From helix-coil transitions to protein folding

Non-activated Esters as Reactive Handles in Direct Post-Polymerization Modification

Non-activated esters are prominently featured functional groups in polymer science, as ester functional monomers display great structural diversity and excellent compatibility with a wide range of polymerization mechanisms. Yet, their direct use as a reactive handle in post-polymerization modification has been typically avoided due to their low reactivity, which impairs the quantitative conversion typically desired in post-polymerization modification reactions. While activated ester approaches are a well-established alternative, the modification of non-activated esters remains a synthetic and economically valuable opportunity. In this review, we discuss past and recent efforts in the utilization of non-activated ester groups as a reactive handle to facilitate transesterification and aminolysis/amidation reactions, and the potential of the developed methodologies in the context of macromolecular engineering.

Einstein Model of a Graph to Characterize Protein Folded/Unfolded States

The folded structures of proteins can be accurately predicted by deep learning algorithms from their amino-acid sequences. By contrast, in spite of decades of research studies, the prediction of folding pathways and the unfolded and misfolded states of proteins, which are intimately related to diseases, remains challenging. A two-state (folded/unfolded) description of protein folding dynamics hides the complexity of the unfolded and misfolded microstates. Here, we focus on the development of simplified order parameters to decipher the complexity of disordered protein structures. First, we show that any connected, undirected, and simple graph can be associated with a linear chain of atoms in thermal equilibrium. This analogy provides an interpretation of the usual topological descriptors of a graph, namely the Kirchhoff index and Randić resistance, in terms of effective force constants of a linear chain. We derive an exact relation between the Kirchhoff index and the average shortest path length for a linear graph and define the free energies of a graph using an Einstein model. Second, we represent the three-dimensional protein structures by connected, undirected, and simple graphs. As a proof of concept, we compute the topological descriptors and the graph free energies for an all-atom molecular dynamics trajectory of folding/unfolding events of the proteins Trp-cage and HP-36 and for the ensemble of experimental NMR models of Trp-cage. The present work shows that the local, nonlocal, and global force constants and free energies of a graph are promising tools to quantify unfolded/disordered protein states and folding/unfolding dynamics. In particular, they allow the detection of transient misfolded rigid states.

Nano-caged shikimate as a multi-site cross-linker of collagen for biomedical applications

Shikimic acid caged silver nanoparticles as multi-site cross-linkers of collagen for tissue engineering applications.

Nonadditivity in the alpha-helix to coil transition

The Lifson-Roig Model (LRM) and all its variants describe the α-helix to coil transition in terms of additive component-free energies within a free energy decomposition scheme, and these contributions are interpreted through sequence-context dependent nucleation and propagation parameters. Although this phenomenological approach is able to adequately fit experimental data on helix content and heat capacity, the number of required parameters increases dramatically with additional sequence variation. Moreover, due to nonadditive competing microscopic effects that are difficult to disentangle within a LRM, large uncertainties within the parameters emerge. We offer an alternative view that removes the need for sequence-context parameterization by focusing on individual microsopic interactions within a free energy decomposition and explicitly account for nonadditivity in conformational entropy through network rigidity using a Distance Constraint Model (DCM). We apply a LRM and a DCM to previously published experimental heat capacity and helix content data for a series of heterogeneous polypeptides. Both models describe the experimental data well, and the parameters from both models are consistent with prior work. However, the number of DCM parameters is independent of sequence-variability, the parameter values exhibit better transferability, and the helix nucleation is predicted by the DCM explicitly through the nonadditive nature of conformational entropy. The importance of these results is that the DCM offers a system-independent approach for modeling stability within polypeptides and proteins, where the demonstrated accuracy for the α-helix to coil transition over a series of heterogeneous polypeptides described here is one case in point.

Analysis of repeat-protein folding using nearest-neighbor statistical mechanical models

The linear "Ising" model, which has been around for nearly a century, treats the behavior of linear arrays of repetitive, interacting subunits. Linear "repeat-proteins" have only been described in the last decade or so, and their folding energies have only been characterized very recently. Owing to their repetitive structures, linear repeat-proteins are particularly well suited for analysis by the nearest-neighbor Ising formalism. After briefly describing the historical origins and applications of the Ising model to biopolymers, and introducing repeat protein structure, this chapter will focus on the application of the linear Ising model to repeat proteins. When applied to homopolymers, the model can be represented and applied in a fairly simplified form. When applied to heteropolymers, where differences in energies among individual subunits (i.e. repeats) must be included, some (but not all) of this simplicity is lost. Derivations of the linear Ising model for both homopolymer and heteropolymer repeat-proteins will be presented. With the increased complexity required for analysis of heteropolymeric repeat proteins, the ability to resolve different energy terms from experimental data can be compromised. Thus, a simple matrix approach will be developed to help inform on the degree to which different thermodynamic parameters can be extracted from a particular set of unfolding curves. Finally, we will describe the application of these models to analyze repeat-protein folding equilibria, focusing on simplified repeat proteins based on "consensus" sequence information.