Publications
211 results found
Yaliraki SN, Barahona M, 2007, Chemistry across scales: from molecules to cells, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 365, Pages: {2921-2934}-{2921-2934}, ISSN: 1364-503X
Many important biological functions are strongly dependent on specific chemical interactions. Modelling how the physicochemical molecular details emerge at much larger scales is an active area of research, currently pursued with a variety of methods. We describe a series of theoretical and computational approaches that aim to derive bottom-up descriptions that capture the specificity that ensues from atomistic detail by extracting relevant features at the different scales. The multiscale models integrate the descriptions at different length and time scales by exploiting the idea of mechanical responses. The methodologies bring together concepts and tools developed in seemingly unrelated areas of mathematics such as algebraic geometry, model reduction, structural graph theory and non-convex optimization. We showcase the applicability of the framework with examples from protein engineering and enzyme catalysis, protein assembly, and with the description of lipid bilayers at different scales. Many challenges remain as it is clear that no single methodology will answer all questions in such multidimensional complex problems.
Hemberg M, Barahona M, 2007, Noise characteristics of interlocked repressilators, BioSysBio
Hemberg M, Barahona M, 2007, Perfect sampling of the master equation for gene regulatory networks, BIOPHYSICAL JOURNAL, Vol: 93, Pages: {401-410}-{401-410}, ISSN: 0006-3495
We present a perfect sampling algorithm that can be applied to the master equation of gene regulatory networks. The method recasts Gillespie’s stochastic simulation algorithm (SSA) in the light of Markov chain Monte Carlo methods and combines it with the dominated coupling from the past (DCFTP) algorithm to provide guaranteed sampling from the stationary distribution. We show how the DCFTP-SSA can be generically applied to genetic networks with feedback formed by the interconnection of linear enzymatic reactions and nonlinear Monod-and Hill-type elements. We establish rigorous bounds on the error and convergence of the DCFTP-SSA, as compared to the standard SSA, through a set of increasingly complex examples. Once the building blocks for gene regulatory networks have been introduced, the algorithm is applied to study properly averaged dynamic properties of two experimentally relevant genetic networks: the toggle switch, a two-dimensional bistable system; and the repressilator, a six-dimensional transcriptional oscillator.
August E, Parker KH, Barahona M, 2007, A dynamical model of lipoprotein metabolism, BULLETIN OF MATHEMATICAL BIOLOGY, Vol: 69, Pages: {1233-1254}-{1233-1254}, ISSN: 0092-8240
We present a dynamical model of lipoprotein metabolism derived by combining a cascading process in the blood stream and cellular level regulatory dynamics. We analyse the existence and stability of equilibria and show that this low-dimensional, nonlinear model exhibits bistability between a low and a high cholesterol state. A sensitivity analysis indicates that the intracellular concentration of cholesterol is robust to parametric variations while the plasma cholesterol can vary widely. We show how the dynamical response to time-dependent inputs can be used to diagnose the state of the system. We also establish the connection between parameters in the system and medical and genetic conditions.
Lazaridis E, Drakakis EM, Barahona M, 2007, Full analogue electronic realisation of the Hodgkin-Huxley neuronal dynamics in weak-inversion CMOS, 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS), Publisher: IEEE, Pages: 1200-1203, ISSN: 1557-170X
Hemberg M, Yaliraki SN, Barahona M, 2006, Stochastic kinetics of viral capsid assembly based on detailed protein structures, BIOPHYSICAL JOURNAL, Vol: 90, Pages: {3029-3042}-{3029-3042}, ISSN: 0006-3495
We present a generic computational framework for the simulation of viral capsid assembly which is quantitative and specific. Starting from PDB files containing atomic coordinates, the algorithm builds a coarse-grained description of protein oligomers based on graph rigidity. These reduced protein descriptions are used in an extended Gillespie algorithm to investigate the stochastic kinetics of the assembly process. The association rates are obtained from a diffusive Smoluchowski equation for rapid coagulation, modified to account for water shielding and protein structure. The dissociation rates are derived by interpreting the splitting of oligomers as a process of graph partitioning akin to the escape from a multidimensional well. This modular framework is quantitative yet computationally tractable, with a small number of physically motivated parameters. The methodology is illustrated using two different viruses which are shown to follow quantitatively different assembly pathways. We also show how in this model the quasi-stationary kinetics of assembly can be described as a Markovian cascading process, in which only a few intermediates and a small proportion of pathways are present. The observed pathways and intermediates can be related a posteriori to structural and energetic properties of the capsid oligomers.
Lazaridis E, Drakakis E M, Barahona M, 2006, A biomimetic CMOS synapse, ISCAS 2006, Pages: 751-754
Jadbabaie A, Motee N, Barahona M, 2005, On the stability of the Kuramoto model of coupled nonlinear oscillators, Pages: {4296-4301}-{4296-4301}, ISSN: 0743-1619
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We also provide a series of bounds for the critical values of the coupling strength.
