Combined molecular/continuum modeling reveals the role of friction during fast unfolding of coiled-coil proteins

Abstract

Coiled-coils are filamentous proteins capable of reversible unfolding. We show that hydrodynamic interactions with the solvent, usually neglected in theories of protein unfolding, are critical to understand their unfolding at high rates.

Unfolding mechanism and free energy landscape of single, stable, alpha helices at low pull speeds

“…The unfolding mechanism does not change noticeably in the velocity range investigated. The initial stretching of the helix occurs without loss of helical structure, in agreement with prior simulations of (metastable) helices 15,17 and similarly to the response of coiled coils in tension 47 and shear. 43,44 Larger strain involves loss of helical structure starting predominantly from the ends of the helix, i.e., in the range of pull velocities investigated, unfolding is a cooperative mechanism.…”

Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs

“…Coiled-coils is a prevalent structural motif occurring in about 10% of the proteins, where α-helices are wrapped around each other [41,55]. An important mechanical feature, key to several biological functions and emerging biomaterials, is its capability to undergo structural transformations, from the coiled state to an unwinded state.…”

“…We here model the mechanical response of the protein as a one-dimensional rod with length L, which is fixed at one end, X = 0, and pulled at the other end, X = L, as in [41]. In this example, the free energy density can be written as a (nonconvex) function of the strain ε, i.e., f = f (ε), and the dissipation potential density as a function of the velocity v, i.e., ψ = ψ(v).…”

“…To generate the training data, we use the double-well free energy landscape obtained from molecular dynamic simulations in [41], shown in Fig. 3(a), as well as their estimated dissipation potential ψ(v) = 1 2 ηv 2 , with η = 8 pN ns nm −2 .…”

“…In addition, F[z] is the system's free energy, D[z, w] is the dissipation potential and P[z, w] is the power supplied by the external forces. This variational principle establishes a competition between energy release and dissipation, and can be used to model a wide range of phenomena, including elastic solids undergoing phase transformations [41] and viscoplasticity [13], phase field models [42], reaction-diffusion systems [43], active soft matter [44], liquid crystals [3], as well as multiphysics problems that combine several of the above [5]. Systems with constraints, such as incompressibility, also exhibit such a variational structure, where the constraints can be naturally added to the variational principle by means of Lagrange multipliers [5].…”