Architecture and Co-Evolution of Allosteric Materials

We introduce a numerical scheme to evolve functional materials that can accomplish a specified mechanical task. In this scheme, the number of solutions, their spatial architectures and the correlations among them can be computed. As an example, we consider an “allosteric” task, which requires the material to respond specifically to a stimulus at a distant active site. We find that functioning materials evolve a less-constrained trumpet-shaped region connecting the stimulus and active sites, and that the amplitude of the elastic response varies non-monotonically along the trumpet. As previously shown for some proteins, we find that correlations appearing during evolution alone are sufficient to identify key aspects of this design. Finally, we show that the success of this architecture stems from the emergence of soft edge modes recently found to appear near the surface of marginally connected materials. Overall, our in silico evolution experiment offers a new window to study the relationship between structure, function and correlations emerging during evolution.

[1]  Nidhi Pashine,et al.  Designing allostery-inspired response in mechanical networks , 2016, Proceedings of the National Academy of Sciences.

[2]  Najeeb M. Halabi,et al.  Protein Sectors: Evolutionary Units of Three-Dimensional Structure , 2009, Cell.

[3]  Stanislas Leibler,et al.  Protein Sectors: Statistical Coupling Analysis versus Conservation , 2014, PLoS Comput. Biol..

[4]  M. Barahona,et al.  Prediction of allosteric sites and mediating interactions through bond-to-bond propensities , 2016, Nature Communications.

[5]  A. Lesk,et al.  Structural mechanisms for domain movements in proteins. , 1994, Biochemistry.

[6]  Giovanni Dietler,et al.  Functional dynamics of PDZ binding domains: a normal-mode analysis. , 2005, Biophysical journal.

[7]  Andrea J. Liu,et al.  The jamming scenario - an introduction and outlook , 2010, 1006.2365.

[8]  F. S. Mathews,et al.  Structural identification of the pathway of long-range communication in an allosteric enzyme , 2008, Proceedings of the National Academy of Sciences.

[9]  Michael D. Daily,et al.  Local motions in a benchmark of allosteric proteins , 2007, Proteins.

[10]  K A Dill,et al.  Are proteins well-packed? , 2001, Biophysical journal.

[11]  N. Goodey,et al.  Allosteric regulation and catalysis emerge via a common route. , 2008, Nature chemical biology.

[12]  Christopher J. Oldfield,et al.  The unfoldomics decade: an update on intrinsically disordered proteins , 2008, BMC Genomics.

[13]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[14]  R. Jernigan,et al.  Anisotropy of fluctuation dynamics of proteins with an elastic network model. , 2001, Biophysical journal.

[15]  C. Kane,et al.  Topological boundary modes in isostatic lattices , 2013, Nature Physics.

[16]  R. Ranganathan,et al.  Evolutionarily conserved pathways of energetic connectivity in protein families. , 1999, Science.

[17]  F. J. Poelwijk,et al.  The spatial architecture of protein function and adaptation , 2012, Nature.

[18]  Jacobs,et al.  Generic rigidity percolation: The pebble game. , 1995, Physical review letters.

[19]  M. Wyart,et al.  Adaptive elastic networks as models of supercooled liquids. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Jack D. Dunitz,et al.  Atomic Dispacement Parameter Nomenclature. Report of a Subcommittee on Atomic Displacement Parameter Nomenclature , 1996 .

[21]  J. Changeux,et al.  Allosteric Mechanisms of Signal Transduction , 2005, Science.

[22]  R. Nussinov,et al.  Allostery in Disease and in Drug Discovery , 2013, Cell.

[23]  Vincenzo Vitelli,et al.  Nonlinear conduction via solitons in a topological mechanical insulator , 2014, Proceedings of the National Academy of Sciences.

[24]  J. Maxwell,et al.  The Scientific Papers of James Clerk Maxwell: On the Calculation of the Equilibrium and Stiffness of Frames , 1864 .

[25]  Mathieu Hemery,et al.  Evolution of sparsity and modularity in a model of protein allostery. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  M. Wyart,et al.  Breakdown of continuum elasticity in amorphous solids. , 2013, Soft matter.

[27]  Matthieu Wyart,et al.  Phonon gap and localization lengths in floppy materials , 2012, 1204.3542.

[28]  M. Wyart,et al.  Evolution of covalent networks under cooling: contrasting the rigidity window and jamming scenarios. , 2014, Physical review letters.

[29]  Le Yan,et al.  Erratum: On variational arguments for vibrational modes near jamming , 2016, 1601.02141.

[30]  D. Sussman,et al.  Topological boundary modes in jammed matter. , 2015, Soft matter.

[31]  Jean-Philippe Bouchaud,et al.  Edge mode amplification in disordered elastic networks. , 2016, Soft matter.

[32]  M. Perutz.  Stereochemistry of Cooperative Effects in Haemoglobin: Haem–Haem Interaction and the Problem of Allostery , 1970, Nature.