Merav Parter

Environmental variability and modularity of bacterial metabolic networks

BackgroundBiological systems are often modular: they can be decomposed into nearly-independent structural units that perform specific functions. The evolutionary origin of modularity is a subject of much current interest. Recent theory suggests that modularity can be enhanced when the environment changes over time. However, this theory has not yet been tested using biological data.ResultsTo address this, we studied the relation between environmental variability and modularity in a natural and well-studied system, the metabolic networks of bacteria. We classified 117 bacterial species according to the degree of variability in their natural habitat. We find that metabolic networks of organisms in variable environments are significantly more modular than networks of organisms that evolved under more constant conditions.ConclusionThis study supports the view that variability in the natural habitat of an organism promotes modularity in its metabolic network and perhaps in other biological systems.

Facilitated Variation: How Evolution Learns from Past Environments To Generalize to New Environments

One of the striking features of evolution is the appearance of novel structures in organisms. Recently, Kirschner and Gerhart have integrated discoveries in evolution, genetics, and developmental biology to form a theory of facilitated variation (FV). The key observation is that organisms are designed such that random genetic changes are channeled in phenotypic directions that are potentially useful. An open question is how FV spontaneously emerges during evolution. Here, we address this by means of computer simulations of two well-studied model systems, logic circuits and RNA secondary structure. We find that evolution of FV is enhanced in environments that change from time to time in a systematic way: the varying environments are made of the same set of subgoals but in different combinations. We find that organisms that evolve under such varying goals not only remember their history but also generalize to future environments, exhibiting high adaptability to novel goals. Rapid adaptation is seen to goals composed of the same subgoals in novel combinations, and to goals where one of the subgoals was never seen in the history of the organism. The mechanisms for such enhanced generation of novelty (generalization) are analyzed, as is the way that organisms store information in their genomes about their past environments. Elements of facilitated variation theory, such as weak regulatory linkage, modularity, and reduced pleiotropy of mutations, evolve spontaneously under these conditions. Thus, environments that change in a systematic, modular fashion seem to promote facilitated variation and allow evolution to generalize to novel conditions.

EXTINCTIONS IN HETEROGENEOUS ENVIRONMENTS AND THE EVOLUTION OF MODULARITY

Extinctions of local subpopulations are common events in nature. Here, we ask whether such extinctions can affect the design of biological networks within organisms over evolutionary timescales. We study the impact of extinction events on modularity of biological systems, a common architectural principle found on multiple scales in biology. As a model system, we use networks that evolve toward goals specified as desired input-output relationships. We use an extinction—recolonization model, in which metapopulations occupy and migrate between different localities. Each locality displays a different environmental condition (goal), but shares the same set of subgoals with other localities. We find that in the absence of extinction events, the evolved computational networks are typically highly optimal for their localities with a nonmodular structure. In contrast, when local populations go extinct from time to time, we find that the evolved networks are modular in structure. Modular circuitry is selected because of its ability to adapt rapidly to the conditions of the free niche following an extinction event. This rapid adaptation is mainly achieved through genetic recombination of modules between immigrants from neighboring local populations. This study suggests, therefore, that extinctions in heterogeneous environments promote the evolution of modular biological network structure, allowing local populations to effectively recombine their modules to recolonize niches.

Sparse Fault-Tolerant BFS Trees

A fault-tolerant structure for a network is required to continue functioning following the failure of some of the network’s edges or vertices. This paper considers breadth-first search (BFS) spanning trees, and addresses the problem of designing a sparse fault-tolerant BFS tree, or FT-BFS tree for short, namely, a sparse subgraph T of the given network G such that subsequent to the failure of a single edge or vertex, the surviving part T′ of T still contains a BFS spanning tree for (the surviving part of) G. For a source node s, a target node t and an edge e ∈ G, the shortest s − t path P s,t,e that does not go through e is known as a replacement path. Thus, our FT-BFS tree contains the collection of all replacement paths P s,t,e for every t ∈ V(G) and every failed edge e ∈ E(G). Our main results are as follows. We present an algorithm that for every n-vertex graph G and source node s constructs a (single edge failure) FT-BFS tree rooted at s with \(O(n \cdot \min\{{\tt Depth}(s), \sqrt{n}\})\) edges, where Depth(s) is the depth of the BFS tree rooted at s. This result is complemented by a matching lower bound, showing that there exist n-vertex graphs with a source node s for which any edge (or vertex) FT-BFS tree rooted at s has Ω(n 3/2) edges. We then consider fault-tolerant multi-source BFS trees, or FT-MBFS trees for short, aiming to provide (following a failure) a BFS tree rooted at each source s ∈ S for some subset of sources S ⊆ V. Again, tight bounds are provided, showing that there exists a poly-time algorithm that for every n-vertex graph and source set S ⊆ V of size σ constructs a (single failure) FT-MBFS tree T *(S) from each source s i ∈ S, with \(O(\sqrt{\sigma} \cdot n^{3/2})\) edges, and on the other hand there exist n-vertex graphs with source sets S ⊆ V of cardinality σ, on which any FT-MBFS tree from S has \(\Omega(\sqrt{\sigma}\cdot n^{3/2})\) edges. Finally, we propose an O(logn) approximation algorithm for constructing FT-BFS and FT-MBFS structures. The latter is complemented by a hardness result stating that there exists no Ω(logn) approximation algorithm for these problems under standard complexity assumptions. In comparison with previous constructions our algorithm is deterministic and may improve the number of edges by a factor of up to \(\sqrt{n}\) for some instances. All our algorithms can be extended to deal with one vertex failure as well, with the same performance.

MST in Log-Star Rounds of Congested Clique

We present a randomized algorithm that computes a Minimum Spanning Tree (MST) in O(log* n) rounds, with high probability, in the Congested Clique model of distributed computing. In this model, the input is a graph on n nodes, initially each node knows only its incident edges, and per round each two nodes can exchange O(log n) bits. Our key technical novelty is an O(log* n) Graph Connectivity algorithm, the heart of which is a (recursive) forest growth method, based on a combination of two ideas: a sparsity-sensitive sketching aimed at sparse graphs and a random edge sampling aimed at dense graphs. Our result improves significantly over the O(log log log n) algorithm of Hegeman et al. [PODC 2015] and the O(log log n) algorithm of Lotker et al. [SPAA 2003; SICOMP 2005].

Vertex fault tolerant additive spanners

A fault-tolerant structure for a network is required to continue functioning following the failure of some of the network’s edges or vertices. In this paper, we address the problem of designing a fault-tolerant additive spanner, namely, a subgraph H of the network G such that subsequent to the failure of a single vertex, the surviving part of H still contains an additive spanner for (the surviving part of) G, satisfying

Distributed power control in the SINR model

\mathrm{dist}(s,t,H{\setminus } \{v\}) \le \mathrm{dist}(s,t,G{\setminus } \{v\})+\beta

Preserving Distances in Very Faulty Graphs.

dist(s,t,H\{v})≤dist(s,t,G\{v})+β for every