Redistribution of Flexibility in Stabilizing Antibody Fragment Mutants Follows Le Chatelier's Principle

Le Châtelier's principle is the cornerstone of our understanding of chemical equilibria. When a system at equilibrium undergoes a change in concentration or thermodynamic state (i.e., temperature, pressure, etc.), La Châtelier's principle states that an equilibrium shift will occur to offset the perturbation and a new equilibrium is established. We demonstrate that the effects of stabilizing mutations on the rigidity ⇔ flexibility equilibrium within the native state ensemble manifest themselves through enthalpy-entropy compensation as the protein structure adjusts to restore the global balance between the two. Specifically, we characterize the effects of mutation to single chain fragments of the anti-lymphotoxin-β receptor antibody using a computational Distance Constraint Model. Statistically significant changes in the distribution of both rigidity and flexibility within the molecular structure is typically observed, where the local perturbations often lead to distal shifts in flexibility and rigidity profiles. Nevertheless, the net gain or loss in flexibility of individual mutants can be skewed. Despite all mutants being exclusively stabilizing in this dataset, increased flexibility is slightly more common than increased rigidity. Mechanistically the redistribution of flexibility is largely controlled by changes in the H-bond network. For example, a stabilizing mutation can induce an increase in rigidity locally due to the formation of new H-bonds, and simultaneously break H-bonds elsewhere leading to increased flexibility distant from the mutation site via Le Châtelier. Increased flexibility within the VH β4/β5 loop is a noteworthy illustration of this long-range effect

Rigidity Emerges during Antibody Evolution in Three Distinct Antibody Systems: Evidence from QSFR Analysis of Fab Fragments

<div><p>The effects of somatic mutations that transform polyspecific germline (GL) antibodies to affinity mature (AM) antibodies with monospecificity are compared among three GL-AM Fab pairs. In particular, changes in conformational flexibility are assessed using a Distance Constraint Model (DCM). We have previously established that the DCM can be robustly applied across a series of antibody fragments (VL to Fab), and subsequently, the DCM was combined with molecular dynamics (MD) simulations to similarly characterize five thermostabilizing scFv mutants. The DCM is an ensemble based statistical mechanical approach that accounts for enthalpy/entropy compensation due to network rigidity, which has been quite successful in elucidating conformational flexibility and Quantitative Stability/Flexibility Relationships (QSFR) in proteins. Applied to three disparate antibody systems changes in QSFR quantities indicate that the VH domain is typically rigidified, whereas the VL domain and CDR L2 loop become more flexible during affinity maturation. The increase in CDR H3 loop rigidity is consistent with other studies in the literature. The redistribution of conformational flexibility is largely controlled by nonspecific changes in the H-bond network, although certain Arg to Asp salt bridges create highly localized rigidity increases. Taken together, these results reveal an intricate flexibility/rigidity response that accompanies affinity maturation.</p></div

Statistically significant changes in rigidity (p<0.01) are tabulated based on the distance between them and the closest constituent mutation.

<p>Note that the average distance in the increased rigidity response (A) is significantly less than increased flexibility (B), 13.6 Å vs. 17.9 Å, respectively.</p

Structures of the three Fab fragments bound with antigens (fluorescein, CD3 and hapten, respectively) are shown.

<p>H and L chains are colored in cyan and green, respectively; epitope is colored in orange.</p

Molecular dynamics trajectories.

<p>FA, CA and EA represent anti-fluorescein, Anti-CD3 and esterase catalytic antibodies, respectively. (A) Root mean square deviations (RMSDs) of Cα are provided each of the molecular dynamics trajectories. The FA(GL) and FA(AM) exhibit larger RMSDs than other antibodies due to change of domain-domain reorientation. (B) Global RMSDs of for the full FA(GL) Fab and individual RMSDs for each domain. All the four domains (VH, VL, CH and CL) show much lower RMSDs than global RMSDs. The small fluctuations within the domains highlight that the global fluctuations are caused by slippage along the domain interface, where the four domains are continually rearranging relative to each other. (C) The slippage along the domain interfaces is indicated in panel (B), where different colors represent snapshots occurring at: 20 ns (red), 40 ns (blue), and 80 ns (green).</p

Conformational fluctuations.

<p>Residue root mean square fluctuations (RMSF) are provided for the six molecular dynamics trajectories (black indicates GL, whereas red indicates AM).</p

Dataset statistics.

<p>Dataset statistics.</p

Cooperativity correlation difference plots highlight differences in pairwise mechanical couplings between the wild type and each mutant.

<p>Red indicates increased correlated flexibility within the mutant structure, whereas blue indicates increased correlated rigidity. White indicates no change. Notice in most mutants (i.e., triple mutant), changes in cooperativity correlation occur throughout the Fv structure, whereas they are primarily isolated to the VH domain in the quadruple mutant.</p

Differences in H-bond between GL and AM antibodies (A for H chain and B for L chain).

<p>The total H-bond counts (donor and acceptor) are averaged across the MD simulation for each residue. Positive values indicate AM antibodies have more hydrogen bonds than the GL antibodies and vice versa. FA, CA and EA represent anti-fluorescein, Anti-CD3 and esterase catalytic antibodies, respectively.</p