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J Mol Evol. An S-RNase-based gametophytic self-incompatibility system evolved only once in eudicots.

A framework for evolutionary systems biology

Genetics Genetic and molecular characterization of three novel S -haplotypes in sour cherry Prunus cerasus L. J Exp Bot. RNase based gametophytic self-incompatibility evolution: questioning the hypothesis of multiple independent recruitments of the S -pollen gene.

J Mol Biol. Evolutionary patterns at the RNase based gametophytic self - incompatibility system in two divergent Rosaceae groups Maloideae and Prunus.

Systems Biology - Evolutionary games

It allows the measurement of phenotypic selection in the wild [ , , ], but does not facilitate the incorporation of molecular functional data [ , ] and depends on phenotypic traits following approximately a Normal distribution after an appropriate transformation [ , ]. Building on Lande's approach, Arnold used path analysis to decompose fitness into fitness components that are determined by functional phenotypic traits [ , — ]. A central component in this approach is the so-called 'G-matrix' that measures the additive genetic variance and covariance of phenotypic traits encoded by many genes.

The G-matrix could be used to predict evolution if the evolutionary dynamics of the G-matrix were known, a problem too complex for existing analytic theory [ ]. A potential way forward could be to integrate these quantitative genetics approaches with the various molecular and current systems biology levels of the adaptive landscape described below.

Indeed, to connect adaptive landscapes to observable molecular functional data, recent work has considered the adaptive landscapes of single proteins and more complex molecular systems [ 91 , , , , 95 ]. The ideal connection of an adaptive landscape to biological data would predict the height by ab initio calculations from observed data and then compare predicted and observed heights.

To subdivide this extraordinarily difficult problem into smaller but still formidable tasks, I define different levels of the adaptive landscape, each with its own height and plane definitions Table 2. To resynthesise the big picture from these levels , one needs to combine all heights of each lower-level landscape to define a point in the plane of the corresponding higher-level landscape.

Mathematically speaking, each level is defined as a function that computes the height for many points in the plane , where each dimension corresponds to a parameter.


Thus for each level:. Combining two levels often requires many evaluations of heights at the lower level to define the plane of the higher level subscripts denote levels :. Since the mathematical formalisms can handle many dimensions in principle, no information is lost, even if it is not possible to visualise the landscapes. When defining such formalisms, one must ensure compatibility between lower-level output and higher-level input. Ignoring environmental changes for the moment, I propose the following seven levels of adaptive landscapes:.

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Successes : General knowledge about mutational effects on proteins [ , ] and structural predictions have been used successfully to detect deleterious mutations [ , ]. Ab initio modelling remains very challenging, despite decades of research [ ]. No insight into the relative importance of mutations in different genes can be obtained. Outlook : A combination of experiments, ab initio modelling and comparative modelling will lead to even more confident prediction tools.

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If only approximate functional rates are required, then experimental methods can provide a shortcut through this and the next level see next level. Data : Direct predictions of functions from structures [ — ] have been developed only recently for proteins using computational methods that build on experimental data. Generally, databases of kinetic measurements [ , ] are growing and if functional effects of mutations are large enough, they can be measured in experiments or observed while evolving in vitro [ — ].

It is also possible to observe protein functions in the form of aggregated rate laws that measure the speed of a group of reactions and can be used to narrow the range of plausible parameters for individual reactions by computational analyses [ ]. Research into structure-function relationships and protein engineering [ ] has matured to the point where some functional properties are amendable by engineering [ , ]. Mutation accumulation experiments can be used to assess the impact of spontaneous mutations on gene regulation [ ]. Having additional copies of genes might affect the intracellular concentration of their proteins [ , — ] and possibly also metabolic flux [ , ].

Successes : In principle it is now possible to extrapolate from known kinetic rates and known protein structures to unknown kinetic rates that employ the same functional mechanism [ ]. Limits : If ab initio predictions of molecular structures are challenging [ ], they are even more so for molecular functions. The new comparative methods have not yet been tested in many different systems. Outlook : Experimental methods allow shortcutting of this and the previous level by providing a direct kinetic measurement associated with a known sequence [ — ], although very small differences can be impossible to distinguish.

The combination of proteomics techniques with the knowledge of reaction networks promises the estimation of a credible range of individual reaction rates for many enzymes from the observation of aggregated rate laws [ ]. Progress on computational methods is impressive [ — ] and could lead to the possibility of routinely predicting small mutational effects on function with some confidence.

Growing knowledge in protein design will lead to more confidence in understanding adaptive landscapes at this level [ 91 , , ]. It is currently not clear, whether computational or experimental approaches will be more efficient in addressing the very hard problem of obtaining kinetic parameters on a massive scale. This level is special as it could also be seen as encapsulating many more fine-grained sublevels that mirror the hierarchical organisation of many organisms. For example, molecular functions affect the properties of a cell, which affect the properties of a tissue, which affect the properties of an organ, which affect the properties of an organism which affect the fitness correlates in level 4.

