From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from statistical physics and non-linear dynamics. In this paper, we look at a few examples of biological networks to see how similar questions can come up in very different contexts. We review some of our recent work that looks at how network structure (e.g., its connection topology) can dictate the nature of its dynamics, and conversely, how dynamical considerations constrain the network structure. We also see how networks occurring in nature can evolve to modular configurations as a result of simultaneously trying to satisfy multiple structural and dynamical constraints. The resulting optimal networks possess hubs and have heterogeneous degree distribution similar to those seen in biological systems.

[1]  Raj Kumar Pan,et al.  Modular networks emerge from multiconstraint optimization. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Robert M. May,et al.  Stability and Complexity in Model Ecosystems , 2019, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  Arnab Chatterjee,et al.  Small-world properties of the Indian railway network. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  U. Bhalla,et al.  Complexity in biological signaling systems. , 1999, Science.

[5]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[6]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[7]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[8]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[9]  D. Mason,et al.  Compartments revealed in food-web structure , 2003, Nature.

[10]  Sitabhra Sinha,et al.  Robust emergent activity in dynamical networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  M. Weigt,et al.  On the properties of small-world network models , 1999, cond-mat/9903411.

[12]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[13]  F. Hainsworth.  Scaling: why is animal size so important? , 1985 .

[14]  Michael W. Deem,et al.  Mathematical adventures in biology , 2007 .

[15]  Kenneth Showalter,et al.  Spatiotemporal dynamics of networks of excitable nodes. , 2006, Chaos.

[16]  N. Chatterjee,et al.  Understanding the mind of a worm: hierarchical network structure underlying nervous system function in C. elegans. , 2008, Progress in brain research.

[17]  E. Bullmore,et al.  A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs , 2006, The Journal of Neuroscience.

[18]  Sitabhra Sinha,et al.  Examining the effects of species richness on community stability: an assembly model approach , 2002 .

[19]  I. Bahar,et al.  Gaussian Dynamics of Folded Proteins , 1997 .

[20]  Sitabhra Sinha,et al.  Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Christopher C Wilmers,et al.  Understanding ecosystem robustness. , 2007, Trends in ecology & evolution.

[22]  Jari Saramäki,et al.  Modelling development of epidemics with dynamic small-world networks. , 2005, Journal of theoretical biology.

[23]  K. Schmidt-Nielsen,et al.  Scaling, why is animal size so important? , 1984 .

[24]  Jari Saramäki,et al.  Emergence of self-sustained patterns in small-world excitable media. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  F. Ashcroft,et al.  Crystal Structure of the Potassium Channel KirBac1.1 in the Closed State , 2003, Science.

[26]  Sitabhra Sinha,et al.  Complexity vs. stability in small-world networks , 2004, nlin/0407053.

[27]  S. Kundu,et al.  Hydrophobic, hydrophilic, and charged amino acid networks within protein. , 2006, Biophysical journal.

[28]  Raj Kumar Pan,et al.  Modularity produces small-world networks with dynamical time-scale separation , 2008, 0802.3671.

[29]  R. Lahesmaa,et al.  Capturing cell-fate decisions from the molecular signatures of a receptor-dependent signaling response , 2007, Molecular systems biology.

[30]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[31]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[32]  Sitabhra Sinha,et al.  Assortative mixing by degree makes a network more unstable , 2005 .

[33]  Raj Kumar Pan,et al.  The Small-world of Modular Networks , 2008 .