Background: Cellular functions are accomplished by the concerted actions of functional modules. The mechanisms driving the emergence and evolution of these modules are still unclear. Here we investigate the evolutionary origins of protein complexes, modules in physical protein-protein interaction networks. Results: We studied protein complexes in Saccharomyces cerevisiae, complexes of known three-dimensional structure in the Protein Data Bank and clusters of pairwise protein interactions in the networks of several organisms. We found that duplication of homomeric interactions, a large class of protein interactions, frequently results in the formation of complexes of paralogous proteins. This route is a common mechanism for the evolution of complexes and clusters of protein interactions. Our conclusions are further confirmed by theoretical modelling of network evolution. We propose reasons for why this is favourable in terms of structure and function of protein complexes. Conclusion: Our study provides the first insight into the evolution of functional modularity in protein-protein interaction networks, and the origins of a large class of protein complexes.

The epidemic spread of infectious diseases is ubiquitous and often has a considerable impact on public health and economic wealth. The large variability in the spatio-temporal patterns of epidemics prohibits simple interventions and requires a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, we introduce a mathematical framework which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution, both in disease prevalence and transmission network topology, is derived from a closed set of partial differential equations for infections without allowing for recovery. The predictions are in excellent agreement with complementarily conducted agent-based simulations. The capacity of this new method is demonstrated in several case studies on HIV epidemics in synthetic populations: it allows us to monitor the evolution of contact behavior among healthy and infected individuals and the contributions of different disease stages to the spreading of the epidemic. This gives both direction to and a test bed for targeted intervention strategies for epidemic control. In conclusion, this mathematical framework provides a capable toolbox for the analysis of epidemics from first principles. This allows for fast, in silico modeling - and manipulation - of epidemics and is especially powerful if complemented with adequate empirical data for parameterization. The way potentially infectious contacts are made strongly influences how fast and how widely epidemics spread in their host population. Therefore, it is important to assess changes in contact behavior throughout an epidemic; these may occur due to external factors, such as demographic change, or as a side effect of the epidemic itself, leading to an accumulation of individuals with risky behavior in the infected population. We have developed a mathematical framework that allows for the study of the mutual interdependencies between epidemic spread and changes in contact behavior. The method is used to study HIV epidemics in model populations. We address the question of whether HIV is primarily spread by highly contagious initially infected hosts or by less contagious latently infected hosts who will, however, encounter more situations for potential transmission. The answer to this question strongly depends on the concurrency of contacts and the maturation stage of the epidemic. Initially infected hosts are major epidemic spreaders in populations with strongly concurrent contacts and during epidemic expansion whereas otherwise latently infected hosts play a more important role. The availability of better data for parameterization will make this approach relevant for public health considerations.

The contact structure between hosts shapes disease spread. Most network-based models used in epidemiology tend to ignore heterogeneity in the weighting of contacts between two individuals. However, this assumption is known to be at odds with the data for many networks (e.g. sexual contact networks) and to have a critical influence on epidemics' behavior. One of the reasons why models usually ignore heterogeneity in transmission is that we currently lack tools to analyze weighted networks, such that most studies rely on numerical simulations. Here, we present a novel framework to estimate key epidemiological variables, such as the rate of early epidemic expansion ( ) and the basic reproductive ratio ( ), from joint probability distributions of number of partners (contacts) and number of interaction events through which contacts are weighted. These distributions are much easier to infer than the exact shape of the network, which makes the approach widely applicable. The framework also allows for a derivation of the full time course of epidemic prevalence and contact behaviour, which we validate with numerical simulations on networks. Overall, incorporating more realistic contact networks into epidemiological models can improve our understanding of the emergence and spread of infectious diseases. Understanding how infectious diseases spread has public health and ecological implications. The contact structure between hosts strongly affects this spread. However, most studies assume that all types of contacts are identical, when in reality some individuals interact more strongly than others. This is particularly striking for sexual-contact networks, where the number of sex acts is not identical for all partnerships. This heterogeneity in activity can either speed up or slow down epidemic spread depending on how strongly the individuals' number of contacts coincides with their activity. There are two limitations to current frameworks that can explain the lack of studies on weighted networks. First, analytical results are difficult to obtain, which requires numerical simulations. Second, inferring weighted networks from survey data is extremely difficult. Here, we present a novel framework that allows to alleviate these two limitations. Building on configuration type network epidemic approaches, we manage to capture disease spread on weighted networks from the distribution of the number of contacts and distribution of the number of interaction events (e.g. sex acts). This allows us to derive analytical estimates for the epidemic threshold and the rate of spread of the disease. It also allows us to readily incorporate survey data, as illustrated in this study with data from the National Survey of Sexual Attitudes and Lifestyles (NATSAL) carried out in the UK.

Coevolution of two coupled quasispecies is studied, motivated by the competition between viral evolution and adapting immune response. In this coadaptive model, besides the classical error catastrophe for high virus mutation rates, a second “adaptation” catastrophe occurs, when virus mutation rates are too small to escape immune attack. Maximizing both regimes of viral error catastrophes is a possible strategy for an optimal immune response, reducing the range of allowed viral mutation rates to a minimum. From this requirement, one obtains constraints on B-cell mutation rates and receptor lengths, yielding an estimate of somatic hypermutation rates in the germinal center in accordance with observation.

Heterologously expressed genes require adaptation to the host organism to ensure adequate levels of protein synthesis, which is typically approached by replacing codons by the target organism’s preferred codons. In view of frequently encountered suboptimal outcomes we introduce the codon-specific elongation model (COSEM) as an alternative concept. COSEM simulates ribosome dynamics during mRNA translation and informs about protein synthesis rates per mRNA in an organism- and context-dependent way. Protein synthesis rates from COSEM are integrated with further relevant covariates such as translation accuracy into a protein expression score that we use for codon optimization. The scoring algorithm further enables fine-tuning of protein expression including deoptimization and is implemented in the software OCTOPOS. The protein expression score produces competitive predictions on proteomic data from prokaryotic, eukaryotic, and human expression systems. In addition, we optimized and tested heterologous expression of manA and ova genes in Salmonella enterica serovar Typhimurium. Superiority over standard methodology was demonstrated by a threefold increase in protein yield compared to wildtype and commercially optimized sequences.