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In this paper we view the folding of polynucleotide (RNA) sequences as a map that assigns to each sequence a minimum free energy pattern of base pairings, known as secondary structure. Considering only the free energy leads to an energy landscape over the sequence space. Taking into account structure generates a less visualizable non-scalar \landscape", where a sequence space is mapped into a space of discrete \shapes". We investigate the statistical features of both types of landscapes by computing autocorrelation functions, as well as distributions of energy and structure distances, as a function of distance in sequence space. RNA folding is characterized by very short structure correlation lengths compared to the diameter of the sequence space. The correlation lengths depend strongly on the size and the pairing rules of the underlying nucleotide alphabet. Our data suggest that almost every minimum free energy structure is found within a small neighborhood of any random sequence. The interest in such landscape results from the fact that they govern natural and arti cial processes of optimization by mutation and selection. Simple statistical model landscapes, like Kau man's n-k model, are often used as a proxy for understanding realistic landscapes, like those induced by RNA folding. We make a detailed comparison between the energy landscapes derived from RNA folding and those obtained from the n-k model. We derive autocorrelation functions for several variants of the n-k model, and brie y summarize work on its ne structure. The comparison leads to an estimate for k = 7 to 8, independent of n, where n is the chain length. While the scaling behaviors agree, the ne structure is considerably di erent in the two cases. The reason is seen to be the extremely high frequency of neutral neighbors, that is: neighbors with identical energy (and structure), in the RNA case.

Packaging is often criticized as a symbol of today’s throwaway society, as it is mostly made of plastic, which is in itself quite controversial, and is usually used only once. However, as packaging’s main function is to protect its content and 30% of all food produced worldwide is lost or wasted along the supply chain, optimized packaging may be one of the solutions to reduce this staggering amount. Developing countries struggle with losses in the supply chain before food reaches the consumer. Here, appropriate packaging may help to protect food and prolong its shelf life so that it safely reaches these households. In developed countries, food tends to be wasted rather at the household’s level due to wasteful behavior. There, packaging may be one of the drivers due to inappropriate packaging sizes and packaging that is difficult to empty. When discussing the sustainability of packaging, its protective function is often neglected and only revolves around the type and amount of material used for production. In this review, drivers, issues, and implications of packaging-related food losses and waste (FLW) are discussed, as well as the implication for the implementation in life cycle assessments (LCA).

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Food packaging helps to protect food from being lost or wasted, nevertheless it is perceived as an environmental problem. The present study gives an overview of methods to assess the environmental sustainability of food packaging. Furthermore, we propose a methodological framework for environmental assessment of food packaging. There is a broad consensus on the definition of sustainable packaging, which has to be effective, efficient, and safe for human health and the environment. Existing frameworks only provide general guidance on how to quantify the environmental sustainability of packaging. Our proposed framework defines three sustainability aspects of food packaging, namely direct environmental effects of packaging, packaging-related food losses and waste, as well as circularity. It provides a list of key environmental performance indicators and recommends certain calculation procedures for each indicator. The framework is oriented towards the Product Environmental Footprint initiative and the Circular Economy Package of the European Union. Further research should develop a method to determine the amount of packaging-related food losses and waste. Moreover, future studies should examine the potential environmental benefits of different measures to make food packaging more circular.