Pecora L, Barahona M, 2005, Synchronization of oscillators in complex networks, Chaos and Complexity Letters, Vol: 1, Pages: 61-91, ISSN: 1556-3995
Barahona M, Doherty AC, Smaier M, et al., 2002, Finite horizon model reduction and the appearance of dissipation in Hamiltonian systems, Pages: {4563-4568}-{4563-4568}, ISSN: 0191-2216
An apparent paradox in classical statistical physics is the mechanism by which conservative, time-reversible microscopic dynamics, can give rise to seemingly dissipative behavior. In this paper we use system theoretic tools to show that dissipation can arise as an artifact of incomplete observations over a finite horizon. In addition, this approach allows us to obtain finite-time, low order, approximations of systems with moderate size, and to establish how the approach to the thermodynamic limit depends on the different physical parameters.
Barahona M, Pecora LM, 2002, Synchronization in small-world systems, PHYSICAL REVIEW LETTERS, Vol: 89, ISSN: 0031-9007
We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shortcuts translates into improved network synchronizability. Applied to networks of low redundancy, the small-world route produces synchronizability more efficiently than standard deterministic graphs, purely random graphs, and ideal constructive schemes. However, the small-world property does not guarantee synchronizability: the synchronization threshold lies within the boundaries, but linked to the end of the small-world region.
Diehl MR, Yaliraki SN, Beckman RA, et al., 2002, Self-assembled, deterministic carbon nanotube wiring networks, ANGEWANDTE CHEMIE-INTERNATIONAL EDITION, Vol: 41, Pages: {353+}-{353+}, ISSN: 1433-7851
Sznaier M, Doherty AC, Barahona M, et al., 2002, A new bound of the L-2[0, T]-induced norm and applications to model reduction, New York, IEEE 20th annual American control conference (ACC), Anchorage, Alaska, Publisher: IEEE, Pages: {1180-1185}-{1180-1185}, ISSN: 0743-1619
We present a simple bound on the finite horizon L-2[0,T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the H-infinity norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena it! statistical physics.
Poon CS, Barahona M, 2001, Titration of chaos with added noise, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, Vol: 98, Pages: {7107-7112}-{7107-7112}, ISSN: 0027-8424
Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has lad to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple “litmus test” for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems.
Poon CS, Barahona M, 1999, Method and apparatus for detecting nonlinearity and chaos in a dynamical system, US5938594 A
Barahona M, Watanabe S, 1998, Row-switched states in two-dimensional underdamped Josephson-junction arrays, PHYSICAL REVIEW B, Vol: 57, Pages: 10893-10912, ISSN: 2469-9950
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- Citations: 8
Van Der Zant HSJ, Barahona M, Duwel AE, et al., 1998, Dynamics of one-dimensional Josephson-junction arrays, Physica D: Nonlinear Phenomena, Vol: 119, Pages: 219-226, ISSN: 0167-2789
We study the dynamics of one-dimensional arrays of Josephson junctions connected in parallel by superconducting wires. These arrays are model systems for the discrete, damped sine-Gordon equation and excellent agreement between theory and experiment is obtained. The influence of boundary conditions and the coupling between two discrete sine-Gordon systems have also been investigated. In Josephson ladders, superconducting islands are connected to other islands by three Josephson junctions. The dynamics of Josephson ladders is more complicated than that of the purely 1D sine-Gordon systems. © 1998 Elsevier Science B.V.
Barahona M, Strogatz SH, 1998, Superconducting states and depinning transitions of Josephson ladders, Physical Review B - Condensed Matter and Materials Physics, Vol: 57, Pages: 1181-1199, ISSN: 1098-0121
We present analytical and numerical studies of pinned superconducting states of open-ended Josephson ladder arrays, neglecting inductances but taking edge effects into account. Treating the edge effects perturbatively, we find analytical approximations for three of these superconducting states—the no-vortex, fully frustrated, and single-vortex states—as functions of the dc bias current (Formula presented) and the frustration (Formula presented). Bifurcation theory is used to derive formulas for the depinning currents and critical frustrations at which the superconducting states disappear or lose dynamical stability as (Formula presented) and (Formula presented) are varied. These results are combined to yield a zero-temperature stability diagram of the system with respect to (Formula presented) and (Formula presented). To highlight the effects of the edges, we compare this dynamical stability diagram to the thermodynamic phase diagram for the infinite system where edges have been neglected. We briefly indicate how to extend our methods to include self-inductances. © 1998 The American Physical Society.
