Landscape mutations

At present, many popular applied molecular evolution protocols do not involve mutation or recombination. The laboratory technique-based models presented in this section are of this type. Incorporating mutation requires fitness landscape models or some other means of relating molecular properties to particular sequences. The more abstract models reviewed later allow for mutation and recombination and are based heavily on landscape structure. The models in the present section are based on affinity distribution p(Ka), the probability that a ligand chosen at random from the library has affinity Ka. 

The fitness function is simply the mapping between points in sequence space and their fitnesses. The fitness landscape is the combination of the fitness function and the neighbor relationship. With neighbors defined by point mutation, for an N-site molecule, the landscape is the N-dimensional surface that results from plotting the fitness function over an N-dimensional Cartesian coordinate sequence space (Fig. 13). 

Several types of autocorrelation are often used for landscapes. In several important papers, Weinberger and Stadler consider both autocorrelation between adjacent points along a random walk in the landscape and autocorrelation between points a given Hamming distance apart independent of any walk [67,77,78,82,83], Both definitions yield similar information about the landscape and can be computed from one another for stationary landscapes. Other types of autocorrelation are based on neighborhoods defined by complex mutation operations such as crossover [45-49,85],... 

REM landscapes have been applied to the maturation of the immune system. When exposed to a new antigen, antibodies undergo on average only 6-10 point mutations in the course of achieving typically a 50-100-fold increase in affinity [70,71], Such short walks from random initial points to local peaks occur in rugged landscapes. The short walks and only modest affinity increase can be interpreted to indicate that the antibody affinity landscape is essentially uncorrelated [14,71,81,91], However, because there is such... 

Another approach is possible if the affinity landscape correlation is known. The mutation rate in a given round can be based on the average fitness of the library in that round. The optimal mutation distance (see above) for a correlated landscape depends on the fitness of the point being mutated and can be converted into a mutation rate. More generally, if there is an estimate of the distribution of fitnesses around a population s average fitness as a function of number of rounds, theoretically a distribution of optimal mutation distances could be calculated, which could yield a mutation rate schedule for an evolving population. 

Search on RNA secondary structure landscapes is distinctly different from search on the spin glass-like models. The difference is a result of the neutral networks that percolate the space. Note that, in practice, the sequences on neutral networks need not have exactly the same fitness, but fitnesses whose differences are below a threshold determined by the mutation rate and noise in the system. As with search on spin glass landscapes, this topic is quite extensive and is reviewed in several papers [39,67,69,113] as well as in Schuster s contribution to this collection, so I will only touch on a few key points. 

The first limitation is that the landscape models are very abstract. Their results apply to molecular search in a general way, but are difficult to relate to laboratory concerns. Ideally, future work will combine the mathematical rigor of landscape-based search with the chemical and experimental details of the laboratory technique-based models. Some work along these lines has started with calculating mutation rates for SELEX schemes based on RNA secondary structure landscape models [114],... 

The optimal mutation distance approach [119,120] can be generalized for arbitrary classes of fitness landscapes and populations of molecules. 

While I have made a clear distinction between laboratory technique-based and landscape-based models, the distinction is more artifactual than representative of fundamental differences. The laboratory technique-based models do not include mutation or crossover, so the only landscape property they depend on is the affinity distribution p(Ka). Once mutation is included, some type of relationship between specific sequences and their affinities must be included. Landscapes are one means of including this relationship. Work with landscape-based models does not include laboratory techniques or parameters because the questions posed in this work do not require this added level of complexity and because of the paucity of experimental data to define actual affinity landscapes. If the landscape work is to solve actual laboratory protocol problems, the laboratory and chemistry details need to be included. Ideally, future work will include mathematically rigorous analyses of landscape-based models that incorporate chemical and experimental details. 

Fig. 4. The role of neutral networks in evolutionary optimization through adaptive walks and random drift. Adaptive walks allow to choose the next step arbitrarily from all directions where fitness is (locally) nondecreasing. Populations can bridge over narrow valleys with widths of a few point mutations. In the absence of selective neutrality (upper part) they are, however, unable to span larger Hamming distances and thus will approach only the next major fitness peak. Populations on rugged landscapes with extended neutral networks evolve along the network by a combination of adaptive walks and random drift at constant fitness (lower part). In this manner, populations bridge over large valleys and may eventually reach the global maximum ofthe fitness landscape.

During experiments, coupling is observed through non-additive mutational effects. Two mutations are considered additive if the combined change in fitness is equal to the sum of the individual contributions of each mutation. Additivity implies a smooth landscape that can be easily... 

In this section, we describe several statistical quantities that capture the gross structural features of the landscape. In Section II.C.l, we discuss the experimental observations of the tolerance of proteins to mutation and describe a correlation between the tolerance and the interresidue coupling. In Section II.C.2, landscape ruggedness is described in terms... 

The correlation of the landscape measures the fitness similarity between a sequence and its d-mutant neighbors, where d is the number of mutations. As a sequence accumulates mutations, the fitness is increasingly altered. On smooth landscapes, the rate of fitness change is slow and therefore the landscape is correlated. Conversely, on rugged landscapes, the rate is more rapid and the landscape is uncorrelated. Studies of the relationship between fitness and distance have been used to quantitate the correlation among population ensembles on the RNA landscape (Fontana and Shuster, 1987), recombination dynamics (Born-holdt, 1998), and the success of genetic algorithms (Manderick et al., 1991 Jones and Forrest, 1995). 

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