Final Report Summary - COLLOIDS WITH DNA (Programmable self-assembly of DNA-coated colloids)
[Since I changed careers nearly at the start of the second year of the project, this final report and the mid-project report cover nearly equal periods in time and are thus identical]
During the tenure of a Marie Curie IIF grant (PIIF-GA-2001-300045 Colloids with DNA), I have made several important contributions in the direction of the projects main objective, namely to advance the theory of DNA-coated colloid (DNACC) interactions, which have moved us forward towards the goal of programmable self-assembly with these versatile building blocks.
First, I developed a substantial generalisation of a self-consistent theory for DNACC interactions, which allows us to accurately calculate the interaction details of any DNACC system (Varilly, Angioletti-Uberti, Mognetti, Frenkel, "A general theory of DNA-mediated and other valence-limited colloidal interactions", J. Chem. Phys. 137, 094108 (2012)). We demonstrated the high accuracy of this theory in previously explored settings (e.g. uniformly and singly coated spherical colloids), and in novel contexts (e.g. plates coated anisotropically to yield DNA-mediated "patchy" interactions). Compared to previous simulations, the effort required to model the details of DNACC interactions is now reduced by several orders of magnitude, making it cost-effective to explore systematically how varying the many tunable parameters of a DNACC system influences its behaviour. Moreover, our theory explicitly separates interactions into a pairwise DNA binding interaction and the combinatorial entropy gained from allowing for a multitude of such interactions to occur simultaneously. We account for the second aspect completely, and can accommodate great variety in the first aspect, so our theory should be generally applicable to ligand-receptor--mediated interactions, e.g. cell adhesion. We developed an open-source program to calculate DNACC interactions under the most general of settings, available on social-coding website Github (https://github.com/patvarilly/DNACC(si apre in una nuova finestra)).
Second, I contributed to developing a closed-form expression for the DNA-mediated interaction energy of a DNACC system (Angioletti-Uberti, Varilly, Mognetti, Tkachenko, Frenkel, "Communication: A simple analytical formula for the free energy of ligand–receptor-mediated interactions", J. Chem. Phys. 138, 021102 (2013)). This advance reduces the effort of modelling interactions by another 1-2 orders of magnitude, to the point where we can prescribe a (realisable) desired DNACC interaction potential and use automatic methods to find the values of the DNACC parameters (coverage density, strand length, hybridisation energy, temperature, etc.) needed to realise that interaction. In subsequent work (manuscript in preparation), I have established a firm connection between this work and the well-established Wertheim theory, which has led to a clear and concise derivation of our closed-form interaction energy expression. Additionally, it then becomes clear how to calculate effective forces in DNACC systems, which opens the door to simulating self-assembly with realistic dynamics. Kinetics often being critical to successful self-assembly, being able to model dynamics is an important step forward.
Third, I used the above theories to study how meso-scale colloidal ``walkers'' could move along a DNA-coated surface where there is a gradient in receptor density (Francisco J. Martinez-Veracoechea, Bortolo M. Mognetti, Stefano Angioletti-Uberti, Patrick Varilly, Daan Frenkel and Jure Dobnikar, ``Designing stimulus-sensitive colloidal walkers'', Soft Matter, in press). Interestingly, we have found that with an appropriate choice of DNA sequences in the surface receptors, we can reverse the direction of motion of the walkers by changing temperature, a feature which may find use in chromatographic separation of colloids that are functionalized differently.
Fourth, in searching for novel DNACC systems, we have discovered (manuscript in preparation) that coating colloids with mobile DNAs on their surface (under experimental development in the Leunissen group at AMOLF and the Chaikin group at NYU) can induce many-body effects that lead to isotropic valence-limited particles (a construct previously studied in theory to model network glasses, but as yet unrealised experimentally). This discovery, made possible only because of the above fully general theory, widens the range of phenomena displayed by DNACCs, and highlights how under-appreciated many-body effects may be harnessed generically to surprising effect.
Finally, together with Bortolo Mognetti and the experimental group of Erika Eiser, we have made a serious effort to understand (at quantitative accuracy) how single-stranded DNAs mediate DNACC interactions (Di Michele, Lorenzo; Mognetti, Bortolo; Yanagishima, Taiki; Varilly, Patrick; Ruff, Zachary; Frenkel, Daan; Eiser, Erika, ``Effect of Inert Tails on the Thermodynamics of DNA Hybridization'', Journal of the Americal Chemical Society, submitted). We have made the surprising discovery that the hybridisation energy of two partially complementary ssDNAs depends sensitively (i.e. with consequences to DNACC experiments) on the details of portions of the DNA that *do not* participate in hybridisation. Although our motivation lay in obtaining quantitative understanding of a set of experiments from John Crocker's group at UPenn, the phenomenon is quite generic, and we joined forces with Erika Eiser's group at the Cavendish Lab at Cambridge to obtain experimental confirmation. The effect is perfectly visible in experiments, although our quantitative understanding of it can still be improved.
I have also strived to advance two areas of research in which I was previously involved: water and hydrophobicity. I've collaborated with Tuomas Knowles at Cambridge on a lattice model of micelle assembly (manuscript in preparation, invited talk at CECAM meeting in Paris on recent methodological advances in modelling hydrophobicity) and on possible effects of hydrophobicity on amyloid assembly (part of an invited talk at ACS Fall Meeting 2012, an invited talk at the Les Houches school on Water at Interfaces, and invited seminars at RPI (Troy, NY) and Oxford). I also completed and published an earlier transition path sampling study of water evaporation (Varilly, Chandler, "Water Evaporation: A Transition Path Sampling Study", J. Phys. Chem. B, 117 (5), 1419-1428).
