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Recent experiments and simulations have demonstrated that proteins can fold on the ribosome. However, the extent and generality of fitness effects resulting from cotranslational folding remain open questions. Here we report a genome-wide analysis that uncovers evidence of evolutionary selection for cotranslational folding. We describe a robust statistical approach to identify loci within genes that are both significantly enriched in slowly translated codons and evolutionarily conserved. Surprisingly, we find that domain boundaries can explain only a small fraction of these conserved loci. Instead, we propose that regions enriched in slowly translated codons are associated with cotranslational folding intermediates, which may be smaller than a single domain. We show that the intermediates predicted by a native-centric model of cotranslational folding account for the majority of these loci across more than 500 Escherichia coli proteins. By making a direct connection to protein folding, this analysis provides strong evidence that many synonymous substitutions have been selected to optimize translation rates at specific locations within genes. More generally, our results indicate that kinetics, and not just thermodynamics, can significantly alter the efficiency of self-assembly in a biological context.

Photonic crystals—a class of materials whose optical properties derive from their structure in addition to their composition—can be created by self-assembling particles whose sizes are comparable to the wavelengths of visible light. Proof-of-principle studies have shown that DNA can be used to guide the self-assembly of micrometer-sized colloidal particles into fully programmable crystal structures with photonic properties in the visible spectrum. However, the extremely temperature-sensitive kinetics of micrometer-sized DNA-functionalized particles has frustrated attempts to grow large, monodisperse crystals that are required for photonic metamaterial applications. Here we describe a robust two-step protocol for self-assembling single-domain crystals that contain millions of optical-scale DNA-functionalized particles: Monodisperse crystals are initially assembled in monodisperse droplets made by microfluidics, after which they are grown to macroscopic dimensions via seeded diffusion-limited growth. We demonstrate the generality of our approach by assembling different macroscopic single-domain photonic crystals with metamaterial properties, like structural coloration, that depend on the underlying crystal structure. By circumventing the fundamental kinetic traps intrinsic to crystallization of optical-scale DNA-coated colloids, we eliminate a key barrier to engineering photonic devices from DNA-programmed materials. DNA-programmed colloidal assembly of macroscopic crystals for photonic applications remains elusive. Here, the authors use insights from studies of nucleation and seeded growth to develop a two-step method for assembling macroscopic photonic crystals.

Many large proteins suffer from slow or inefficient folding in vitro. It has long been known that this problem can be alleviated in vivo if proteins start folding cotranslationally. However, the molecular mechanisms underlying this improvement have not been well established. To address this question, we use an all-atom simulation-based algorithm to compute the folding properties of various large protein domains as a function of nascent chain length. We find that for certain proteins, there exists a narrow window of lengths that confers both thermodynamic stability and fast folding kinetics. Beyond these lengths, folding is drastically slowed by nonnative interactions involving C-terminal residues. Thus, cotranslational folding is predicted to be beneficial because it allows proteins to take advantage of this optimal window of lengths and thus avoid kinetic traps. Interestingly, many of these proteins’ sequences contain conserved rare codons that may slow down synthesis at this optimal window, suggesting that synthesis rates may be evolutionarily tuned to optimize folding. Using kinetic modeling, we show that under certain conditions, such a slowdown indeed improves cotranslational folding efficiency by giving these nascent chains more time to fold. In contrast, other proteins are predicted not to benefit from cotranslational folding due to a lack of significant nonnative interactions, and indeed these proteins’ sequences lack conserved C-terminal rare codons. Together, these results shed light on the factors that promote proper protein folding in the cell and how biomolecular self-assembly may be optimized evolutionarily.

Atomistic simulations can provide valuable, experimentally-verifiable insights into protein folding mechanisms, but existing ab initio simulation methods are restricted to only the smallest proteins due to severe computational speed limits. The folding of larger proteins has been studied using native-centric potential functions, but such models omit the potentially crucial role of non-native interactions. Here, we present an algorithm, entitled DBFOLD, which can predict folding pathways for a wide range of proteins while accounting for the effects of non-native contacts. In addition, DBFOLD can predict the relative rates of different transitions within a protein’s folding pathway. To accomplish this, rather than directly simulating folding, our method combines equilibrium Monte-Carlo simulations, which deploy enhanced sampling, with unfolding simulations at high temperatures. We show that under certain conditions, trajectories from these two types of simulations can be jointly analyzed to compute unknown folding rates from detailed balance. This requires inferring free energies from the equilibrium simulations, and extrapolating transition rates from the unfolding simulations to lower, physiologically-reasonable temperatures at which the native state is marginally stable. As a proof of principle, we show that our method can accurately predict folding pathways and Monte-Carlo rates for the well-characterized Streptococcal protein G. We then show that our method significantly reduces the amount of computation time required to compute the folding pathways of large, misfolding-prone proteins that lie beyond the reach of existing direct simulation. Our algorithm, which is available online , can generate detailed atomistic models of protein folding mechanisms while shedding light on the role of non-native intermediates which may crucially affect organismal fitness and are frequently implicated in disease.

