In this work, we consider the controlled agreement problem for multi-agent networks, where a collection of agents take on leader roles while the remaining agents execute local, consensus-like protocols. Our aim is to identify reflections of graph-theoretic notions on systemtheoretic properties of such systems. In particular, we show how the symmetry structure of the network, characterized in terms of its automorphism group, directly relates to the controllability of the corresponding multi-agent system. Moreover, we introduce network equitable partitions as a means by which such controllability characterizations can be extended to the multileader setting.

This paper addresses the connectedness issue in multiagent coordination, i.e., the problem of ensuring that a group of mobile agents stays connected while achieving some performance objective. In particular, we study the rendezvous and the formation control problems over dynamic interaction graphs, and by adding appropriate weights to the edges in the graphs, we guarantee that the graphs stay connected.

In this paper, the problem of driving a collection of mobile robots to a given target destination is studied. In particular, we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader-agents, while the remaining agents, only employ local interaction rules. To this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop-go rules for the leader-agents. Non-Zenoness, liveness and convergence of the resulting system are also analyzed.

The relationship between DNA sequence recognition and catalytic specificity in a DNA-modifying enzyme was explored using paramagnetic Cu 2þ ions as probes for ESR spectroscopic and biochemical studies. Electron spin echo envelope modulation spectroscopy establishes that Cu 2þ coordinates to histidine residues in the EcoRI endonuclease homodimer bound to its specific DNA recognition site. The coordinated His residues were identified by a unique use of Cu 2þ -ion based long-range distance constraints. Double electron-electron resonance data yield Cu 2þ -Cu 2þ and Cu 2þ -nitroxide distances that are uniquely consistent with one Cu 2þ bound to His114 in each subunit. Isothermal titration calorimetry confirms that two Cu 2þ ions bind per complex. Unexpectedly, Mg 2þ -catalyzed DNA cleavage by EcoRI is profoundly inhibited by Cu 2þ binding at these hitherto unknown sites, 13 Å away from the Mg 2þ positions in the catalytic centers. Molecular dynamics simulations suggest a model for inhibition of catalysis, whereby the Cu 2þ ions alter critical protein-DNA interactions and water molecule positions in the catalytic sites. In the absence of Cu 2þ , the Mg 2þ -dependence of EcoRI catalysis shows positive cooperativity, which would enhance EcoRI inactivation of foreign DNA by irreparable doublestrand cuts, in preference to readily repaired single-strand nicks. Nonlinear Poisson-Boltzmann calculations suggest that this cooperativity arises because the binding of Mg 2þ in one catalytic site makes the surface electrostatic potential in the distal catalytic site more negative, thus enhancing binding of the second Mg 2þ . Taken together, our results shed light on the structural and electrostatic factors that affect site-specific catalysis by this class of endonucleases.T he biochemical basis of specificity in the interaction of proteins with DNA sites is a major problem of modern molecular genetics. Studies of many protein-DNA complexes by crystallography have elucidated the intermolecular recognition contacts (1), but it is clear that point-to-point contacts cannot fully explain specificity. Solution biochemical and computational studies have shown that a comprehensive view of specificity determination must also include factors such as shape recognition (2), mutual accommodation of the macromolecules through DNA distortion or conformational selection (1, 3-6), and/or DNA-induced protein folding (5, 7). Thermodynamic studies have revealed that specific protein-DNA association is often driven primarily by the favorable entropy increase provided by desolvation of the apposed complementary surfaces (8-10).For those DNA-binding proteins that are also DNA-modifying enzymes (nucleases, methylases, recombinases, repair enzymes, etc.) a key question is the relationship between DNA-binding specificity and catalytic specificity. One exemplary system for addressing specificity determination is the EcoRI endonuclease (3, 11), a 62 kDa homodimer that recognizes the DNA site 5′-GAATTC-3′ and binds as much as 90,000-fold better (3, 12) than a...

No abstract