Protein folding and structure

Reading

Dobson CM. Experimental investigation of protein folding and misfolding.

Methods. 2004 Sep;34(1):4-14. Review.

Dobson CM. Protein folding and misfolding.

Nature. 2003 Dec 18;426(6968):884-90. Review.

Lindorff-Larsen K, Best RB, Depristo MA, Dobson CM, Vendruscolo M. Simultaneous determination of protein structure and dynamics. Nature. 2005 Jan 13;433(7022):128-32.

Lindorff-Larsen K, Vendruscolo M, Paci E, Dobson CM. Transition states for protein folding have native topologies despite high structural variability.Nat Struct Mol Biol. 2004 May;11(5):443-9.

Dedmon MM, Lindorff-Larsen K, Christodoulou J, Vendruscolo M, Dobson CM. Mapping long-range interactions in alpha-synuclein using spin-label NMR and ensemble molecular dynamics simulations.

J Am Chem Soc. 2005 Jan 19;127(2):476-7.

Klein-Seetharaman J, Oikawa M, Grimshaw SB, Wirmer J, Duchardt E, Ueda T, Imoto T, Smith LJ, Dobson CM, Schwalbe H. Long-range interactions within a nonnative protein.

Science. 2002 Mar 1;295(5560):1719-22.

Chan HS, Dill KA. Protein folding in the landscape perspective: chevron plots and non-Arrhenius kinetics.

Proteins. 1998 Jan;30(1):2-33. Review.

Schonbrun J, Dill KA. Fast protein folding kinetics.

Proc Natl Acad Sci U S A. 2003 Oct 28;100(22):12678-82.

Liwo A, Khalili M, Scheraga HA Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains.

Proc Natl Acad Sci U S A. 2005

Questions

  1. Explain
  2. Native state, unfolded state, denatured state, metastable state, denaturation, renaturation
  3. Why has a folded protein lower free energy G in spite of unfavorable conformational entropyS.
  4. Levinthal paradox
  5. -value analysis
  6. contact order and folding rate
  7. Chevron-plot
  8. Transition state ensemble
  9. Free energy funnel of folding
  10. Chaperones
  11. Difference between a prion disease and amyloid disease
  12. Thermodynamic and kinetic hypothesis of protein folding
  13. Why it is difficult to observe directly transition state
  1. What experimental techniques there are to study protein folding?
  2. Real time methods, (H-D exchange using stop-flow techniques)
  3. Steady-state, denaturant, chemical modification
  1. Folding can be described as transition between the native and unfolded state. In increasing concentrations of denaturant, a fold disintegrates with a rate

when the concentration of denaturant is abovethat needed to unfold 50 % of protein. Conversely folding takes place with rate

when the concentration of denaturant is below that needed to unfold 50 % of protein.

Write an equation for the observed rate constant ln kobs and plot it (Chevron plot) as a function of denaturant concentration.

How do you determine from the figure kfH2O?

How will the Chevron plot change when a mutation will affect the transition state?

  1. Near the transition temperature Tm the Gibbsin free energy is

Show that there will be another transition temperature Tm’ < Tm.

Provide an estimate of Tm’ using an approximation

  1. Describe experiments that allow you to follow the unfolding of a globular protein

.

  1. All proteins are increasingly unstable with increasing temperature, but only few regain full activity on cooling back to room temperature. Why?
  1. Why is the unfolding curve of a protein often sigmoidal as a function of denaturant concentration.
  1. Why many protein display rollover in Chevron plots? K. Dill
  1. Draw Kratky-plot I(S)*S2 vs. S, where I is the intensity as a function of scattering vector, for a fully unfolded protein. You may consider the unfolded polypeptide as a chain that scatters as

.

where RG is the radius of gyration. At high values of scattering vector you may treat the elements of a chain as a needle

where L is the length of the needle.

How does the scattering differ from that of a folded protein at small values of S

And at high values of S

  1. Rearrange equation H - TS = RTln[D]/[N], where [D] is the concentration of the denatured and [N] the native protein, to [D]/([D]+[N]) that is determined by measurement (spectroscopy). Draw the curve [D]/([D]+[N]) vs. T and identify the midpoint as Tm.
  1. Below are given thermodynamic parameters for folding of few proteins at 25 ºC. What is the most stable protein? What are the melting temperatures assuming that enthalpy and entropy do not change with temperature?

Protein / G (kJ/mol) / H (kJ/mol) / S (kJ/Kmol)
Ribonuclease / -46 / -280 / -790
Chymotrypsin / -55 / -270 / -720
Lysozyme / -62 / -220 / -530
Cytochrome C / -44 / -52 / -27
  1. Ribonuclease structure is stabilized by G = -7.1 kJ/mol at pH 2.5 and T = 25 ºC. What is the ratio between folded and denatured molecules? The enthalphy for folding is 238.6 kJ/mol at 25 ºC. Assume that enthalpy and entropy do not change when temperature is raised to 37 ºC. What is G at 37 ºC and what is the ratio between folded and denatured molecules? Finally what is the Tm for ribonuclease at pH 2.5?
  1. The action of a denaturant such as urea or guanidinium chloride is to solubilize all parts of the polypeptide. To a good approximation the free energy change is proportional to the denaturant concentration G =GH2O – m[denaturant] where m is a constant (gradient of G). Rewrite the equation in 2 for [D]/([D]+[N]) vs. [denaturant] and draw the curve.
  1. Show that there is a temperature Ts where the protein structure is most stable from the expression of free energy

where Tm is the melting temperature. Assume constant pressure.

