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from mdtraj.html import TrajectoryView, enable_notebook
enable_notebook()

Notes on: "The ensemble nature of allostery" (Motlagh, Wrabl, Li, and Hilser, 2014, Nature) http://www.nature.com/nature/journal/v508/n7496/pdf/nature13001.pdf

Allostery: nonlocal effects of binding in macromolecules
Effects are statistical: must consider conformational ensemble
Motivation: allostery required for molecular understanding of signaling and disease, but we do not yet have a general, quantifiable, and predictive atomic description
History: allostery concepts shaped by experimental accessibility-- early days strongly influenced by static structural images of e.g. hemoglobin; current models reveal:
- rigid body movement
- folded yet dynamic structure
- intrinsic disorder

Early statement of allostery: multiple binding sites within a protein can interact at a distance (Changeux, ref. 2) $\to$ two dominant phenomenological models of change between two well-defined end states:
- "sequential" (Koshland, Nemethy, Filmer)
  - protein flexibility: "induced fit" of a binding site
- "symmetric" (Monod, Wyman, Changeux)
  - ligand-binding changes equilibrium between two pre-existing quaternary states: tensed (T) and relaxed (R)
How does the structure facilitate allosteric communication between sites?
- Structure-centric approach (Perutz): understand allostery in terms of structural changes inferred from hi-res structure
  - Limitations: must also understand factors that "poise" an allosteric protein for structural change-- allosteric transitions involve multiple states
- Dynamic allostery without conformational change
  - Width of conformational distribution indicates allostery (Cooper, Dryden, 1984) -- changes in frequency and amplitude of thermal fluctuations in a protein upon ligand binding $\to$ cooperative energies of $O\left(\frac{\text{kcal}}{\text{mol}}\right)$

Solution NMR:
- measure fast internal motion as a proxy for conformational entropy
- can now detect motion in proteins over a wide range of timescales
- pico- to nano-second range most important for detecting conformational entropy
From least to most disordered:
- Rigid body motions (e.g. hemoglobin)
- Side-chain dynamics (e.g. PDZ domain)
- Backbone dynamics (e.g. CAP)
- Local unfolding (e.g. AAC, TetR)
- Intrinsically disordered (Phd, AS, E1A)

Structured allosteric proteins show dynamic changes in many cases and are convenient to probe with NMR
Following (Cooper, Dryden, 1984) -- allostery without structural change demonstrated in several studies (highlighting limitations of inferring mechanism from static structure):
- CAP (homodimeric transcription factor with a cAMP binding domain and DNA binding domain)
- PDZ domain
CAP
- cAMP binding $\to$ $\Delta$ conformational entropy (via backbone and side-chain dynamics)



In [18]:

    
CAP = mdtraj.load_pdb("http://www.rcsb.org/pdb/files/1cgp.pdb")
widget = TrajectoryView(CAP, secondaryStructure='ribbon')
widget

PDZ domain: removal of an $\alpha$-helix:
- increases side-chain dynamics of distal binding site
- decreases binding affinity 25-fold (almost entirely due to entropic contributions)



In [19]:

    
PDZ = mdtraj.load_pdb("http://www.rcsb.org/pdb/files/1BE9.pdb")
widget = TrajectoryView(PDZ, secondaryStructure='ribbon')
widget

intrinsic disorder enables "tunable" coupling between sites
AAC
- structure: homodimeric enzyme
- function: confers resistance to amino-glycoside antibiotics
- allosteric effector: acetyl-CoA
  - binds with positive cooperativity at low temperatures, negative cooperativity at high temperatures due to local unfolding
$\alpha$-synuclein
- N-terminal membrane-binding domain
- C-terminal IDR
- Nitration shifts conformational ensemble to more globally extended conformation, reducing affinity of membrane-binding domain
Many TFs contain intrinsically disordered regions, and many are also allosterically regulated, simultaneously exhibiting:
- high specificity for multiple targets
- low-affinity binding
- fast association and dissociation rate
- enrichment of PTM sites

Historical side-note: Early example of treating allosteric proteins as ensembles: $\lambda$ repressor in phage (consideration of all accessible ligated states required to understand function)
All ensembles have tunable sensitivity, and may contain a large number of potential allosteric mechanisms



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