Modeling amyloid fibril formation: a free-energy approach.

Amyloid fibrils are structures consisting of many proteins with a well-defined conformation. The formation of these fibrils has been the subject of intense research, largely due to their connection to several diseases. We focus here on the computational studies and discuss these from a free-energy point of view.

Concentration dependence of alpha-synuclein fibril length assessed by quantitative atomic force microscopy and statistical-mechanical theory.

The initial concentration of monomeric amyloidogenic proteins is a crucial factor in the in vitro formation of amyloid fibrils. We use quantitative atomic force microscopy to study the effect of the initial concentration of human alpha-synuclein on the mean length of mature alpha-synuclein fibrils, which are associated with Parkinson's disease. We determine that the critical initial concentration, below which low-molecular-weight species dominate and above which fibrils are the dominant species, lies at approximately 15 muM, in good agreement with earlier measurements using biochemical methods.

The formation of fibrils by intertwining of filaments: model and application to amyloid Abeta protein.

We outline a model that describes the interaction of rods that form intertwined bundles. In this simple model, we compare the elastic energy penalty that arises due to the deformation of the rods to the gain in binding energy upon intertwining. We find that, for proper values of the bending Young's modulus and the binding energy, a helical pitch may be found for which the energy of intertwining is most favorable.

Amplification of chirality in benzene tricarboxamide helical supramolecular polymers.

The chirality of benzene tricarboxamides is expressed and amplified into the helicity of self-assembled columnar aggregates according to 'sergeants and soldiers' and 'majority rules' principles; the strength of the amplification is analysed quantitatively and the effect of the number of chiral groups in the sergeants is studied.

A statistical-mechanical theory of fibril formation in dilute protein solutions.

We outline a theoretical treatment that describes fibril formation in dilute protein solutions. For this, we combine a theory describing self-assembly and conformational transition with a description of the lateral association of linear chains. Our statistical-mechanical model is able to predict the mean degree of polymerization and the length of the fibrils and their precursors, as well as the weight fractions of the different aggregated species in solution.

Amplification of chirality of the majority-rules type in helical supramolecular polymers: the impact of the presence of achiral monomers.

We present a theoretical treatment describing the conformational state of helical supramolecular polymers that consist of three types of monomer: right-handed and left-handed chiral monomers and achiral ones. We find that chirality amplification of the majority-rules type, that is, a disproportionately large shift in the helix screw sense due to a small enantiomeric excess, can occur in these polymers. The strength of the chirality amplification depends on the free-energy penalty of a helix reversal along the self-assembled chain and on that of a mismatch between the conformation of a bond and the preferred conformation of the preceding monomer.

Impact of steric interactions on the helical transition in assemblies of discotic molecules.

We investigate theoretically the effect of excluded-volume interactions on the helical configurational transition of supramolecular assemblies in solutions of chiral disklike molecules. To this end, we set up a second-virial theory within the context of the helical self-assembly of rodlike objects. We find that interaggregate interactions shift both the helical-transition point and the sharpness of the transition.

"Majority-rules" operative in chiral columnar stacks of C3-symmetrical molecules.

C(3)-symmetrical disks 1, preorganized by acylated 2,2'-bipyridine-3,3'-diamine moieties and decorated with nine identical chiral, lipophilic tails, aggregate into a dynamic helix in apolar solvents. The aggregates, previously shown to be governed by the "sergeants-and-soldiers" principle when mixed with achiral analogues, are now also revealed to obey the "majority-rules" effect, a phenomenon not earlier observed in nonpolymers. Our experimental circular dichroism data can be accurately described with a recently developed theory.

Amplification of chirality in helical supramolecular polymers beyond the long-chain limit.

The optical activity of helical homopolymers devoid of chiral centers increases drastically when a small amount of homochiral monomers is incorporated into them. We study this so-called sergeants-and-soldiers effect of chirality amplification in solutions of helical supramolecular polymers with a theoretical model that bears a strong resemblance to a one-dimensional, two-component Ising model. In the limit of very long self-assembled helical polymers, the strength of the sergeants-and-soldiers effect depends strongly on the free energy of a helix reversal and less so on the concentration of aggregating material.