Self-folding robot is usually modeled as rigid origami, a class of origami whose entire surface remains rigid during folding except at crease lines. In this work, we focus on finding valid folding motion that brings the origami from the unfolded state continuously to the folded state. Although recent computational methods allow rapid simulation of folding process of certain rigid origamis, thes...

Protein molecules adopt a specific global 3D structure in order to carry out their biological function. To achieve this native state a newly formed protein molecule has to fold. The folding process and the final fold are both determined by the sequence of amino acids making up the protein chain. It is not currently possible to predict the conformation of the native state from the amino acid seq...

A change in the perception of the protein folding problem has taken place recently. The nature of the change is outlined and the reasons for it are presented. An essential element is the recognition that a bias toward the native state over much of the effective energy surface may govern the folding process. This has replaced the random search paradigm of Levinthal and suggests that there are ma...

Many protein systems fold in a two-state manner. Random models, however, rarely display two-state kinetics and thus such behavior should not be accepted as a default. While theories for the prevalence of two-state kinetics have been presented, none sufficiently explain the breadth of experimental observations. A model, making minimal assumptions, is introduced that suggests two-state behavior i...

The role of local interactions in protein folding has recently been the subject of some controversy. Here we investigate an extension of Zwanzig’s simple and general model of folding in which local and nonlocal interactions are represented by functions of single and multiple conformational degrees of freedom, respectively. The kinetics and thermodynamics of folding are studied for a series of e...

We investigated the impact of hydrodynamic interactions (HI) on protein folding using a coarse-grained model. The extent of the impact of hydrodynamic interactions, whether it accelerates, retards, or has no effect on protein folding, has been controversial. Together with a theoretical framework of the energy landscape theory (ELT) for protein folding that describes the dynamics of the collecti...

The protein folding is regarded as a quantum transition between torsion states on polypeptide chain. The deduction of the folding rate formula in our previous studies is reviewed. The rate formula is generalized to the case of frequency variation in folding. Then the following problems about the application of the rate theory are discussed: 1) The unified theory on the two-state and multi-state...

The extracellular bacterial protease, alpha-lytic protease (alphaLP), is synthesized with a large, two-domain pro region (Pro) that catalyzes the folding of the protease to its native conformation. In the absence of its Pro folding catalyst, alphaLP encounters a very large folding barrier (DeltaG = 30 kcal mol(-1)) that effectively prevents the protease from folding (t(1/2) of folding = 1800 ye...

The impact of folding funnels and folding simulations on the way experimentalists interpret results is examined. The image of the transition state has changed from a unique species that has a strained configuration, with a correspondingly high free energy, to a more ordinary folding intermediate, whose balance between limited conformational entropy and stabilizing contacts places it at the top ...

Our recent experiments on the molten globule state and other protein folding intermediates lead to following conclusions: (i) the molten globule is separated by intramolecular first-order phase transitions from the native and unfolded states and therefore is a specific thermodynamic state of protein molecules; (ii) the novel equilibrium folding intermediate (the 'pre-molten globule' state) exis...