Energy landscapes and functions of supramolecular systems

Abstract

By means of two supramolecular systems--peptide amphiphiles engaged in hydrogen-bonded β-sheets, and chromophore amphiphiles driven to assemble by π-orbital overlaps--we show that the minima in the energy landscapes of supramolecular systems are defined by electrostatic repulsion and the ability of the dominant attractive forces to trap molecules in thermodynamically unfavourable configurations. These competing interactions can be selectively switched on and off, with the order of doing so determining the position of the final product in the energy landscape. Within the same energy landscape, the peptide-amphiphile system forms a thermodynamically favoured product characterized by long bundled fibres that promote biological cell adhesion and survival, and a metastable product characterized by short monodisperse fibres that interfere with adhesion and can lead to cell death. Our findings suggest that, in supramolecular systems, functions and energy landscapes are linked, superseding the more traditional connection between molecular design and function.

Figure 1. Energy landscapes of PA self-assembly and pathways to access each well

a, Schematic representation of the free energy landscapes of PA assemblies under conditions with relatively high (front) and low (back) charge repulsion between PA molecules. At low intermolecular repulsion, long fibres with β-sheets are favoured and monodisperse short fibres represent a metastable state. At high repulsion, a kinetically trapped assembly and a thermodynamically favoured product separated by an energy barrier (E_b) of 171 kJ/mole were found. b, Freshly prepared PA solutions at 4.4 mM in water contain polydisperse fibrous assemblies with β-sheet internal structure. By first switching off the β-sheets (dilution) and then equilibrating the assemblies (annealing), the thermodynamically favoured product of monodisperse ~150 nm fibres without β-sheet is obtained. Addition of salt switches back on the β-sheet, giving rise to short metastable monodisperse fibres. In contrast, if the fibres are first equilibrated (annealing) and then diluted kinetically trapped fibres with β-sheets are obtained. Addition of salt to those solutions does not alter the morphology, as the β-sheets remain. Fibres with β-sheets are represented with red stripes; fibres with coil-like internal structure are blue.

Figure 2. Micrographs and spectroscopic assessment of morphologies of all products

Cryo-TEM micrographs of (a) thermodynamic product and (b) kinetically trapped product under low ionic strength conditions (I<I_c). c, Fibre-lengths as measured by cryo-TEM. Box-and-whisker plots show mean and 5th-95th percentiles from data of n>180. d, CD-spectra of thermodynamic product at low ionic strength (blue), kinetically trapped product at low ionic strength before (red) and after (black) re-annealing. Cryo-TEM micrographs of (e) thermodynamic product and (f) metastable product under high ionic strength conditions (I>I_c). g, The extremes in CD intensity around 200 nm as a measure of β-sheet content (positive) or random coil content (negative) and (h) molar scattering intensity by DLS during the process of annealing at high and low ionic strengths. All scale bars are 100 nm.

Figure 3. Assessment of morphological transitions of PA assemblies as a function of ionic strength

a, CD signal at 202 nm spectra plotted as a function of PA and salt concentrations. Negative CD intensities denote a random coil structure; positive values correspond to a β-sheet signal. b, The blueshift of Nile Red fluorescence as an indicator of internal hydrophobicity of the assemblies as a function of PA concentration. c, Atomistic modelling at a relatively high and low ionic strength showing difference in β-sheet hydrogen bonding between the two conditions. Dark blue: alkyl tails, yellow: β-sheet hydrogen bonding, cyan: β-turn, grey: random coil. In the top views the alkyl tail is left out for clarity. d, Intensities and distribution of β-sheet hydrogen bonding within the peptide region of PA assemblies calculated from atomistic simulations that mimic conditions below (black) and above (red) I_c.

Figure 4. Implications of the thermodynamic state of PA assemblies on their cytotoxicity

Images or graphs in blue represent short fibre conditions and those in red represent long fibre conditions. a, Live (green) and dead (red) staining of C2C12 pre-myoblasts 3 h after treated with media containing short or long cationic PA assemblies at 27.5 μM. b, Quantification of viable cells after 3 h. c, Quantification of viable cells over time at 110 μM. Error bars depict ± standard error of the mean for n ≥ 3, and a two-way ANOVA with a Bonferroni post-test is used: *** p<0.001, compared among assemblies at each concentration or time. d, Phase micrographs showing morphology of cells 15 min after exposure to media containing short or long PA fibres at 110 μM. Arrows indicate dead cells. e, Release profiles of calcein from liposomes after exposure to media alone (black) or media containing short or long fibres. f, Representative DSC thermograms for DMPC liposomes in media alone (black) or media containing short or long fibres.

Figure 5. Implications of the thermodynamic state of PA assemblies on their bioactivity as a scaffold

Images or graphs in blue represent short fibre conditions and those in red represent long fibre conditions. a, SEM micrographs of surfaces coated with short or long fibres assembled using RGDS PA. b, Immunofluorescent staining revealing morphology of C2C12 pre-myoblasts cultured on the RGDS PA coated substrates. Analysis of cell morphology by (c) projected surface area and (d) aspect ratio. Graphs plot mean ± standard error of the mean of n≥4 from two individual experiments with a total of more than 200 cells per substrate. e, Filopodial movement rate against time. Graphs plot mean ± standard error of the mean of n≥4. f, Elastic modulus and (g) adhesion force of the substrates obtained by AFM force spectroscopy. Adhesion force is defined by a maximum pull-off force measured from an unloading curve. Box-and-whisker plots show mean and 5^th-95^th percentiles from data of n>150 from two separated experiments. All statistical analysis was performed using unpaired two-tailed Student's t-test; *** p<0.001).