The thermodynamics and statistical mechanics of protein folding

The physics of self-organization and complexity is manifested on a variety of biological scales, from large ecosystems to the molecular level. Protein molecules exhibit characteristics of complex systems in terms of their structure, dynamics, and function. Proteins have the extraordinary ability to fold to a specific functional three-dimensional shape, starting from a random coil, in a biologically relevant time. How they accomplish this is one of the secrets of life. In this work, theoretical research into understanding this remarkable behavior is discussed. Thermodynamic and statistical mechanical tools are used in order to investigate the protein folding dynamics and stability. Theoretical analyses of the results from computer simulation of the dynamics of a four-helix bundle show that the excluded volume entropic effects are very important in protein dynamics and crucial for protein stability. The dramatic effects of changing the size of sidechains imply that a strategic placement of amino acid residues with a particular size may be an important consideration in protein engineering. Another investigation deals with modeling protein structural transitions as a phase transition. Using finite size scaling theory, the nature of unfolding transition of a four-helix bundle protein was investigated and critical exponents for the transition were calculated for various hydrophobic strengths in the core. It is found that the order of the transition changes from first to higher order as the strength of the hydrophobic interaction in the core region is significantly increased. Finally, a detailed kinetic and thermodynamic analysis was carried out in a model two-helix bundle. The connection between the structural free-energy landscape and folding kinetics was quantified. I show how simple protein engineering, by changing the hydropathy of a small number of amino acids, can enhance protein folding by significantly changing the free energy landscape so that kinetic traps are removed. The results have general applicability in protein engineering as well as understanding the underlying physical mechanisms of protein folding. ^

Quantifying protein folding pathways

A deep understanding of the proteins folding dynamics can be get quantifying folding landscape by calculating how the number of microscopic configurations (entropy) varies with the energy of the chain, Ω=Ω(E). Because of the incredibly large number of microstates available to a protein, direct enumeration of Ω(E) is not possible on realistic computer simulations. An estimate of Ω(E) can be obtained by use of a combination of statistical mechanics and thermodynamics. By combining different definitions of entropy that are valid for a system whose probability for occupying a state is given by the canonical Boltzmann probability, computers allow the determination of Ω(E). ^ The energy landscapes of two similar, but not identical model proteins were studied. One protein contains no kinetic tracks. Results show a smooth funnel for the folding landscape. That allows the contour determination of the folding funnel. Also it was presented results for the folding landscape for a modified protein with kinetic traps. Final results show that the computational approach is able to distinguish and explore regions of the folding landscape that are due to kinetic traps from the native state folding funnel.^

Synthesis of aromatic monothiols and aromatic dithiols to increase the folding rate and yield of disulfide containing proteins

Most pharmaceutically relevant proteins and many extracellular proteins contain disulfide bonds. Formation of the correct disulfide bonds is essential for stability in almost all cases. Disulfide containing proteins can be rapidly and inexpensively overexpressed in bacteria. However, the overexpressed proteins usually form aggregates inside the bacteria, called inclusion bodies, which contains inactive and non-native protein. To obtain native protein, inclusion bodies need to be isolated and resolubilized, and then the resulting protein refolded in vitro. In vitro protein folding is aided by the addition of a redox buffer, which is composed of a small molecule disulfide and/or a small molecule thiol. The most commonly used redox buffer contains reduced and oxidized glutathione. Recently, aliphatic dithiols and aromatic monothiols have been employed as redox buffers. Aliphatic dithiols improved the yield of native protein as compared to the aliphatic thiol, glutathione. Dithiols mimic the in vivo protein folding catalyst, protein disulfide isomerase, which has two thiols per active site. Furthermore, aromatic monothiols increased the folding rate and yield of lysozyme and RNase A relative to glutathione. By combining the beneficial properties of aliphatic dithiols and aromatic monothiols, aromatic dithiols were designed and were expected to increase in vitro protein folding rates and yields. Aromatic monothiols (1-4) and their corresponding disulfides (5-8), two series of ortho- and para-substituted ethylene glycol dithiols (9-15), and a series of aromatic quaternary ammonium salt dithiols (16-17) were synthesized on a multigram scale. Monothiols and disulfides (1-8) were utilized to fold lysozyme and bovine pancreatic trypsin inhibitor. Dithiols (11-17) were tested for their ability to fold lysozyme. At pH 7.0 and pH 8.0, and high protein concentration (1 mg/mL), aromatic dithiols (16, 17) and a monothiol (3) significantly enhanced the in vitro folding rate and yield of lysozyme relative to the aliphatic thiol, glutathione. Additionally, aromatic dithiols (16, 17) significantly enhance the folding yield as compared to the corresponding aromatic monothiol (3). Thus, the folding rate and yield enhancements achieved in in vitro protein folding at high protein concentration will decrease the volume of renaturation solution required for large scale processes and consequently reduce processing time and cost.

Synthesis of aromatic monothiols to increase the folding rate and yields of disulfide-containing proteins

Almost all pharmaceutically relevant proteins and many extracellular proteins contain disulfide bonds, which are essential for protein functions. In many cases, disulfidecontaining proteins are produced via in vitro protein folding that involves the oxidation of reduced protein to native protein, a complex process. The in vitro folding of reduced lysozyme has been extensively studied as a model system because native lysozyme is small, inexpensive, and has only four disulfide bonds. The folding of reduced lysozyme is conducted with the aid of a redox buffer consisting of a small molecule disulfide and a small molecule thiol, such as oxidized and reduced glutathione. Herein, in vitro folding rates and yields of lysozyme obtained in the presence of a series of aromatic thiols and oxidized glutathione are compared to those obtained with reduced and oxidized glutathione. Results showed that aromatic thiols significantly increase the folding rate of lysozyme compared to glutathione.

On-screen pre-deblurring of digital images using the wavefront aberration function of the human eye to improve computer access for the visually impaired

Traditional Optics has provided ways to compensate some common visual limitations (up to second order visual impairments) through spectacles or contact lenses. Recent developments in wavefront science make it possible to obtain an accurate model of the Point Spread Function (PSF) of the human eye. Through what is known as the "Wavefront Aberration Function" of the human eye, exact knowledge of the optical aberration of the human eye is possible, allowing a mathematical model of the PSF to be obtained. This model could be used to pre-compensate (inverse-filter) the images displayed on computer screens in order to counter the distortion in the user's eye. This project takes advantage of the fact that the wavefront aberration function, commonly expressed as a Zernike polynomial, can be generated from the ophthalmic prescription used to fit spectacles to a person. This allows the pre-compensation, or onscreen deblurring, to be done for various visual impairments, up to second order (commonly known as myopia, hyperopia, or astigmatism). The technique proposed towards that goal and results obtained using a lens, for which the PSF is known, that is introduced into the visual path of subjects without visual impairment will be presented. In addition to substituting the effect of spectacles or contact lenses in correcting the loworder visual limitations of the viewer, the significance of this approach is that it has the potential to address higher-order abnormalities in the eye, currently not correctable by simple means.