During the tenure of a Marie Curie IIF grant (PIIF-GA-2001-300045 Colloids with DNA), I have made several important contributions in the direction of the projects main objective, namely to advance the theory of DNA-coated colloid (DNACC) interactions, which have moved us forward towards the goal of programmable self-assembly with these versatile building blocks.
First, I developed a substantial generalisation of a self-consistent theory for DNACC interactions, which allows us to accurately calculate the interaction details of any DNACC system (Varilly, Angioletti-Uberti, Mognetti, Frenkel, "A general theory of DNA-mediated and other valence-limited colloidal interactions", J. Chem. Phys. 137, 094108 (2012)). We demonstrated the high accuracy of this theory in previously explored settings (e.g. uniformly and singly coated spherical colloids), and in novel contexts (e.g. plates coated anisotropically to yield DNA-mediated "patchy" interactions). Compared to previous simulations, the effort required to model the details of DNACC interactions is now reduced by several orders of magnitude, making it cost-effective to explore systematically how varying the many tunable parameters of a DNACC system influences its behaviour. Moreover, our theory explicitly separates interactions into a pairwise DNA binding interaction and the combinatorial entropy gained from allowing for a multitude of such interactions to occur simultaneously. We account for the second aspect completely, and can accommodate great variety in the first aspect, so our theory should be generally applicable to ligand-receptor--mediated interactions, e.g. cell adhesion. We developed an open-source program to calculate DNACC interactions under the most general of settings, available on social-coding website Github (https://github.com/patvarilly/DNACC(si apre in una nuova finestra)).
Second, I contributed to developing a closed-form expression for the DNA-mediated interaction energy of a DNACC system (Angioletti-Uberti, Varilly, Mognetti, Tkachenko, Frenkel, "Communication: A simple analytical formula for the free energy of ligand–receptor-mediated interactions", J. Chem. Phys. 138, 021102 (2013)). This advance reduces the effort of modelling interactions by another 1-2 orders of magnitude, to the point where we can prescribe a (realisable) desired DNACC interaction potential and use automatic methods to find the values of the DNACC parameters (coverage density, strand length, hybridisation energy, temperature, etc.) needed to realise that interaction. In subsequent work (manuscript in preparation), I have established a firm connection between this work and the well-established Wertheim theory, which has led to a clear and concise derivation of our closed-form interaction energy expression. Additionally, it then becomes clear how to calculate effective forces in DNACC systems, which opens the door to simulating self-assembly with realistic dynamics. Kinetics often being critical to successful self-assembly, being able to model dynamics is an important step forward.
Third, I used the above theories to study how meso-scale colloidal ``walkers'' could move along a DNA-coated surface where there is a gradient in receptor density (Francisco J. Martinez-Veracoechea, Bortolo M. Mognetti, Stefano Angioletti-Uberti, Patrick Varilly, Daan Frenkel and Jure Dobnikar, ``Designing stimulus-sensitive colloidal walkers'', Soft Matter, in press). Interestingly, we have found that with an appropriate choice of DNA sequences in the surface receptors, we can reverse the direction of motion of the walkers by changing temperature, a feature which may find use in chromatographic separation of colloids that are functionalized differently.
Fourth, in searching for novel DNACC systems, we have discovered (manuscript in preparation) that coating colloids with mobile DNAs on their surface (under experimental development in the Leunissen group at AMOLF and the Chaikin group at NYU) can induce many-body effects that lead to isotropic valence-limited particles (a construct previously studied in theory to model network glasses, but as yet unrealised experimentally). This discovery, made possible only because of the above fully general theory, widens the range of phenomena displayed by DNACCs, and highlights how under-appreciated many-body effects may be harnessed generically to surprising effect.
Finally, together with Bortolo Mognetti and the experimental group of Erika Eiser, we have made a serious effort to understand (at quantitative accuracy) how single-stranded DNAs mediate DNACC interactions (Di Michele, Lorenzo; Mognetti, Bortolo; Yanagishima, Taiki; Varilly, Patrick; Ruff, Zachary; Frenkel, Daan; Eiser, Erika, ``Effect of Inert Tails on the Thermodynamics of DNA Hybridization'', Journal of the Americal Chemical Society, submitted). We have made the surprising discovery that the hybridisation energy of two partially complementary ssDNAs depends sensitively (i.e. with consequences to DNACC experiments) on the details of portions of the DNA that *do not* participate in hybridisation. Although our motivation lay in obtaining quantitative understanding of a set of experiments from John Crocker's group at UPenn, the phenomenon is quite generic, and we joined forces with Erika Eiser's group at the Cavendish Lab at Cambridge to obtain experimental confirmation. The effect is perfectly visible in experiments, although our quantitative understanding of it can still be improved.
I have also strived to advance two areas of research in which I was previously involved: water and hydrophobicity. I've collaborated with Tuomas Knowles at Cambridge on a lattice model of micelle assembly (manuscript in preparation, invited talk at CECAM meeting in Paris on recent methodological advances in modelling hydrophobicity) and on possible effects of hydrophobicity on amyloid assembly (part of an invited talk at ACS Fall Meeting 2012, an invited talk at the Les Houches school on Water at Interfaces, and invited seminars at RPI (Troy, NY) and Oxford). I also completed and published an earlier transition path sampling study of water evaporation (Varilly, Chandler, "Water Evaporation: A Transition Path Sampling Study", J. Phys. Chem. B, 117 (5), 1419-1428).