The Holy Grail: Quantitative Stability/Flexibility Relationships (QSFR)

The mDCM is a heterogeneous mean field theory that directly relates thermal stability to mechanical flexibility Livesay et al. (2004). FEBS Letters 576: Jacobs & Dallakyan (2005). Biophysical J. 88:

mDCM work flow… Livesay et al. (2004). FEBS Letters 576: Jacobs & Dallakyan (2005). Biophysical J. 88:

What are the DCM parameters? Fitting ubiquitin and HBP C p measurements Jacobs & Dallakyan (2005). Biophysical J. 88:

Introducing a global flexibility order parameter  = #IDF / residue

Relative free energy (kcal/mol) Comparison of ubiquitin and HBP free energy landscapes Global flexibility order parameter Global flexibility order parameter Relative free energy (kcal/mol) K 335 K 338 K 330 K UbiquitinHistidine binding protein Jacobs & Dallakyan (2005). Biophysical J. 88:

Relative free energy (kcal/mol) Global flexibility order parameter Global flexibility order parameter Relative free energy (kcal/mol) K 335 K 338 K 400 K 330 K Comparison of ubiquitin and HBP free energy landscapes UbiquitinHistidine binding protein Jacobs & Dallakyan (2005). Biophysical J. 88:

Model generality: Holding  max and  dis fixed while fitting the remaining 3 parameters Livesay et al. (2004). FEBS Letters 576:

Flexibility IndexProb. to Rotate Prob. of IDOF  G(na) Thioredoxin Jacobs, Livesay, et al. (2006). J Mol Biol 358, 882–904

Quantifying Molecular Cooperativity Gly33 Met37 Gln50 Arg73 Jacobs, Livesay, et al. (2006). J Mol Biol 358, 882–904

The extent of cooperativity correlation within the ensemble is dependent on temperature

Introducing QSFR…

The mesophilic/thermophilic RNase H pair * 1ril -RKRVALFTDGACLGNPGPGGWAALLRFHAHEKLLSGGEACTTNNRMELKAAIEGLKALKE 2rn2 MLKQVEIFTDGSCLGNPGPGGYGAILRYRGREKTFSAGYTRTTNNRMELMAAIVALEALKE * 1ril PCEVDLYTDSHYLKKAFTEGWLEGWRKRGWRTAEGKPVKNRDLWEALLLAMAPHRVRFHFV 2rn2 HCEVILSTDSQYVRQGITQ-WIHNWKKRGWKTADKKPVKNVDLWQRLDAALGQHQIKWEWV 1ril KGHTGHPENERVDREARRQAQSQAKT rn2 KGHAGHPENERCDELARAAAMNPTLEDTGYQVEV Alpha-helix; Beta-strand; Catalytic site Identity conserved Chemically conserved Without conservation

Not all theories are created equal… A simple electrostatics-only model actually predicts the mesophilic ortholog to be more stable than its thermophilic counterpart! pH 3.5 Poisson-Boltzmann ElectrostaticsThe Distance Constraint Model Parameter differences are believed to retain physical meaning. Because these experiments are done under identical experimental conditions and their structures are remarkably similar, parameter differences should reflect intrinsic thermodynamic differences between the pair. Livesay, Jacobs (2006). Proteins 62: Ishikawa et al., (1993) J. Mol. Biology 230: “Thus the exquisite rearrangement of the hydrophobic side-chains, including some favorable aromatic-aromatic interactions, is likely to contribute to the increased stability of T. thermophilus RNase H.”

Livesay, Jacobs (2006). Proteins 62:

Hollien & Marqusee (1999), PNAS

The mDCM can identify allostery through flexibility correlation Livesay, Jacobs (2006). Proteins 62:

The mDCM can identify allostery through flexibility correlation

Parameter error analysis indicates that the flexibility quantities are remarkably robust P R (native basin only) Livesay, Jacobs (2006). Proteins 62:

Parameter error analysis indicates that the flexibility quantities are remarkably robust Livesay, Jacobs (2006). Proteins 62: A random good fitAnother random good fit A bad fitThe best fit 10 random good vs. a bad fit E. coli T. thermophilus

Parameter error analysis indicates that the flexibility quantities are remarkably robust Livesay, Jacobs (2006). Proteins 62: Supp. Fig. 1. Best fit u,v pairs are plotted against a coarse-grained  nat range. In all instances, the best fit u,v pairs indicate that an additional cohesive force (interpreted as hydrophobic in nature) is present within the thermophilic ortholog. The robustness of the observed cohesive force strongly substantiates the conclusions made herein regarding the improved hydrophobic packing of the thermophilic ortholog.

QSFR variability emerges through (subtle) differences within the H-bond network

The bacterial Periplasmic Binding Protein family bPBP ATP-binding domains Transmembrane domains Substrate -- Extracellular Periplasm Cytosol --

Structure superposition of four bPBP homologs Livesay, et al. (2008). Chemistry Central Journal, 2:17.

Local vs. global structural similarity Livesay, et al. (2008). Chemistry Central Journal, 2:17.

Diversity within QSFR arises from subtle differences within the H-bond network R = 0.92R = Livesay, et al. (2008). Chemistry Central Journal, 2:17.

Comparisons to apo vs. halo DSC experiments strongly supports the diversity observed within the mDCM results apo-HBP ligated-HBP LAOBP GBP mDCM resultsKreimer et al. (2000), Eur J. Biochem.  T m ~ 10K Livesay, et al. (2008). Chemistry Central Journal, 2:17.

Backbone flexibility is predicted to be conserved Livesay, et al. (2008). Chemistry Central Journal, 2:17.

Despite flexibility similarity along the backbone, cooperatively correlation varies significantly HBPLAOBPGBP Livesay, et al. (2008). Chemistry Central Journal, 2:17.

Diversity within QSFR characteristics arise from subtle differences within the H-bond network HBP (red) vs. LAOBP (blue)HBP (red) vs. GBP (green) Livesay, et al. (2008). Chemistry Central Journal, 2:17.

Similar amounts of (dis)similarity are observed when comparing open vs. closed conformations Ligated (closed) Apo (open) Flexibility index Livesay, et al. (2008). Chemistry Central Journal, 2:17.

Not quite science fiction: The ability to design a protein with a specific cooperative response may not be that far away… Using this protocol, we designed a de novo hydrogen bond network…

A similar narrative is emerging from our comparisons of the thioredoxin family Mottonen, et al., Proteins, in press.

The TRX family Mottonen, et al., Proteins, in press.

Rigid cluster susceptibility Mottonen, et al., Proteins, in press.

Relative locations of key points describing the mechanical vs. thermodynamic transitions Mottonen, et al., Proteins, in press.

As with the bPBP family, backbone flexibility is mostly conserved across the TRX family Mottonen, et al., Proteins, in press.

As with the bPBP family, backbone flexibility is mostly conserved across the TRX family Mottonen, et al., Proteins, in press.

QSFR diversity is explained by comparing key points along the mechanical vs. thermodynamic transition Mottonen, et al., Proteins, in press.

The observed QSFR differences are consistent with the amount of differences within the H-bond network Mottonen, et al., Proteins, in press.

TRX ox vs. TRX red QSFR response is a long-range effect Mottonen, et al., Proteins, in press.

A similar narrative is emerging from our comparisons of the thioredoxin family Periplasm (an oxidizing environment) Cytosol (a reducing environment) DsbA red DsbA ox Trx red Trx ox Mottonen, Livesay, Jacobs. In preparation.

The mDCM correctly predicts trends within known DsbA vs. Trx functional roles Mottonen, Livesay, Jacobs. In preparation.