Preprints:Information content of downwelling skylight for non-imaging visual systems (bioRxiv, Sep 2018) R. Thiermann, A. Sweeney, A. Murugan Many organisms have light-sensitive proteins (opsins) in unexpected places like in the brain and in reproductive organs. What are these opsins "looking" at? We don't know for sure but disrupting them often disrupts reproductive behaviors synchronized to the lunar cycle. Using experimental observations of natural light by our collaborator Alison Sweeney and cloud and humidity models, we show that these opsins can reliably infer the day of the lunar cycle from the color of twilight. Non-equilibrium statistical mechanics of continuous attractors (arXiv, Sep 2018)W. Zhong, Z. Lu, D.J.Schwab, A. Murugan Recent experiments suggest that memories of multiple spatial environments involve the same neurons in the brain. Why do we not get confused? Classic theories of neural networks explain when such confusion is avoided but they do not apply to spatial memories which are extended objects (`continuous attractors'). Further, spatial memories are recalled at a finite speed as you physically explore your surroundings. We show that the faster you run, the less you remember and compute the speed-dependent "non-equilibrium" memory capacity of a neural network. |

Biophysical clocks face a trade-off between internal and external noise resistanceW Pittayakanchit*, Z Lu*, J Chew, M J Rust, A. MuruganeLife (2018);7:e37624 Many organisms have internal clocks with 24-hour self-sustained rhythms but others have simpler `hourglass' clocks that must be driven by sunrise and sunset. By studying the geometry of the underlying dynamical systems, we show that self-sustained clocks are better at dealing with external fluctuations (e.g., weather) but are more vulnerable to internal molecular fluctuations when compared to simpler hourglass clocks. So simpler clock architectures can be better when the clock hardware itself is error prone. High Protein Copy Number Is Required to Suppress Stochasticity in the Cyanobacterial Circadian Clock J. Chew, E. Leypunskiy, J. Lin, A. Murugan, M. RustNature Communications 9:3004 (2018)Related experiments in Prof. Michael Rust's lab show that P. marinus, a cyanobacterium with an hourglass clock, has very few clock proteins compared to a sister species S. elongatus that has a self-sustained clock. These experiments also suggest that P. marinus is better off with a simple hourglass clock than with a self-sustained clock, given how unreliable the clock reactions in P. marinus are. |

Shaping the topology of folding pathways in mechanical systemsM. Stern, V. Jayaram, A. MuruganNature Communications 9:4303 (2018) When pressured to change shape, elastic materials sometimes face a fork in the road and they take it. But it's hard to tell which branch they will take, so we'd rather not give them the choice. We found that stiffening some parts of the material can cause `bifurcations' that relocate or even remove forks, so the network of roads only connects places you like. Even better, we found that you can make some roads accessible only at 60 mph while others accessible only at 20 mph. For these elastic materials, the destination is determined by how quickly you press the material. |

The Complexity of Folding Self-Folding OrigamiM. Stern, M. Pinson, A. Murugan Physical Review X 7, 041070 (2017) The dream of self-folding origami is to program a flat sheet with carefully placed creases so the sheet folds itself into a swan when pushed anywhere. We show that, much like with protein folding, the very act of programming a sheet to fold in one way (e.g., a swan) also lets it fold into an exponential number of other undesired shapes. Folding such a sheet is as difficult as solving a Suduko puzzle. |

Self-folding origami at any energy scaleM. Pinson*, M. Stern*, A. Carruthers, T. Witten, E. Chen, A. MuruganNature Communications 8:15477 (May 2017) "Mechanisms" are motions in mechanical systems that cost exactly zero energy. Clever people over time have designed elaborate mechanisms, from James Watt's steam engine linkage to recent advances in folding sheets (origami). But physics does not sharply distinguish "exactly zero energy" vs nearly zero energy. We describe the expanded universe of folding motions in sheets opened up by giving up on "exactly zero energy". We describe what "typical" folding motions of each energy level look like. |

Associative pattern recognition through macro-molecular self-assemblyW. Zhong, D.J. Schwab, A. MuruganJournal of Statistical Physics, Kadanoff memorial issue (2017) |

Topologically protected modes in non-equilibrium stochastic systemsA. Murugan, S. VaikuntanathanNature Communications 8, 13881 (2017) |

The Information Capacity of Specific Interactions M. Huntley*, A. Murugan* , M. Brenner,Proceedings of the National Academy of Sciences (2016) |

Receptor libraries optimized for natural statistics D. Zwicker, A. Murugan*, M. Brenner*, (* corresp. authors)Proceedings of the National Academy of Sciences (2016) When you play a game of 20 questions, the optimal questions to ask each divide the set in half and are `orthogonal' to each other. For example 'Are you thinking of a man or a woman?', 'Is the person dead or alive?' and so on. What is optimal set of 20 questions to ask of odors in your natural environment? The answer provides design principles for the set of olfactory receptors in your nose. |

Biological implications of dynamical phases in non-equilibrium reaction networks, A. Murugan, S. Vaikuntanathaninvited contribution to the Journal of Statistical Physics (special issue), 2016, 162 (5) JSP arXiv Many biochemical mechanisms use non-equilibrium driving to dramatically change the state in which a bio-molecular system spends most of its time when biologically desired but not otherwise. In this review, we relate such abilities, which underly biochemical error correction and adaption, to the idea of non-equilibrium dynamical phases. We find that dynamical phase coexistence creates special `common-sense' points in the energy-accuracy tradeoff where you achieve 80% of your goals with 20% effort. |