Barahona M, Strogatz SH, 1998, Pinned states in Josephson arrays: A general stability theorem, Physical Review B - Condensed Matter and Materials Physics, Vol: 58, Pages: 5215-5218, ISSN: 1098-0121
Using the lumped circuit equations, we derive a stability criterion for superconducting pinned states in two-dimensional arrays of Josephson junctions. The analysis neglects quantum, thermal, and inductive effects, but allows disordered junctions, arbitrary network connectivity, and arbitrary spatial patterns of applied magnetic flux and dc current injection. We prove that a pinned state is linearly stable if and only if its corresponding stiffness matrix is positive definite. This algebraic condition can be used to predict the critical current and frustration at which depinning occurs. © 1998 The American Physical Society.
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- Citations: 2
Barahona M, Trias E, Orlando TP, et al., 1997, Resonances of dynamical checkerboard states in Josephson arrays with self-inductance, PHYSICAL REVIEW B, Vol: 55, Pages: 11989-11992, ISSN: 0163-1829
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- Citations: 18
Trfas E, Barahona M, Orlando TP, et al., 1997, Intrinsic phase-locked state in two-dimensional nb josephson arrays, IEEE Transactions on Applied Superconductivity, Vol: 7, Pages: 3103-3106, ISSN: 1051-8223
We present experimental results and numerical simulations of a new phase-locked state in twodimensional arrays when nearly fully frustrated and driven by a dc current. In this state all the rows of the array act coherently and phase-lock at a voltage that depends on the geometric loop inductance and junction capacitance. We also experimentally observe the resonance in one-dimensional ladder arrays implying that two-dimensional arrays have inter-row phase-locking mechanisms. The horizontal junctions also appear to play a role in the dynamics. © 1997 IEEE.
Barahona M, Poon CS, 1996, Detection of nonlinear dynamics in short, noisy time series, NATURE, Vol: 381, Pages: 215-217, ISSN: 0028-0836
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- Citations: 180
Poon CS, Barahona M, Merrill CK, 1996, Method and apparatus for detecting nonlinearity in a dynamical system, United States Patent 5792062, World WO1997043722
MORAN E, AMADOR U, BARAHONA M, et al., 1989, Ba2(RE)Cu3O7−δ(RE=La, Pr, Nd, Sm, Gd): Crystal growth, structure and magnetic properties, SOLID STATE IONICS, Vol: 32-3, Pages: {1154-1159}-{1154-1159}, ISSN: 0167-2738
MORAN E, AMADOR U, BARAHONA M, et al., 1988, BA2PRCU3O7 - CRYSTAL-GROWTH, STRUCTURE AND MAGNETIC-PROPERTIES, SOLID STATE COMMUNICATIONS, Vol: 67, Pages: 369-372, ISSN: 0038-1098
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- Citations: 30
MORAN E, AMADOR U, BARAHONA M, et al., 1988, BA2PR4+.3PR3+.7 CU3+.7 CU2+2.3O7 - CRYSTAL-GROWTH, STRUCTURE AND MAGNETIC-PROPERTIES, PHYSICA C, Vol: 153, Pages: 423-424, ISSN: 0921-4534
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- Citations: 6
MORAN E, AMADOR U, BARAHONA M, et al., 1988, REBA2CU3O7-DELTA (RE = PR, ND, SM, GD) - CRYSTAL-GROWTH, STRUCTURE AND MAGNETISM, SOLID STATE IONICS, Vol: 26, Pages: 167-167, ISSN: 0167-2738
Alario-Franco MA, Morán-Miguélez E, Sáez-Puche R, et al., 1988, The rare-earth H.T.S.C. family Ba2(RE)Cu3O7; structural, electrical and magnetic studies (RE=Y,Nd,Sm,Eu,Gd,Dy,Ho,Er,Tm), Materials Research Bulletin, Vol: 23, Pages: 313-321, ISSN: 0025-5408
Wittlin A, Genzel L, Cardona M, et al., 1988, Superconducting energy gap in MBa2Cu3O7 - Type materials, Physical Review B, Vol: 37, Pages: 652-655, ISSN: 0163-1829
We present a far-infrared study of ceramic superconductors of the MBa2Cu3O7 family with M=Dy, Sm0.5Ho0.5, and Sm0.5Y0.5. Emphasis is placed on the determination of the position of the superconducting energy gap Eg and its temperature dependence. We find that for all compositions studied EgkBTc3.20.3. We also find indications of the temperature dependence of the gap and discuss the influence of the phonon features on the quantitative determination of the gap position. © 1988 The American Physical Society.
Cardona M, Liu R, Thomsen C, et al., 1988, Infrared and Raman spectra of the new superconducting cuprate perovskites MBa2Cu3O7, M =Nd, Dy, Er, Tm, Solid State Communications, Vol: 65, Pages: 71-75, ISSN: 0038-1098
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