Publications
211 results found
Beguerisse-Díaz M, Wang B, Desikan R, et al., 2012, Squeeze-and-breathe evolutionary Monte Carlo optimization with local search acceleration and its application to parameter fitting, Journal of The Royal Society Interface
Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy datasets. Over the years, a variety of heuristics have been proposed to solve this complex optimization problem, with good results in some cases yet with limitations in the biological setting. In this work, we develop an algorithm for model parameter fitting that combines ideas from evolutionary algorithms, sequential Monte Carlo and direct search optimization. Our method performs well even when the order of magnitude and/or the range of the parameters is unknown. The method refines iteratively a sequence of parameter distributions through local optimization combined with partial resampling from a historical prior defined over the support of all previous iterations. We exemplify our method with biological models using both simulated and real experimental data and estimate the parameters efficiently even in the absence of a priori knowledge about the parameters.
Strelkowa N, Barahona M, 2012, Stochastic Oscillatory Dynamics of Generalized Repressilators, NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B, Vol: 1479, Pages: 662-666, ISSN: 0094-243X
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- Citations: 2
Georgiou PS, Yaliraki SN, Drakakis EM, et al., 2012, Quantitative Measure of Hysteresis for Memristors through Explicit Dynamics, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol: 468, Pages: 2210-2229, ISSN: 1471-2946
Dominguez-Huttinger E, Ono M, Barahona M, et al., 2011, Mathematical modelling approach for systems-level understanding of skin barrier homeostasis in Atopic dermatitis, Annual Congress of the British-Society-for-Immunology, Publisher: WILEY-BLACKWELL, Pages: 36-36, ISSN: 0019-2805
Yuan Y, Stan G-B, Barahona M, et al., 2011, Decentralised minimal-time consensus, Publisher: IEEE, Pages: 4282 -4289-4282 -4289, ISSN: 0743-1546
This study considers the discrete-time dynamics of a network of agents that exchange information according to the nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the consensus value of the whole network in finite time using only the minimal number of successive values of its own history. We show that this minimal number of steps is related to a Jordan block decomposition of the network dynamics and present an algorithm to obtain the minimal number of steps in question by checking a rank condition on a Hankel matrix of the local observations. Furthermore, we prove that the minimal number of steps is related to other algebraic and graph theoretical notions that can be directly computed from the Laplacian matrix of the graph and from the underlying graph topology.
Wu J, Barahona M, Tan Y-J, et al., 2011, Spectral Measure of Structural Robustness in Complex Networks, Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, Vol: 41, Pages: 1244 -1252-1244 -1252, ISSN: 1083-4427
We introduce the concept of natural connectivity as a measure of structural robustness in complex networks. The natural connectivity characterizes the redundancy of alternative routes in a network by quantifying the weighted number of closed walks of all lengths. This definition leads to a simple mathematical formulation that links the natural connectivity to the spectrum of a network. The natural connectivity can be regarded as an average eigenvalue that changes strictly monotonically with the addition or deletion of edges. We calculate both analytically and numerically the natural connectivity of three typical networks: regular ring lattices, random graphs, and random scale-free networks. We also compare the proposed natural connectivity to other structural robustness measures within a scenario of edge elimination and demonstrate that the natural connectivity provides sensitive discrimination of structural robustness that agrees with our intuition.
Delmotte A, Tate EW, Yaliraki SN, et al., 2011, Protein multi-scale organization through graph partitioning and robustness analysis: application to the myosin-myosin light chain interaction, PHYSICAL BIOLOGY, Vol: 8, ISSN: 1478-3975
Despite the recognized importance of the multi-scale spatio-temporal organization of proteins, most computational tools can only access a limited spectrum of time and spatial scales, thereby ignoring the effects on protein behavior of the intricate coupling between the different scales. Starting from a physico-chemical atomistic network of interactions that encodes the structure of the protein, we introduce a methodology based on multi-scale graph partitioning that can uncover partitions and levels of organization of proteins that span the whole range of scales, revealing biological features occurring at different levels of organization and tracking their effect across scales. Additionally, we introduce a measure of robustness to quantify the relevance of the partitions through the generation of biochemically-motivated surrogate random graph models. We apply the method to four distinct conformations of myosin tail interacting protein, a protein from the molecular motor of the malaria parasite, and study properties that have been experimentally addressed such as the closing mechanism, the presence of conserved clusters, and the identification through computational mutational analysis of key residues for binding.
