs in the maturing secretory granule, most likely through autocatalysis, and 7B2 association does not appear to be directly required for this cleavage event. However, if proPC2 has not encountered 7B2 intracellularly, it cannot generate a catalytically active mature species. The molecular mechanism behind the intriguing intracellular association of 7B2 and proPC2 is still unknown, but may involve conformational rearrangement or stabilization of a proPC2 conformer mediated by a 36-residue internal segment of 21-kDa 7B2.

Refolding studies on the tetrameric loop deletion mutant RM6 of ROP protein.

Previous DSC and X-ray studies on RM6, a loop deletion mutant of wtROP protein, have shown that removal of five amino acids from the loop causes a dramatic reorganization of the wild-type structure. The new tetrameric molecule exhibits a significantly higher stability (Lassalle, M.W. et al., J. Mol. Biol., 1998, 279, 987-1000) and unfolds in a second order reaction (Lassalle, M.W. and Hinz, H.-J., Biochemistry, 1998, 37, 8465-8472). In the present investigation we report extensive refolding studies of RM6 at different temperatures and GdnHCl concentrations monitored by CD and fluorescence to probe for changes in secondary and tertiary structure, respectively. The measurements permitted us to determine activation parameters as a function of denaturant concentration. The results demonstrate convincingly that the variation with GdnHCl concentration of the activation parameters deltaH#, deltaS# and deltaG# is very similar for unfolding and refolding. For both processes the activation properties approach a maximum in the vicinity of the denaturant concentration, c(K=1), where the equilibrium constant equals 1, i.e. deltaG0 equals zero. CD and fluorescence refolding kinetics are described by identical constants suggesting that the formation of secondary and tertiary structure occurs simultaneously. Refolding is, however, characterized by a more complex mechanism than unfolding. Although the general pattern is dominated by the sequence monomers to dimers to tetramers, parallel side reactions involving dimers and monomers have to be envisaged in the initial folding phase, supporting the view that the native state of RM6 can be reached by several rather than a single pathway.

Hydrogen bonds in molecular assemblies of natural, synthetic and ‘designer’ peptides

The initial folding of the backbone of peptides and the subsequent arrangement of the molecules into a supramolecular assembly is primarily associated with NH⋯OC hydrogen bonds where the N⋯O distance is 2.8–3.0 Å and to a lesser extent with water molecules that act as donors and acceptors for hydrogen bonds, both within a peptide molecule and between peptide molecules. In helical peptides, the transition between 3 10-helices (with 10 atoms in a hydrogen-bond ring) and α-helices (with 13 atoms in a hydrogen bond ring) merely requires a shift from one CO to an adjacent CO and is often quite facile. Among examples to be presented are two crystal structures of a heptapeptide wherein the helices are the 3 10-type when the amino end group is Boc and the α-type when the amino end is Ac. A new type of regular helix was synthesized and characterized by x-ray diffraction analysis using β-amino acid residues, rather than α-amino acid residues. The new helix was named β-foldamer and it is characterized by 14-atom hydrogen-bond rings rather than the 13-atom rings present in α-helices. An NH group will not always form a hydrogen bond with any CO (or H 2O) that is present in a crystal. Examples are shown in which the N⋯O distance is > 3.30 A ̊ and also examples of structures in which there is no O acceptor or any other kind of acceptor within possible reach of an available NH. Assemblies with ‘free’ NH groups are presented in which there is no possibility for a ‘cooperative hydrogen bond’ between NH and the center of a phenyl group, although other structures with a close NH⋯phenyl approach will be discussed.

Evolution of three–dimensional folds for a non–Newtonian plate in a viscous medium

We derive analytical solutions for the three-dimensional time-dependent buckling of a non-Newtonian viscous plate in a less viscous medium. For the plate we assume a power-law rheology. The principal, axes of the stretching D-ij in the homogeneously deformed ground state are parallel and orthogonal to the bounding surfaces of the plate in the flat state. In the model formulation the action of the less viscous medium is replaced by equivalent reaction forces. The reaction forces are assumed to be parallel to the normal vector of the deformed plate surfaces. As a consequence, the buckling process is driven by the differences between the in-plane stresses and out of plane stress, and not by the in-plane stresses alone as assumed in previous models. The governing differential equation is essentially an orthotropic plate equation for rate dependent material, under biaxial pre-stress, supported by a viscous medium. The differential problem is solved by means of Fourier transformation and largest growth coefficients and corresponding wavenumbers are evaluated. We discuss in detail fold evolutions for isotropic in-plane stretching (D-11 = D-22), uniaxial plane straining (D-22 = 0) and in-plane flattening (D-11 = -2D(22)). Three-dimensional plots illustrate the stages of fold evolution for random initial perturbations or initial embryonic folds with axes non-parallel to the maximum compression axis. For all situations, one dominant set of folds develops normal to D-11, although the dominant wavelength differs from the Biot dominant wavelength except when the plate has a purely Newtonian viscosity. However, in the direction parallel to D-22, there exist infinitely many modes in the vicinity of the dominant wavelength which grow only marginally slower than the one corresponding to the dominant wavelength. This means that, except for very special initial conditions, the appearance of a three-dimensional fold will always be governed by at least two wavelengths. The wavelength in the direction parallel to D-11 is the dominant wavelength, and the wavelength(s) in the direction parallel to D-22 is determined essentially by the statistics of the initial state. A comparable sensitivity to the initial geometry does not exist in the classic two-dimensional folding models. In conformity with tradition we have applied Kirchhoff's hypothesis to constrain the cross-sectional rotations of the plate. We investigate the validity of this hypothesis within the framework of Reissner's plate theory. We also include a discussion of the effects of adding elasticity into the constitutive relations and show that there exist critical ratios of the relaxation times of the plate and the embedding medium for which two dominant wavelengths develop, one at ca. 2.5 of the classical Biot dominant wavelength and the other at ca. 0.45 of this wavelength. We propose that herein lies the origin of parasitic folds well known in natural examples.