Undesired usage and the robust self-assembly of heterogeneous structures, in collaboration with: J. Zou, and M. Brenner Nature Communications 6, 6203 (Jan 2015) Nat Comm. Correct self-assembly of structures made of many distinct species must compete against a combinatorially enormous number of undesired structures. However, these entropic challenges can be overcome to a remarkable extent by tuning control parameters (like concentrations) to reflect the 'undesired usage' of species. That is, you must set your control knobs based on *undesired* structures, instead of the desired structure as usually assumed. Hence, somewhat counterintuitively, highly non-stoichiometric concentrations can greatly enhance the yield of desired structures. |

Multifarious Assembly Mixtures: Systems Allowing Retrieval of Diverse Stored Structures, in collaboration with: Z. Zeravcic, S. Leibler and M. Brenner Proceedings of the National Academy of Sciences 112(1) 54-59 (Dec 2014) arXiv PNAS Inspired by associative memory in Hopfield's neural networks, we generalized the self-assembly framework to a soup of particles (proteins/DNA tiles) that can simultaneously 'store' the ability to assemble multiple different structures. Such a soup of particles can then assemble ('retrieve') any one of the stored structures ('memories') when presented with a signal vaguely reminiscent of one of those memories ('association'). However, store one too many memories and promiscuous interactions between particles prevent faithful retrieval of any memory. Secretly, such self-assembly is mathematically equivalent to Hippocampus place cell networks and equivalent spin glass models. |

Discriminatory proofreading regimes in non-equilibrium systems, in collaboration with: D.A. Huse, and S. Leibler Physical Review X 4 (2), 021016 PRX Usually, non-equilibrium error correction is understood to increase the occupancy of the ground state and reduce the occupancy of all higher energy states. However, we found that a proofreading mechanism can act differently in different energy bands, reducing occupancy of unstable states in a given energy band while increasing the occupancy of less stable higher energy states ('anti-proofreading'). And you can switch between different designer occupancy of states by simply changing the external driving forces. |

Speed, dissipation, and error in kinetic proofreading, in collaboration with: D.A. Huse, and S. Leibler Proceedings of the National Academy of Sciences 109(30):12034-9 (2012) PDF SI A new twist on the classic model of kinetic proofreading. Proofreading uses 'catastrophes' to slow down biochemical reactions while improving their fidelity. We introduced `rescues' that mitigate catastrophes and speed up reactions at the cost of increased errors. Surprisingly, we found a non-equilibrium phase transition as you tune the rescue rate. At this transition, you achieve, loosely speaking, 80% of the max possible error-correction at only 20% of the max speed cost. Why would you go any further (as the traditional limit does) unless you really care about errors and really don't care about speed at all? We took the terms catastrophes and rescues from non-equilibrium microtubule growth. The connection to 'dynamic inability' of microtubules suggests a broader context for proofreading as a stochastic search strategy, balancing exploration and exploitation. |

AdS4/CFT3 - squashed, stretched and warped, in collaboration with: I.R.Klebanov and T.Klose Journal of High Energy Physics 0903 140 (2009) arxiv:0809.3773 [hep-th] PDF In its earliest form, the AdS/CFT correspondence related a gravitational theory on an Anti-de Sitter space \times a perfect sphere to the most supersymmetric conformal quantum field theory -- which has very little physics left because of all the symmetries. What happens if you take the perfect 7-dimensional round sphere of the gravitational theory and squash it, stretch it and then also warp it? |

Goldstone Bosons and Global Strings in a Warped Resolved Conifold, in collaboration with: I. R. Klebanov, D. Rodriguez-Gomez and J. Ward Journal of High Energy Physics 0805, 090 (2008), arXiv:0712.2224 [hep-th] PDF The AdS/CFT correspondence relies heavily on matching symmetries of a gravitational theory with the symmetries of a quantum field theory. What happens when some of these symmetries are spontaneously broken? What do Goldstone modes of the field theory correspond to on the gravitational side? |

Entanglement as a Probe of Confinement, in collaboration with: I. R. Klebanov and D. Kutasov Nuclear Physics B 796, 274 (2008), arXiv:0709.2140 [hep-th] PDF Entanglement entropy was traditionally not used much in high-energy physics (outside of black hole physics). We proposed a concrete use of entanglement entropy in particle physics - as a test of whether quarks are confined by gluons. Quark confinement is a basic feature of the real world but it can surprisingly difficult and subtle to check if a proposed theory of quarks really shows confinement. Entanglement entropy provides a tractable way. |

Gauge/Gravity Duality and Warped Resolved Conifold, in collaboration with: I. R. KlebanovJournal of High Energy Physics 0703, 042 (2007), arXiv:hep-th/0701064 PDF Conical singularities in Einstein's theory of gravitation can be `resolved' away (in the sense of algebraic resolutions); the singularity is then replaced with a sphere of smaller dimension. We worked out what such resolution means for dual quantum field theories. |

On D3-brane potentials in compactifications with fluxes and wrapped D-branesin collaboration with: D. Baumann, A. Dymarsky, I. R. Klebanov, J. M. Maldacena and L. P. McAllisterJournal of High Energy Physics 0611, 031 (2006), arXiv:hep-th/0607050 PDF String theorists wanted to build models of cosmic inflation based on string theory, which usually amounts to a balling rolling down a potential and emitting gravitational waves. However, such calculations for potentials obtained through string theory were too difficult. We made these calculations easy for a wide class of models by outlining a geometric method. |

Fatgraph expansion for noncritical superstrings, in collaboration with: Anton Kapustin PDFarXiv:hep-th/0404238 (2004) We studied a fatgraph expansion for noncritical strings. |