Discovering optimal kinetic pathways for self-assembly using automatic differentiation.

Macromolecular complexes are often composed of diverse subunits. The self-assembly of these subunits is inherently nonequilibrium and must avoid kinetic traps to achieve high yield over feasible timescales. We show how the kinetics of self-assembly benefits from diversity in subunits because it generates an expansive parameter space that naturally improves the "expressivity" of self-assembly, much like a deeper neural network. By using automatic differentiation algorithms commonly used in deep learning, we searched the parameter spaces of mass-action kinetic models to identify classes of kinetic protocols that mimic biological solutions for productive self-assembly. Our results reveal how high-yield complexes that easily become kinetically trapped in incomplete intermediates can instead be steered by internal design of rate-constants or external and active control of subunits to efficiently assemble. Internal design of a hierarchy of subunit binding rates generates self-assembly that can robustly avoid kinetic traps for all concentrations and energetics, but it places strict constraints on selection of relative rates. External control via subunit titration is more versatile, avoiding kinetic traps for any system without requiring molecular engineering of binding rates, albeit less efficiently and robustly. We derive theoretical expressions for the timescales of kinetic traps, and we demonstrate our optimization method applies not just for design but inference, extracting intersubunit binding rates from observations of yield-vs.-time for a heterotetramer. Overall, we identify optimal kinetic protocols for self-assembly as a powerful mechanism to achieve efficient and high-yield assembly in synthetic systems whether robustness or ease of "designability" is preferred.

Discovering optimal kinetic pathways for self-assembly using automatic differentiation.

During self-assembly of macromolecules ranging from ribosomes to viral capsids, the formation of long-lived intermediates or kinetic traps can dramatically reduce yield of the functional products. Understanding biological mechanisms for avoiding traps and efficiently assembling is essential for designing synthetic assembly systems, but learning optimal solutions requires numerical searches in high-dimensional parameter spaces. Here, we exploit powerful automatic differentiation algorithms commonly employed by deep learning frameworks to optimize physical models of reversible self-assembly, discovering diverse solutions in the space of rate constants for 3-7 subunit complexes. We define two biologically-inspired protocols that prevent kinetic trapping through either internal design of subunit binding kinetics or external design of subunit titration in time. Our third protocol acts to recycle intermediates, mimicking energy-consuming enzymes. Preventative solutions via interface design are the most efficient and scale better with more subunits, but external control via titration or recycling are effective even for poorly evolved binding kinetics. Whilst all protocols can produce good solutions, diverse subunits always helps; these complexes access more efficient solutions when following external control protocols, and are simpler to design for internal control, as molecular interfaces do not need modification during assembly given sufficient variation in dimerization rates. Our results identify universal scaling in the cost of kinetic trapping, and provide multiple strategies for eliminating trapping and maximizing assembly yield across large parameter spaces.

Temporal control by cofactors prevents kinetic trapping in retroviral Gag lattice assembly.

For retroviruses like HIV to proliferate, they must form virions shaped by the self-assembly of Gag polyproteins into a rigid lattice. This immature Gag lattice has been structurally characterized and reconstituted in vitro, revealing the sensitivity of lattice assembly to multiple cofactors. Due to this sensitivity, the energetic criterion for forming stable lattices is unknown, as are their corresponding rates. Here, we use a reaction-diffusion model designed from the cryo-ET structure of the immature Gag lattice to map a phase diagram of assembly outcomes controlled by experimentally constrained rates and free energies, over experimentally relevant timescales. We find that productive assembly of complete lattices in bulk solution is extraordinarily difficult due to the large size of this ∼3700 monomer complex. Multiple Gag lattices nucleate before growth can complete, resulting in loss of free monomers and frequent kinetic trapping. We therefore derive a time-dependent protocol to titrate or "activate" the Gag monomers slowly within the solution volume, mimicking the biological roles of cofactors. This general strategy works remarkably well, yielding productive growth of self-assembled lattices for multiple interaction strengths and binding rates. By comparing to the in vitro assembly kinetics, we can estimate bounds on rates of Gag binding to Gag and the cellular cofactor IP6. Our results show that Gag binding to IP6 can provide the additional time delay necessary to support smooth growth of the immature lattice with relatively fast assembly kinetics, mostly avoiding kinetic traps. Our work provides a foundation for predicting and disrupting formation of the immature Gag lattice via targeting specific protein-protein binding interactions.

Prophylactic lithium alleviates splenectomy-induced cognitive dysfunction possibly by inhibiting hippocampal TLR4 activation in aged rats.

Though the pathogenesis of postoperative cognitive dysfunction (POCD) remains unclear, evidence is accumulating for a pivotal role of neuroinflammation in the disease process. Advanced age and severe surgical trauma are two main risk factors for POCD. Lithium, a neuroprotective agent, can alleviate peripheral surgery-induced memory impairment in aged rats. The results of in vivo and in vitro experiments also showed that toll like receptor 4 (TLR4) was associated with the occurrence and development of neuroinflammation and POCD. So we hypothesized that inhibition of TLR4 signaling in the hippocampus maybe involved in the protective effects of prophylactic lithium on the occurrence of inflammation and POCD. In the present study, we incubated BV-2 microglia with 1µg/ml lipopolysaccharide (LPS) to mimic neuroinflammation in vitro. We found that pretreatment with 10mM of lithium or 100nM of TLR4 siRNA could inhibit the tumor necrosis factor (TNF)-α and TLR4 mRNA expression induced by LPS in BV-2 microglia. Furthermore, combination of prophylactic lithium and TLR4 siRNA even decreased their mRNA expression to the baseline levels, which showed that TLR4 signaling may be vital in protective effects of prophylactic lithium on neuroinflammation. So we further undergone the in vivo experiment. Then, we firstly demonstrated that prophylactic 2mM/kg of lithium alleviated splenectomy-induced cognitive impairments, decreased splenectomy-associated systemic, central, and hippocampal TNF-α and interleukin (IL)-1ß expression and reduced the increase of CD11b(+) area in hippocampal CA1 region caused by the surgery. Then, we also found that splenectomy merely increased hippocampal TLR2 and TLR4 mRNA levels in aged rats. At last, we confirmed that prophylactic lithium reduced the increased levels of hippocampal TLR4/NF-κB induced by splenectomy. Taken together, these results demonstrate that TLR4 signaling inactivation may contribute to the protective effects of prophylactic lithium on the occurrence of POCD by inhibiting systemic inflammation and especially neuroinflammation.