The best choice of sublevels depends on the structure of the multi-level systems biology models considered e. If the primary adaptive landscape under investigation depends on lower-level units of replication [ ] with their own adaptive landscapes, then these can be accommodated as additional sublevels here. Such 'nested landscapes' help, for example, understanding the conflicts of selection in cancer [ , ]. Key question : How do changes in macromolecular function affect the emergent properties of the whole system?

Data : The computing of systemic functions is the goal of systems biology modelling, hence many such models have been constructed recently [ 11 , 13 , 31 , , — ]. Some of their emergent properties can be determined experimentally [ 11 , 13 , , ] and can be used to improve the models. Some biochemical networks have a special function during development and their analysis has become increasingly mechanistic e. The realisation of the importance of such networks for the evolution of morphological features has fuelled the rise of 'evo-devo', which combines evolutionary biology and developmental biology [ — , — ].

The quality of all computational models at this level is important for further analyses that build on corresponding output. Quality here is hard to measure but will mostly reflect the quantitative accuracy, which in many cases requires the completeness of the mechanistic model. Successes : It is easy to test the sensitivity of many systems biology models with regard to changes in various molecular kinetic parameters.

Comparative analyses have shown that some universal properties might exist [ ]. Experimental confirmation of some predictions are possible [ 11 , 13 , , , 9 ]. Successful modelling has been achieved in systems as diverse as metabolic reaction systems [ 9 ] and developmental modules [ — ]. Limits : Computational complexity and poorly known parameters frequently limit the accuracy of computational systems biology models [ 26 ]. Outlook : Excitement about and investments in current systems biology [ , ] provide reason for hoping that many more high quality systems biology models will be developed to serve as a basis for predicting the emergent properties of molecular, tissue and organismal systems.

These can also be seen as quantitative traits. Key question : How do observable fitness correlates depend on other emergent properties of the system? The goal is to define computable fitness correlates that are directly proportional to observable fitness correlates. Data : A functional understanding of the system and the mechanistic basis for observable fitness correlates serves as the basis for defining this level of the adaptive landscape.

Such understanding was experimentally confirmed in some systems [ 13 , , , 9 ] see discussion of fitness correlates below. Independent theory : A longstanding question in evolutionary theory has been, how fitness depends on various quantitative traits that could be viewed as dimensions in the emerging-property-space. A rich body of quantitative genetics theory has been developed to predict fitness effects from changes in an underlying multi-dimensional adaptive quantitative trait space [ 45 , — , , , , — , — ].

Despite the absence of detailed biochemical information, such work can have experimental predictive power [ ], might infer the effective number of 'molecular phenotypes' of a gene from DNA sequences [ ] and could be used to decompose fitness correlates into functional components [ , — ]. Advances in quantitative genetics methods also allow the estimation of selection on fitness correlates in the wild [ ] and the identification of quantitative trait loci if their impact on phenotypic properties is large enough [ ]. Such work does not require a mechanistic understanding of the traits as would be gained from quantifying levels 1 — 3 above.

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While this limits the direct applicability of quantitative genetics approaches, one could use the experience with quantitative traits to inspire the definition of computable fitness correlates. Successes : Computable fitness correlates can be defined in metabolic networks with the help of flux balance analysis models [ 9 ] and in circadian clocks using other approaches [ ]. The former are supported by experiments [ 13 , 16 , , 9 ]. Observations also confirm predictions from abstract general models that map quantitative traits to fitness [ ].

enter site Limits : To provide a good mapping of the adaptive landscape at this level, one either needs a thorough mechanistic understanding of the corresponding fitness correlates or a firm grasp of a general theory that allows for reasonable predictions in the presence of many poorly known interactions. Neither may be easy to obtain for some systems.

Testing the accuracy of a given mapping with the help of the Linear Fitness Correlate Hypothesis see below can inspire research towards obtaining better mappings. Outlook : The most difficult groundwork for this step is the availability of good computational systems biology models. Defining computational fitness correlates for these models is usually only a minor addition that is based on biological intuition.

Once such work has been pioneered for particular types of systems, patterns are likely to emerge. The computational nature of these models makes it easy to analyse very small effects and thus provides an empirical foundation for theoretical analyses that otherwise have to make many non testable assumptions.

It will be interesting to see how much of the independently developed quantitative genetics theory that maps quantitative traits to fitness will be confirmed by mechanistically explicit adaptive landscapes of this level. The purpose of this level is to test the Linear Fitness Correlate Hypothesis LFCH and to make heuristic quantitative adjustments, if computed and observed fitness correlate differences do not match. These have to be observed experimentally to calibrate the computational fitness correlates.

Key question : Does the computational model reflect biological reality? Experiments with many well-characterised mutants will be required to detect deviations from a 'L-1D' landscape.