Probability distributions for a) proportion C of distinct gene products that change state and b) magnitude S of change in gene products. Experiments are shown for degenerate G:P mappings using the same conditions as in Figure 4b, but with the following modifications: 1) perturbations to the system are of single null mutations only and 2) systems are initialized with different amounts of excess resources (% excess indicated by data set label).

Overview of genome-proteome model. a) Genotype-phenotype mapping conditions and pleiotropy: Each gene contributes to system traits through the expression of a protein product that can bind with functionally relevant targets (based on genetically determined protein specificity). b) Phenotypic expression: Target availability is influenced by the environment and by competition with functionally redundant proteins. The attractor of the phenotype can be loosely described as the binding of each target with a protein. c) Functional overlap of genes: Redundant genes can affect the same traits in the same manner. Degenerate traits only have a partial similarity in what traits they affect.

Illustration of degeneracy and related concepts. Components (C) within a system have a functionality that depends on their context (E) and can be functionally active (filled nodes) or inactive (clear nodes). When a component exhibits qualitatively different functions (indicated by node color) that depend on the context, we refer to that component as being functionally plastic (panel a). Pure redundancy occurs when two components have identical functions in every context (panels b and c). Functional redundancy is a term often used to describe two components with a single (but same) function whose activation (or capacity for utilization) depends on the context in different ways (panel d). Degeneracy describes components that are functionally plastic and functionally redundant, i.e. where the functions are similar in some situations but different in others (panel e).

Local and distributed sources of robustness in protein systems designed according to purely redundant and purely degenerate G:P mappings. a) Differential robustness as a function of the percentage of genes that are mutated in each protein system. Differential robustness is defined as the probability for a system phenotype to maintain fitness after it was allowed to adjust to a change in conditions (here: gene mutations). Source: [43] b) Versatility-robustness as a function of initial excess protein resources. Versatility is measured as the number of null mutation combinations ("neutral network size") for which the system phenotype maintains fitness. Source: [43]. c) Frequency distribution for the proportion C of distinct gene products that change their function when versatility is evaluated (as of panel b experiments) in systems with 0% initial excess resources. d) Versatility of redundant and degenerate systems when the system response to null mutations is restricted to local compensation only; i.e. gene products can only change their functional contribution if they are directly related to those functions lost as a result of a null mutation.

Conceptual model of a buffering network. Each agent is depicted by a pair of connected nodes that represent two types of tasks/functions that the agent can perform, e.g. see dashed circle in panel a). Node pairs that originate or end in the same node cluster ("Functional group") correspond to agents that can carry out the same function and thus are interchangeable for that function. Darkened nodes indicate the task an agent is currently performing. If that task is not needed then the agent is an excess resource or "buffer". Panel a) Degeneracy in multi-functional agents. Agents are degenerate when they are only similar in one type of task. Panel b) End state of a sequence of task reassignments or resource reconfigurations. A reassignment is indicated by a blue arrow with switch symbol. The diagram illustrates a scenario in which requests for tasks in the Z functional group have increased and requests for tasks of type X have decreased. Thus resources for X are now in excess. While no agent exists in the system that performs both Z and X, a pathway does exist for reassignment of resources (X→Y, Y→Z). This illustrates how excess resources for one type of function can indirectly support unrelated functions. Panel c) Depending on where excess resources are located, reconfiguration options are potentially large as indicated by the different reassignment pathways shown. Panel d) A reductionist system design with only redundant system buffers cannot support broad resource reconfiguration options. Instead, agent can only participate in system responses related to its two task type capabilities.^vi