Handedness of β-α-β motif Presented by Chen Zhang

Pre-word My original topic is about domain prediction I did a lot but it turned out not fruitful enough Just changed to this project in the morning Sorry that It would not be long It would not be comprehensive May have error.. New project Survey & explain β-α-β motif handedness Possible extension Survey & research on twist/chirality effects

Background of β-α-β motif (Prof. Li) This is called the β-α-β motif. Occurs in almost all proteins with parallel β sheets. Left: right-handed connection, via a right- handed α helix. All β-α-β motifs are connected this way. Right: Theoretically, left-handed connection is possible (below the plane). But never occur. No convincing argument explaining this. Possible project: survey and explain.

The Question Why right-handed for almost all β-α-β ? Intuition: Lower energy? Yes [2] Two principles have a dominating influence on how secondary structures associate. [1] Residues that become buried in the interior of a protein close-pack: they occupy a volume similar to that which they occupy in crystals of their amino acid (3, 4). Associated secondary structures retain a conformation close to the minimum free energy conformation of the isolated secondary structures.

How lower energy is got? What happens internally? Right handed twist of β sheet [3] Sheets themselves have lower free energy Twist affects structure, shows handedness preference Protein folding path way [4]

Right handed twist of β sheet [3] Why twist? A sheet with a right-hand twist when viewed along the polypeptide chain direction has a lower free energy than sheets which are straight or have a left-hand twist. We can best consider the conformation of β sheets by reference to the Ramachandran diagram.

Right handed twist has lower energy The free energy of an assembly, G, is related to enthalpy, H, and entropy, S, by the equation G = H - TS. The entropy is given by X = k In Ω, where Ω is the number of a priori equally probable macromolecular states of the assembly. All Φ, Ψ values within the normally allowed region of the Ramachandran plot in previous Figure represent equally probable macromolecular states. Therefore, polypeptide chains with a right-hand twist will have a greater entropy than those which have a left-hand twist or are straight.

Right handed twist has lower energy Thus, from theoretical calculation and empirical observation we can say that the absolute minimum energy (enthalpy) conformation for extended polypeptide chains occurs to the right of the line n = 2 and it will therefore have a right-hand twist. [3] This is mainly due to a left-hand twist of the polypeptide chain moving the carbonyl group too near to the residue side chains as shown in the following Figure.

Right handed twist of β sheet

Due to Right handed twist of β sheet If the unit had no right-handed preference, the probability of observing such a distribution by chance is very small. [2] How is the twisted β sheet influence the handedness of crossover connection?

Due to Right handed twist of β sheet As shown that a right-handed connection in the β x β unit allows a direct path for the chain to connect the strands In contrast, a left-handed one would require the chain to negotiate a more complex path to avoid steric interactions with the ends of the strands.

Protein folding path way Proteins fold through a series of intermediate states called a pathway. [11] The helix would tend to form at least as early in the folding process as the strands. there can be a smooth transition to a right-handed loop with the helix unwinding slightly at the ends. In this case, the preference for righthandedness depends on the righthandedness of the a-helix, combined with the fact that it is much more likely for the backbone to leave both ends of the helix in a fairly smooth continuous direction than for both ends to reverse sharply at that point. [4]

The shown folding path way folds in a one-step process of bringing together the two β strands. It is a two-step folding process in which first the intervening chain folds against one β strand, and then the second β strand folds down next to the first. A characteristic which enables the shown pathway to prejudice handedness is the condition that the ends of the folding section of chain are held approximately in place over very short time spans by the rest of the protein mass. Protein folding path way

Concluding Remark It may be that the nearly compulsory right- handedness of crossover-connection loops is a combined result of several contributing causes as we mentioned but not limited to, however, each of those happens to prejudice the result in the same direction.

Future work Do more extensive survey and try to find better explanations to the problem Do extended survey about twist/chirality Main issues that I try to find in the extended survey will be: Twist and handedness affect structure What other effects could they have? How to better consider them in prediction? …

Reference [1] Chothia et al., Structure of proteins: Packing of a-helices and pleated sheets [2] Sternburg et al., On the Conformation of Proteins: The Handedness of the β Strand-α Helix-β Strand Unit [3] Chothia, Conformation of Twisted β-pleated Sheets in Proteins [4] Richardson, Handedness of crossover connections in β sheets [5] Braun, Representation of Short and Long-range Handedness in Protein Structures by Signed Distance Maps [6] Scheeff et al., Fundamentals of protein structure. [7] Weatherford et al, Confirmations of twisted parallel β–sheets and the origin of chirality in protein structures. [8] Levitt, Structural patterns in globular proteins [9] Kuntz, An Approach to the Tertiary Structure of Globular Proteins [10] Efimov, Structural Trees for Protein Superfamilies [11] Bystroff et al., Modeling Protein Folding Pathways [12] Skolnick, A unified approach to the predictiion of protein structure and function