What determines fold?

In general, the amino-acid sequence of a protein determines the 3D shape of a protein [Anfinsen et al., 1950s]

• there are some exceptions • all proteins can be denatured • some molecules have multiple conformations • some proteins get folding help from chaperons • prions can change the conformation of other

proteins

β hairpin

β corners / α hairpins / α-α corner >2

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Helix-turn-helix

β−α−β

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What Determines Fold? What physical properties of the protein determine its fold?

• rigidity of backbone • interactions among amino acids, including • electrostatic interactions • van der Waals forces • volume constraint • hydrogen, disulfide bonds • interactions of amino acids with water

Protein Folding

• Linear proteins rapidly fold into predefined 3D structures

• The properties of any protein is largely determined by its structure

• Proteins can be denatured by heat or chemical agents, but then fold back to their original shape

Folding – Why is it so hard? Protein structures can be experimentally determined (X-Rays or NMR) but this is not always feasible procedure. The folded structure of a sequence is determined by the sequence of successive solid bend angles, where each solid angle can be represented by two planar angles. Such a problem can be made discrete (at some loss of accuracy) by limiting the number of ways to bend each joint.

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Folding - The Leventhal's Paradox 3100 = 5 × 1047 conformations Fastest motions 10- 15 sec so sampling all conformations would take 5 × 1032 sec 60 × 60 × 24 × 365 = 31536000 = 3.1536 x 107

seconds in a year Sampling all conformations will take 1.6 × 1025

years, much longer than the age of the universe Folding - The Leventhal's Paradox Leventhal's paradox is that proteins correctly fold into their pre-ordained shape less than a minute after being synthesized. How does nature solve this NP-complete problem? Possible reasons around this problem are 1. theoretical models used to prove folding are not what

nature is trying to optimize 2. evolution may have selected for proteins which fold easily 3. proteins may well fold in locally, not globally optimal ways

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Protein states How do we describe the state of a protein? What do we even mean with this term? For an atom or molecule we can define the state of the system

Do we need concepts like “glassy states”, “conformational sub-states” and “molten globule”? What do they mean, and are these concepts important for the functioning of proteins (especially enzymes)?

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What is the conformational coordinate? Multidimensional set of coordinates. What are the basic ideas behind such concepts, and why do we even want to bring in such descriptions? We have seen that the proteins have very definite structures. These structures result mostly from x-ray diffraction studies, and in general they give the impression that the proteins exist in “one” static state that is unique.

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We have seen very beautiful pictures in earlier lectures, which have given us insight into the way which proteins fold. From these structures we are even able to rationalize the physical interactions and forces that contribute to the folded structure of the different proteins. We can see how the secondary units, such as the α-helices, the β-sheets and the coil-turns combine to allow the folding of the polypeptides into unique structural units, and then eventually into molecular machines. This type of reasoning using static structures often leads to conclusions that even fractions of Angstroms may be important for the correct functioning of particular enzymes. However, there is evidence indicating that some proteins retain a fair amount of residual flexibility in their native folded states. Example: how oxygen get to the heme in of myoglobin? They may occupy more than just a tiny, limited region around some unique static conformation within their conformational space; they may occupy a significantly larger

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portion of their allowed conformational space, leading to a large number of “conformational substates”. How do we quantify this, and even more importantly, how do we measure such a thing?

Folding

When we talk about “folding” what do we mean? How can we unfold a structure? We can “unfold” a structure by heating it. Or, sometimes the protein unfolds when we cool it. This latter phenomenon apparently happens even though the entropy decreases when hydrophobic groups come into contact with water. Reasoning: As the temperature is lowered the entropy change accompanying the unfolding of the protein becomes less important; therefore, it is not so unfavorable for non-polar groups to break away from the “oily” regions of the structure into the aqueous solvent. Other ways of unfolding are: changing the pH of the solution, adding co-solvents which change the water structure (such as urea and guanidium hydrochloride, changing the hydrostatic pressure. These are quasi-universal mechanisms. So, by “folding” we mean taking the protein from some unfolded state (maybe partially unfolded), and making it fold into a state that is closer to its natural structure.

