Biomolecular condensates appear throughout the cell serving a wide variety of functions. Many condensates appear to form by the assembly of multivalent molecules, which produce phase-separated networks with liquidlike properties. These networks then recruit client molecules, with the total composition providing functionality. Here we use a model system of poly-SUMO and poly-SIM proteins to understand client−network interactions and find that the structure of the network plays a strong role in defining client recruitment and thus functionality. The basic unit of assembly in this system is a zipperlike filament composed of alternating poly-SUMO and poly-SIM molecules. These filaments have defects of unsatisfied bonds that allow for both the formation of a 3D network and the recruitment of clients. The filamentous structure constrains the scaffold stoichiometries and the distribution of client recruitment sites that the network can accommodate. This results in a nonmonotonic client binding response that can be tuned independently by the client valence and binding energy. These results show how the interactions within liquid states can be disordered yet still contain structural features that provide functionality to the condensate.

The United States (US) is the largest alfalfa (Medicago sativa L.) producer in the world. More than 44% of the US alfalfa is produced under rainfed conditions, although it requires a relatively high amount of water compared to major field crops. Considering that yield and production of rainfed alfalfa have been relatively stagnant in the country for decades, there is a need to better understand the magnitude of yield loss due to water limitation and how far from yield potential current yields are. In this context, the main objective of this study was to estimate the current yield gap of rainfed alfalfa in the US. We collected 10 year (2009–2018) county-level government-reported yield and weather data from 393 counties within 12 major US rainfed alfalfa producing states and delineated alfalfa growing season using probabilistic approaches based on temperature thresholds for crop development. We then calculated county-level growing season rainfall (GSR), which was plotted against county-level yield to determine attainable yield (Ya) using frontier function analysis, and water-limited potential yield (Yw) using boundary function analysis. Average and potential water use efficiencies (WUE) were estimated, and associated yield gap referring to attainable (YGa) or water-limited yields (YGw) were calculated. Finally, we used conditional inference trees (CIT) to identify major weather-related yield-limiting factors to alfalfa forage yield. The frontier model predicted a mean Ya of 9.6 ± 1.5 Mg ha−1 and an associated optimum GSR of 670 mm, resulting in a mean YGa of 34%. The boundary function suggested a mean Yw of 15.3 ± 3 Mg ha−1 at the mean GSR of 672 ± 153 mm, resulting in a mean yield gap of 58%. The potential alfalfa WUE was 30 kg ha−1 mm−1 with associated minimum water losses of 24% of mean GSR, which was three times greater than the mean WUE of 10 kg ha−1 mm−1. The CIT suggested that GSR and minimum temperature in the season were the main yield-limiting weather variables in rainfed alfalfa production in the US. Our study also revealed that alfalfa was only limited by water availability in 21% of the environments. Thus, future research on management practices to narrow yield gaps at current levels of water supply is necessary.

Biomolecular condensates appear throughout the cell serving a wide variety of functions. Many condensates appear to form by the assembly of multivalent molecules, which produce phase separated networks with liquid-like properties. These networks then recruit client molecules, with the total composition providing functionality. Here we use a model system of poly-SUMO and poly-SIM proteins to understand client-network interactions and find that the structure of the network plays a strong role in defining client recruitment, and thus functionality. The basic unit of assembly in this system is a zipper-like filament composed of alternating poly-SUMO and poly-SIM molecules.These filaments have defects of unsatisfied bonds that allow for both the formation of a 3D network and the recruitment of clients. The filamentous structure constrains the scaffold stoichiometries and the distribution of client recruitment sites that the network can accommodate. This results in a non-monotonic client binding response that can be tuned independently by the client valence and binding energy. These results show how the interactions within liquid states can be disordered yet still contain structural features that provide functionality to the condensate. I. INTRODUCTIONMany cellular structures have been shown to form by the spontaneous condensation of biomolecules into liquidlike states [1,2], often through liquid-liquid phase transitions. While these condensates may contain hundreds of different molecules, typically only a small number of molecules with high interaction valence and high connectivity to other molecules in the structure contribute strongly to phase separation [3][4][5]. These are said to have scaffoldlike properties depending on how strongly they promote phase separation. The remaining molecules, which exhibit client-like properties, are recruited through interactions with scaffolds [6,7]. Together, the collection of molecules in a condensate determines its functionality.Since the molecules driving phase separation are multivalent, polymer-like species, many treatments of condensate formation are based on polymer theories [8][9][10][11]. In particular, scaffold condensation can be understood as the interaction between attractive stickers separated by inert spacers [11,12]. These efforts explain universal features of condensates, such as how multivalency can amplify the effect of weak interactions to tune the phase coexistence line to within physiologically relevant regions of phase space (e.g. physiological concentrations) [8]. However, there are also many non-universal features of biomolecular condensates. Experiments are revealing a striking diversity of functions performed by condensates [2,7,[13][14][15][16], and each of these assemblies will be under evolutionary pressure to optimize its specific function. This begs the question of how the disordered network of interactions within a liquid structure can affect its properties.

The yield and production of alfalfa (Medicago sativa L.) have not been significantly improved in Kansas for the last 30 years even though farmers are using improved varieties. We have noted a significant yield difference between average alfalfa yield reported by farmers and researchers. The magnitude of yield gap in Kansas and its underlying factors are still unknown. Thus, understanding of potential yield is essential to meet the future forage demand with the limited production resources. The main objective of this study was, therefore, to quantify the current yield gap and identify the main yield-limiting factor for rainfed alfalfa grown in Kansas. To achieve this objective, we selected 24 counties in Kansas based on the rainfed production area and total production, and used county-level yield, daily temperature, and rainfall data from the past 30 yrs (1988–2017) of those selected counties. We applied four statistical approaches: (i) probability distribution function to delineate county-level alfalfa growing season, (ii) stochastic frontier yield function to estimate optimum growing season rainfall (GSR) and attainable yield, (iii) linear boundary function to estimate minimum water loss, water use efficiency, and water-limited potential yield, and (iv) conditional inference tree to identify the major yield contributing weather variables. The probability distribution function delineated the alfalfa growing season starting from mid-March to mid-November in Kansas. The frontier model estimated the attainable yield of 9.2 Mg ha−1 at an optimum GSR of 664 mm, generating a current yield gap of 18%. The linear boundary function estimated the water-limited potential yield of 15.5 Mg ha−1 at an existing GSR of 624 mm, generating a yield gap of 50%. The conditional inference tree revealed that 24% of the variation in rainfed alfalfa yield in Kansas was explained by weather variables, mainly due to GSR followed minimum temperature. However, we found only 7% GSR deficit in the study area, indicating that GSR is not the only cause for such a wide yield gap. Thus, further investigation of other yield-limiting management factors is essential to minimize the current yield gap. The statistical models used in this study might be particularly useful when yield estimation using remote sensing and crop simulation models are not applicable in terms of time, resources, facilities, and investments.