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• Journal article
  Strelkowa N, Barahona M, 2010,

  Switchable genetic oscillator operating in quasi-stable mode

  , JOURNAL OF THE ROYAL SOCIETY INTERFACE, Vol: 7, Pages: {1071-1082}-{1071-1082}, ISSN: 1742-5689

  Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behaviour in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie the sustained oscillations observed in even rings in the stochastic regime, even if these circuits are expected to behave as switches. The existence of such solutions can also be exploited for control purposes: operation of the system around the quasi-stable orbit allows us to turn on and off the oscillations reliably and on demand. We illustrate these ideas with a simple protocol based on optical interference that can induce oscillations robustly both in the stochastic and deterministic regimes.

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• Conference paper
  Drakakis E, Yaliraki S, Barahona M, 2009,

  Memristors and Bernoulli Dynamics

  , Berkeley, IEEE CNNA, Publisher: IEEE, Pages: 1-6
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• Journal article
  Hemberg M, Barahona M, 2008,

  A Dominated Coupling From The Past algorithm for the stochastic simulation of networks of biochemical reactions

  , BMC SYSTEMS BIOLOGY, Vol: 2, ISSN: 1752-0509

  Background: In recent years, stochastic descriptions of biochemical reactions based on the Master Equation (ME) have become widespread. These are especially relevant for models involving gene regulation. Gillespie’s Stochastic Simulation Algorithm (SSA) is the most widely used method for the numerical evaluation of these models. The SSA produces exact samples from the distribution of the ME for finite times. However, if the stationary distribution is of interest, the SSA provides no information about convergence or how long the algorithm needs to be run to sample from the stationary distribution with given accuracy. Results: We present a proof and numerical characterization of a Perfect Sampling algorithm for the ME of networks of biochemical reactions prevalent in gene regulation and enzymatic catalysis. Our algorithm combines the SSA with Dominated Coupling From The Past (DCFTP) techniques to provide guaranteed sampling from the stationary distribution. The resulting DCFTP-SSA is applicable to networks of reactions with uni-molecular stoichiometries and sub-linear, (anti-) monotone propensity functions. We showcase its applicability studying steady-state properties of stochastic regulatory networks of relevance in synthetic and systems biology. Conclusion: The DCFTP-SSA provides an extension to Gillespie’s SSA with guaranteed sampling from the stationary solution of the ME for a broad class of stochastic biochemical networks.

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• Journal article
  Chang HH, Hemberg M, Barahona M, Ingber DE, Huang Set al., 2008,

  Transcriptome-wide noise controls lineage choice in mammalian progenitor cells

  , NATURE, Vol: 453, Pages: {544-U10}-{544-U10}, ISSN: 0028-0836

  Phenotypic cell-to-cell variability within clonal populations may be a manifestation of ‘gene expression noise’(1-6), or it may reflect stable phenotypic variants(7). Such ‘non-genetic cell individuality’(7) can arise from the slow fluctuations of protein levels(8) in mammalian cells. These fluctuations produce persistent cell individuality, thereby rendering a clonal population heterogeneous. However, it remains unknown whether this heterogeneity may account for the stochasticity of cell fate decisions in stem cells. Here we show that in clonal populations of mouse haematopoietic progenitor cells, spontaneous ‘outlier’ cells with either extremely high or low expression levels of the stem cell marker Sca-1 (also known as Ly6a; ref. 9) reconstitute the parental distribution of Sca-1 but do so only after more than one week. This slow relaxation is described by a gaussian mixture model that incorporates noise- driven transitions between discrete subpopulations, suggesting hidden multi-stability within one cell type. Despite clonality, the Sca-1 outliers had distinct transcriptomes. Although their unique gene expression profiles eventually reverted to that of the median cells, revealing an attractor state, they lasted long enough to confer a greatly different proclivity for choosing either the erythroid or the myeloid lineage. Preference in lineage choice was associated with increased expression of lineage-specific transcription factors, such as a > 200-fold increase in Gata1 (ref. 10) among the erythroid-prone cells, or a > 15-fold increased PU.1 (Sfpi1) (ref. 11) expression among myeloid-prone cells. Thus, clonal heterogeneity of gene expression level is not due to independent noise in the expression of individual genes, but reflects metastable states of a slowly fluctuating transcriptome that is distinct in individual cells and may govern the reversible, stochastic priming of multipotent progenitor cells in cell fate decision

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• Journal article
  Alley SH, Ces O, Barahona M, Templer RHet al., 2008,

  X-ray diffraction measurement of the monolayer spontaneous curvature of dioleoylphosphatidylglycerol

  , CHEMISTRY AND PHYSICS OF LIPIDS, Vol: 154, Pages: {64-67}-{64-67}, ISSN: 0009-3084

  Phosphatidylglycerol (PG) is an anionic lipid commonly found in large proportions in the cell membranes of bacteria and plants and, to a lesser extent, in animal cells. PG plays an important role in the regulation and determination of the elastic properties of the membrane. Using small angle X-ray scattering experiments, we obtain that the monolayer spontaneous curvature of dioleoylphosphatidylglycerol (DOPG) is -1/150 +/- 0.021 nm(-1) when measured in 150mM NaCl. When the experiments are carried out in 150 mM NaCl and 20 mM MgCl2, the value obtained for the monolayer spontaneous curvature is -1/8.7 +/- 0.037 nm(-1). These values are of importance in modelling the effects of curvature elastic stress in membrane lipid homeostasis in the bacterium Acholeplasma laidlawii [Alley, S.H., Barahona, M., Ces, O., Templer, R.H., in press. Biophysical regulation of lipid biosynthesis in the plasma membrane. Biophys. J.] and indicate that divalent cations can play a significant role in altering curvature elastic stress. (C) 2008 Elsevier Ireland Ltd. All rights reserved.

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• Journal article
  Alley SH, Ces O, Templer RH, Barahona Met al., 2008,

  Biophysical regulation of lipid biosynthesis in the plasma membrane

  , BIOPHYSICAL JOURNAL, Vol: 94, Pages: {2938-2954}-{2938-2954}, ISSN: 0006-3495

  We present a cellular model of lipid biosynthesis in the plasma membrane that couples biochemical and biophysical features of the enzymatic network of the cell-wall-less Mycoplasma Acholeplasma laidlawii. In particular, we formulate how the stored elastic energy of the lipid bilayer can modify the activity of curvature-sensitive enzymes through the binding of amphipathic a-helices. As the binding depends on lipid composition, this results in a biophysical feedback mechanism for the regulation of the stored elastic energy. The model shows that the presence of feedback increases the robustness of the steady state of the system, in the sense that biologically inviable nonbilayer states are less likely. We also show that the biophysical and biochemical features of the network have implications as to which enzymes are most efficient at implementing the regulation. The network imposes restrictions on the steady-state balance between bilayer and nonbilayer lipids and on the concentrations of particular lipids. Finally, we consider the influence of the length of the amphipathic a-helix on the efficacy of the feedback and propose experimental measurements and extensions of the modeling framework.

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• Journal article
  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.

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• Journal article
  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.

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• Journal article
  August E, Parker KH, Barahona M, 2006,

  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.

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• Conference paper
  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
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