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Reference aside: The field of Protein Folding, which is essentially what we are now discussing, is very active and very diverse field, with not only many different views, but also many different enthusiastic proponents of different points of view. We cannot possibly even review the field. There are a few recent excellent textbooks that I recommend that you browse through. There are also many reviews that I will list sometime during the semester on the web. 1) “Proteins: Structures and Molecular Properties”, Thomas E. Creighton, second edition, Freeman & Co., 1993. This book covers many of the basic aspects of proteins, from their assembly with the amino acids, through their spectroscopic, functional, structural and dynamic properties. It is very

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thorough, with many references. The information presented is very useful. He discussed practical techniques, as well as theoretical aspects. 2) “Protein Folding”, Thomas Creighton, Ed., Freeman & Co., 1992. This is quite an authoritative account of these topics. It is not difficult to read, and mostly descriptive, but well done. 3) “Recent Developments in Theoretical Studies of Proteins”, Ron Elber, ed., Advanced Series in Physical Chemistry, Vol. 7, World Scientific, 1996. This is an interesting book dealing with modeling and theoretical studies of biological molecules. The topics are selected, but the discussions go into depth in many respects, and not just cursory descriptions. 4) “Spin Glasses and Biology”, Directions in Condensed Matter Physics, Vol. 6, Daniel L. Stein, 1992. This book deals not only with protein folding, but shows some uses of the concepts in spin glasses in biology. 5) “Physical Approaches to Biological Evolution”, Mikhail V. Volkenstein, Springer Verlag, 1994. This in an interesting account of molecular evolution but has chapters dealing with interesting aspects of the structure and dynamics of proteins, with references.

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Let’s start by looking at some average dimensions and shapes of proteins: In the “old days” much time was spent on determining the overall shapes, using light scattering, ultra-centrifugation, neutron diffraction and measurements of diffusion and viscosity. Explaining the technical aspects of these experiments, and describing how to interpret the results, actually took up a good deal of time in earlier courses in Biophysics, or Biophysical Chemistry. These measurements are still important, but they no longer play such an important role because we often have sequence information, and x-ray or NMR data. For instance, we are not really going to cover any details of any of these techniques, and we will not spend time on discussing the overall rough shapes of proteins. E.g.: D=kT/ftrans, f=6πηR;

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Shapes: These molecular shapes are also consistent with the view “nonpolar side-groups inside and polar side groups outside” (the oil drop idea). No doubt, within certain limits, this idea is correct. We find many non-polar groups inside of the protein structures, and most of the polar side groups are in contact with the solvent. Note: no chemical structures. Crystal structures: Static? A very important fact to keep in mind, is that the molecular structures that we can “download” from the protein data banks, are determined from crystals that have anywhere from 30% to 50% water by “weight”. So, these crystals are NOT dry. They contain quite a number of solvent molecules. Charged groups 15-30 per group Polar 2-3 per group Non-polar 10-20 per group In accord with this, it is found that the structures determined in crystals are often quite consistent with structural information gained from a variety of “solution” techniques, such as NMR, circular dichroism and fluorescence. This is undoubtedly because there are so many solvent molecules associated with the crystals, so that the forces on the different parts of the proteins are not so much different from what is found in solution.

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Stereo view of the NMR determine structure of DS111M in solution

If the x-ray structures are even close to the solution structures, this also means that the structures of most proteins in solution - when they exist as independent separate molecules - are not random by any means, but seem to exist in fairly well defined shapes and configurations. So, no matter what we think the importance of conformational distributions and dynamics are, if the x-ray structural information is available, we always take these structures into account.

Representation of the conformations of DS111M in solution

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We also have to keep in mind that a very large number of small interactions contribute to the stability and uniqueness of the different protein structures. Each one of these individual intermolecular interactions would not be particularly stable. And yet, in most cases, the associations of the different monomeric residues in most folded proteins are quite specific. The “lock-and-key” concept was originally proposed with static structures in mind, and the lock-and-key concept has been very productive. This seems compatible with the crystal structures. Enzymes

Enzymes are organic catalysts made of proteins. They speed up reactions inside an organism. The molecule which an enzyme catalyzes is called a substrate. Enzymes can only act on the substrate that they were designed for. This is again because of protein shape. If the substrate molecule's shape matches the enzyme's active site, it undergoes the reaction specified. This is called the lock-and-key theory of enzyme action.

Enzymes can either break or put together substrates. And they can enhance the rate of reactions to over half-a-million reactions per second. Because of the lock-and-key theory, enzymes must retain their shape to keep their function. If the temperature is too high, the enzyme will change its shape,

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becoming almost like a random mass of coils, in a process called denaturation, and thus losing its function. Some dangerous poisons work by deactivating enzymes by changing their shapes. There is still quite a bit of librational motion in crystals of proteins. The amount of movement depends on where the residues sit in the protein structure. This can be measured, and it is now possible to make picosecond and nanosecond time-resolved measurements on crystal structures using Synchrotron beams.

Debye-Waller factors determined by x-ray.

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