Niall M. Mangan

Abstract Advances in DNA sequencing and machine learning are providing insights into protein sequences and structures on an enormous scale 1 . However, the energetics driving folding are invisible in these structures and remain largely unknown 2 . The hidden thermodynamics of folding can drive disease 3,4 , shape protein evolution 5–7 and guide protein engineering 8–10 , and new approaches are needed to reveal these thermodynamics for every sequence and structure. Here we present cDNA display proteolysis, a method for measuring thermodynamic folding stability for up to 900,000 protein domains in a one-week experiment. From 1.8 million measurements in total, we curated a set of around 776,000 high-quality folding stabilities covering all single amino acid variants and selected double mutants of 331 natural and 148 de novo designed protein domains 40–72 amino acids in length. Using this extensive dataset, we quantified (1) environmental factors influencing amino acid fitness, (2) thermodynamic couplings (including unexpected interactions) between protein sites, and (3) the global divergence between evolutionary amino acid usage and protein folding stability. We also examined how our approach could identify stability determinants in designed proteins and evaluate design methods. The cDNA display proteolysis method is fast, accurate and uniquely scalable, and promises to reveal the quantitative rules for how amino acid sequences encode folding stability.

Many carbon-fixing bacteria rely on a CO2 concentrating mechanism (CCM) to elevate the CO2 concentration around the carboxylating enzyme ribulose bisphosphate carboxylase/oxygenase (RuBisCO). The CCM is postulated to simultaneously enhance the rate of carboxylation and minimize oxygenation, a competitive reaction with O2 also catalyzed by RuBisCO. To achieve this effect, the CCM combines two features: active transport of inorganic carbon into the cell and colocalization of carbonic anhydrase and RuBisCO inside proteinaceous microcompartments called carboxysomes. Understanding the significance of the various CCM components requires reconciling biochemical intuition with a quantitative description of the system. To this end, we have developed a mathematical model of the CCM to analyze its energetic costs and the inherent intertwining of physiology and pH. We find that intracellular pH greatly affects the cost of inorganic carbon accumulation. At low pH the inorganic carbon pool contains more of the highly cell-permeable H2CO3, necessitating a substantial expenditure of energy on transport to maintain internal inorganic carbon levels. An intracellular pH ≈8 reduces leakage, making the CCM significantly more energetically efficient. This pH prediction coincides well with our measurement of intracellular pH in a model cyanobacterium. We also demonstrate that CO2 retention in the carboxysome is necessary, whereas selective uptake of HCO3 (-) into the carboxysome would not appreciably enhance energetic efficiency. Altogether, integration of pH produces a model that is quantitatively consistent with cyanobacterial physiology, emphasizing that pH cannot be neglected when describing biological systems interacting with inorganic carbon pools.

Abstract Many eukaryotic photosynthetic organisms enhance their carbon uptake by supplying concentrated CO 2 to the CO 2 -fixing enzyme Rubisco in an organelle called the pyrenoid. Ongoing efforts seek to engineer this pyrenoid-based CO 2 -concentrating mechanism (PCCM) into crops to increase yields. Here we develop a computational model for a PCCM on the basis of the postulated mechanism in the green alga Chlamydomonas reinhardtii . Our model recapitulates all Chlamydomonas PCCM-deficient mutant phenotypes and yields general biophysical principles underlying the PCCM. We show that an effective and energetically efficient PCCM requires a physical barrier to reduce pyrenoid CO 2 leakage, as well as proper enzyme localization to reduce futile cycling between CO 2 and HCO 3 − . Importantly, our model demonstrates the feasibility of a purely passive CO 2 uptake strategy at air-level CO 2 , while active HCO 3 − uptake proves advantageous at lower CO 2 levels. We propose a four-step engineering path to increase the rate of CO 2 fixation in the plant chloroplast up to threefold at a theoretical cost of only 1.3 ATP per CO 2 fixed, thereby offering a framework to guide the engineering of a PCCM into land plants.

We show that periodically driven superconducting vortices in the presence of quenched disorder exhibit a transition from reversible to irreversible flow under increasing vortex density or cycle period. This type of behavior has recently been observed for periodically sheared colloidal suspensions and we demonstrate that driven vortex systems exhibit remarkably similar behavior. We also provide evidence that the onset of irreversible behavior is a dynamical phase transition.

The spatial organization of metabolism is common to all domains of life. Enteric and other bacteria use subcellular organelles known as bacterial microcompartments to spatially organize the metabolism of pathogenicity-relevant carbon sources, such as 1,2-propanediol. The organelles are thought to sequester a private cofactor pool, minimize the effects of toxic intermediates, and enhance flux through the encapsulated metabolic pathways. We develop a mathematical model of the function of the 1,2-propanediol utilization microcompartment of Salmonella enterica and use it to analyze the function of the microcompartment organelles in detail. Our model makes accurate estimates of doubling times based on an optimized compartment shell permeability determined by maximizing metabolic flux in the model. The compartments function primarily to decouple cytosolic intermediate concentrations from the concentrations in the microcompartment, allowing significant enhancement in pathway flux by the generation of large concentration gradients across the microcompartment shell. We find that selective permeability of the microcompartment shell is not absolutely necessary, but is often beneficial in establishing this intermediate-trapping function. Our findings also implicate active transport of the 1,2-propanediol substrate under conditions of low external substrate concentration, and we present a mathematical bound, in terms of external 1,2-propanediol substrate concentration and diffusive rates, on when active transport of the substrate is advantageous. By allowing us to predict experimentally inaccessible aspects of microcompartment function, such as intra-microcompartment metabolite concentrations, our model presents avenues for future research and underscores the importance of carefully considering changes in external metabolite concentrations and other conditions during batch cultures. Our results also suggest that the encapsulation of heterologous pathways in bacterial microcompartments might yield significant benefits for pathway flux, as well as for toxicity mitigation.