The field of complex self-assembly is moving toward the design of multiparticle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such “addressable complexity,” we need to understand the factors that optimize the yield and the kinetics of self-assembly. Here we use a simple theoretical method to explain the key features responsible for the unexpected success of DNA-brick experiments, which are currently the only demonstration of reliable self-assembly with such a large number of components. Simulations confirm that our theory accurately predicts the narrow temperature window in which error-free assembly can occur. Even more strikingly, our theory predicts that correct assembly of the complete structure may require a time-dependent experimental protocol. Furthermore, we predict that low coordination numbers result in nonclassical nucleation behavior, which we find to be essential for achieving optimal nucleation kinetics under mild growth conditions. We also show that, rather surprisingly, the use of heterogeneous bond energies improves the nucleation kinetics and in fact appears to be necessary for assembling certain intricate 3D structures. This observation makes it possible to sculpt nucleation pathways by tuning the distribution of interaction strengths. These insights not only suggest how to improve the design of structures based on DNA bricks, but also point the way toward the creation of a much wider class of chemical or colloidal structures with addressable complexity.

DNA-coated colloids can self-assemble into an incredible diversity of crystal structures, but their applications have been limited by poor understanding and control over the crystallization dynamics. To address this challenge, we use microfluidics to quantify the kinetics of DNA-programmed self-assembly along the entire crystallization pathway, from thermally activated nucleation through reaction-limited and diffusion-limited phases of crystal growth. Our detailed measurements of the temperature and concentration dependence of the kinetics at all stages of crystallization provide a stringent test of classical theories of nucleation and growth. After accounting for the finite rolling and sliding rates of micrometer-sized DNA-coated colloids, we show that modified versions of these classical theories predict the absolute nucleation and growth rates with quantitative accuracy. We conclude by applying our model to design and demonstrate protocols for assembling large single crystals with pronounced structural coloration, an essential step in creating next-generation optical metamaterials from colloids.

Most proteins must remain soluble in the cytosol in order to perform their biological functions. To protect against undesired protein aggregation, living cells maintain a population of molecular chaperones that ensure the solubility of the proteome. Here we report simulations of a lattice model of interacting proteins to understand how low concentrations of passive molecular chaperones, such as small heat-shock proteins, suppress thermodynamic instabilities in protein solutions. Given fixed concentrations of chaperones and client proteins, the solubility of the proteome can be increased by tuning the chaperone-client binding strength. Surprisingly, we find that the binding strength that optimizes solubility while preventing irreversible chaperone binding also promotes the formation of weakly bound chaperone oligomers, although the presence of these oligomers does not significantly affect the thermodynamic stability of the solution. Such oligomers are commonly observed in experiments on small heat-shock proteins, but their connection to the biological function of these chaperones has remained unclear. Our simulations suggest that this clustering may not have any essential biological function, but rather emerges as a natural side-effect of optimizing the thermodynamic stability of the proteome.

To optimize a self-assembly reaction, it is essential to understand the factors that govern its pathway. Here, we examine the influence of nucleation pathways in a model system for addressable, multicomponent self-assembly based on a prototypical “DNA-brick” structure. By combining temperature-dependent dynamic light scattering and atomic force microscopy with coarse-grained simulations, we show how subtle changes in the nucleation pathway profoundly affect the yield of the correctly formed structures. In particular, we can increase the range of conditions over which self-assembly occurs by using stable multisubunit clusters that lower the nucleation barrier for assembling subunits in the interior of the structure. Consequently, modifying only a small portion of a structure is sufficient to optimize its assembly. Due to the generality of our coarse-grained model and the excellent agreement that we find with our experimental results, the design principles reported here are likely to apply generically to addressable, multicomponent self-assembly.

Phase separation in polymer solutions often correlates with single-chain and two-chain properties, such as the single-chain radius of gyration, , and the pairwise second virial coefficient, . However, recent studies have shown that these metrics can fail to distinguish phase-separating from non-phase-separating heteropolymers, including intrinsically disordered proteins (IDPs). Here we introduce an approach to predict heteropolymer phase separation from two-chain simulations by analyzing contact maps, which capture how often specific monomers from the two chains are in physical proximity. Whereas summarizes the overall attraction between two chains, contact maps preserve spatial information about their interactions. To compare these metrics, we train phase-separation classifiers for both a minimal heteropolymer model and a chemically specific, residue-level IDP model. Remarkably, simple statistical properties of two-chain contact maps predict phase separation with high accuracy, vastly outperforming classifiers based on and alone. Our results thus establish a transferable and computationally efficient method to uncover key driving forces of IDP phase behavior based on their physical interactions in dilute solution.

Phase separation in biomolecular mixtures can result from multiple physical interactions, which may act either complementarily or antagonistically. In the case of protein-nucleic acid mixtures, charge plays a key role but can have contrasting effects on phase behavior. Attractive electrostatic interactions between oppositely charged macromolecules are screened by added salt, reducing the driving force for coacervation. By contrast, base-pairing interactions between nucleic acids are diminished by charge repulsion and thus enhanced by added salt, promoting associative phase separation. To explore this interplay, we combine experiment and theory to map the complex phase behavior of a model solution of poly-L-lysine (PLL) and self-complementary DNA nanostars (NS) as a function of temperature, ionic strength, and macromolecular composition. Despite having opposite salt dependences, we find that electrostatics and base pairing cooperate to stabilize NS-PLL coacervation at high ionic strengths and temperatures, leading to two-phase or three-phase coexistence under various conditions. We further observe a variety of kinetic pathways to phase separation at different salt concentrations, resulting in the formation of nonequilibrium aggregates or droplets whose compositions evolve on long timescales. Finally, we show that the cooperativity between electrostatics and base pairing can be used to create multiphase coacervates that partition various NS species at intermediate salt concentrations. Our results illustrate how the interplay between distinct interaction modes can greatly increase the complexity of the phase behavior relative to systems with a single type of interaction.