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We develop integrated co-evolution and dynamic coupling (ICDC) approach to identify, mutate, and assess distal sites to modulate function. We validate the approach first by analyzing the existing mutational fitness data of TEM-1 β-lactamase and show that allosteric positions co-evolved and dynamically coupled with the active site significantly modulate function. We further apply ICDC approach to identify positions and their mutations that can modulate binding affinity in a lectin, cyanovirin-N (CV-N), that selectively binds to dimannose, and predict binding energies of its variants through Adaptive BP-Dock. Computational and experimental analyses reveal that binding enhancing mutants identified by ICDC impact the dynamics of the binding pocket, and show that rigidification of the binding residues compensates for the entropic cost of binding. This work suggests a mechanism by which distal mutations modulate function through dynamic allostery and provides a blueprint to identify candidates for mutagenesis in order to optimize protein function.

 

Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane bending elasticity. Their open edges and micrometer-length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. Here, we find that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped surfaces with complex edge structures. The saddle-shaped membranes are well approximated by Enneper’s minimal surfaces. Theoretical modeling demonstrates that their formation is driven by increasing the positive Gaussian modulus, which in turn, is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to diverse topologically distinct structures, including shapes similar to catenoids, trinoids, four-noids, and higher-order structures. At long timescales, we observe the formation of a system-spanning, sponge-like phase. The unique features of colloidal membranes reveal the topological transformations that accompany coalescence pathways in real time. We enhance the functionality of these membranes by making their shape responsive to external stimuli. Our results demonstrate a pathway toward control of thin elastic sheets’ shape and topology—a pathway driven by the emergent elasticity induced by compositional heterogeneity. 

Using a combination of theory and experiments we study the interface between two immiscible domains in a colloidal membrane composed of rigid rods of different lengths. Geometric considerations of rigid rod packing imply that a domain of sufficiently short rods in a background membrane of long rods is more susceptible to twist than the inverse structure, a long-rod domain in a short-rod membrane background. The tilt at the inter-domain edge forces splay, which in turn manifests as a spontaneous edge curvature whose energetics are controlled by the length asymmetry of constituent rods. A thermodynamic model of such tilt-curvature coupling at inter-domain edges explains a number of experimental observations, including a non-monotonic dependence of the edge twist on the domain radius, and annularly shaped domains of long rods. Our work shows how coupling between orientational and compositional degrees of freedom in two-dimensional fluids give rise to complex shapes and thermodynamics of domains, analogous to shape transitions in 3D fluid vesicles.