  1. Based on the previous result, show first that TsTm and then that there is another temperature Tm´ below Ts where protein denatures anew. Express Tm´.
  1. Use your previous results and draw curves for free energy, enthalpy and entropy as function of temperature for a protein with Tm = 60 ºC, H(Tm) = 500 kJ/mol and specific heat Cp = 10 kJ/(Kmol).
  1. Pressure and temperature will affect together protein stability according to

where V is the change in the specific volume,  is the change in the isothermal compressibility (∂V/∂P)T and  is the change in the thermal expansivity (∂V/∂T)P = -(∂S/∂P)T. Make an approximation (T - To)/To < 1 to cast G(P,T) to a quadratic form. What is the condition in terms of Cp and To for the quadratic equation to be an ellipse in the P,T-plane?

  1. Find an expression for the center of the G(P,T)-ellipse and write the condition to determine whether pressure will simply destabilize the protein or the most stable state is at an elevated pressure.
  1. Paramagnetic relaxation of nuclear spins is governed by

wheret is time and paramagnetic relaxation rate is

and r is the distance from the paramagnetic site. All other symbols are constants

In the figure you see paramagnetic enhancement to nuclear spin relaxation for unfolded apomyoglobin at pH 2.3. The histograms show the intensity ratios (Ipara/I) for each residue when the cysteine bound label is (A) E18C*, (B) K77C*, and (C) K133C*.

Sketch in each panel the expected intensity ratios for a random coil.

Deduce from the differences between the expected random curve and experimental data which of the sites 18, 77 and 133 are involved in a clustering and draw a residue-residue contact map.

  1. Why it is difficult to simulate protein folding using atomic models but instead simplified models such the one below are used?

In the simple model side chains are presented as pseudoatoms (SC) that move in a cone given by  and  angles. The backbone is also reduced to a single pseudoatom between two C and having  and  as the degrees of freedom. Pseudoatoms are connected by virtual bonds d.

Construct a force field, i.e. a potential energy function U, for this simplified model that contains potential energy terms related to the degrees of freedom and pair wise interactions.

Assume you are running a molecular dynamics (MD) simulation using you force field. At a given time step t the model has a set of coordinates q(t). How do you obtain from U[q(t)] accelerations d2q/dt2?

  1. Relaxation rates of nuclear spins are sensitive to the mobility i.e. to the effective size of the molecular fragment. Below you see relaxation data from lysozyme that has been chemically modified to prevent it from folding.
  1. Below on left you see free energy changes G of afolded WW protein introduced by mutations. Which parts of the protein are important for its thermal stability.


On right are shown  values. What residues are important for folding?

  1. Hydrogen deuterium exchange …
  1. Explain how a free energy funneldevoid of major barriers may cause apparent two-state folding kinetics.
  1. Observed chemical reaction kinetics is described microscopically by specific rate limiting atomic structures. Observed protein folding kinetics resembles observed chemical reaction kinetics, however, how does the microscopic macromolecular description differ from the chemical one?
  1. How do mass-action and statistical mechanics models of protein folding differ?
  1. The free energy landscape (funnel) is a high-dimensional surface E(1,2,3,…m) where s present lateral coordinatesthat relate to the degrees of freedom. What is the meaning of the internal free energy E? Can one measure it? How does temperature or denaturant affect E?
  1. Simple protein folding models contain only a chain of hydrophobic and polar beads that can “walk” in a (2D) grid. What kind of pair wise interaction you could set among the beads and how would the corresponding energy level diagrams and landscapes look like?
  1. What is the distinction between thermodynamic (Q) and kinetic () reaction coordinates? Are they correlated? Often Q = 1/2 is taken to define the transition mid-point. How is Q biased according to the kinetic description.
  1. Monte Carlo method is used in a wide range of optimization tasks. Usually the probability for the transition is obtained using Metropolis sampling. Why this sampling may not be optimal for studies of folding but Kawasaki sampling should be used?
  1. Proteins unfold upon heating and perhaps surprisingly also upon cooling. To account for the temperature dependence using a HP model, where there is only attractive interaction HH between the hydrophobic residues, the simplest approximation is that  does not depend on T, the second approximation is  (T) and the third is A(T) where A is the rate of conformational transition. Plot schematically folding and unfolding rates using the first, second and third approximations vs 1/T.
  1. Describe the differences between homopolymer and heteropolymer folding kinetics.
  1. How does protein folding in cell (in vivo) differ from that achievable in vitro or in silico.
  1. The native state, i.e. a folded and functional protein, is often the subject of primary interest. What other forms or states a polypeptide may adopt?
  1. Proteins are dynamic. Give examples of the motions that ragen over many time and length scales.
  1. Protein structure determination by NMR involves minimization of penalty function

to match the experimental data, i.e. distances between atoms ro, dihedrals o, etc. However the target values denoted by subscript o are averages over the dynamic ensemble. Discuss the properties and qualities of the model that has been obtained by minimization of E.

One may also acquire dynamic information, e.g. order parameter S2. How would you need to modify the minimization of the penalty function to incorporate the dynamic nature.

  1. Transition states are claimed to have native-like topology. What does it mean?
  1. In the figure transverse relaxation rates have been measured from lysozyme that has been chemically modified to trap a folding intermediate.

How would you build on the basis of data a model of the intermediate. Suppose the residue indicated with 5. was mutated. What kind of data you would expect to record then?

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