Georgiou PS, Barahona M, Yaliraki SN, et al., 2011, Device Properties of Bernoulli Memristors, Proceedings of the IEEE, Vol: 100, Pages: 1-13, ISSN: 0018-9219
Vangelov B, Barahona M, 2011, A COMPUTATIONAL FRAMEWORK FOR RECONSTRUCTION OF EPIGENETIC LANDSCAPES FROM GENE EXPRESSION DATA, Publisher: ELSEVIER SCIENCE INC, Pages: S89-S89, ISSN: 0301-472X
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- Citations: 1
Lambiotte R, Sinatra R, Delvenne JC, et al., 2011, Flow graphs: Interweaving dynamics and structure, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol: 84, ISSN: 1539-3755
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential because different dynamical processes may be affected very differently by network topology. A full characterization of such systems thus requires a formalization that encompasses both aspects simultaneously, rather than relying only on the topological adjacency matrix. To achieve this, we introduce the concept of flow graphs, namely weighted networks where dynamical flows are embedded into the link weights. Flow graphs provide an integrated representation of the structure and dynamics of the system, which can then be analyzed with standard tools from network theory. Conversely, a structural network feature of our choice can also be used as the basis for the construction of a flow graph that will then encompass a dynamics biased by such a feature. We illustrate the ideas by focusing on the mathematical properties of generic linear processes on complex networks that can be represented as biased random walks and their dual consensus dynamics, and show how our framework improves our understanding of these processes. © 2011 American Physical Society.
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- Citations: 62
Wu J, Barahona M, Tan Y-J, et al., 2011, Robustness of regular ring lattices based on natural connectivity, International Journal of Systems Science, Vol: 42, Pages: 1085-1092-1085-1092, ISSN: 0020-7721
It has been recently proposed that natural connectivity can be used to efficiently characterise the robustness of complex networks. The natural connectivity quantifies the redundancy of alternative routes in the network by evaluating the weighted number of closed walks of all lengths and can be seen as an average eigenvalue obtained from the graph spectrum. In this article, we explore both analytically and numerically the natural connectivity of regular ring lattices and regular random graphs obtained through degree-preserving random rewirings from regular ring lattices. We reformulate the natural connectivity of regular ring lattices in terms of generalised Bessel functions and show that the natural connectivity of regular ring lattices is independent of network size and increases with K monotonically. We also show that random regular graphs have lower natural connectivity, and are thus less robust, than regular ring lattices.
Strelkowa N, Barahona M, 2011, Transient dynamics around unstable periodic orbits in the generalized repressilator model, CHAOS, Vol: 21, ISSN: 1054-1500
We study the temporal dynamics of the generalized repressilator, a network of coupled repressing genes arranged in a directed ring topology, and give analytical conditions for the emergence of a finite sequence of unstable periodic orbits that lead to reachable long-lived oscillating transients. Such transients dominate the finite time horizon dynamics that is relevant in confined, noisy environments such as bacterial cells (see our previous work [Strelkowa and Barahona, J. R. Soc. Interface 7, 1071 (2010)]), and are therefore of interest for bioengineering and synthetic biology. We show that the family of unstable orbits possesses spatial symmetries and can also be understood in terms of traveling wave solutions of kink-like topological defects. The long-lived oscillatory transients correspond to the propagation of quasistable two-kink configurations that unravel over a long time. We also assess the similarities between the generalized repressilator model and other unidirectionally coupled electronic systems, such as magnetic flux gates, which have been implemented experimentally. (C) 2011 American Institute of Physics. [doi:10.1063/1.3574387]
August E, Barahona M, 2011, Obtaining certificates for complete synchronisation of coupled oscillators, Physica D: Nonlinear Phenomena, Vol: 240, Pages: 795-803, ISSN: 0167-2789
In this paper, we provide a novel reformulation of sufficient conditions that guarantee global complete synchronisation of coupled identical oscillators to make them computationally implementable. To this end, we use semidefinite programming techniques. For the first time, we can efficiently search for and obtain certificates for synchronisability and, additionally, also optimise associated cost functions. In this paper, a Lyapunov-like function (certificate) is used to certify that all trajectories of a networked system consisting of coupled dynamical systems will eventually converge towards a common one, which implies synchronisation. Moreover, we establish new conditions for complete synchronisation, which are based on the so called Bendixson’s Criterion for higher dimensional systems. This leads to major improvements on the lower bound of the coupling constant that guarantees global complete synchronisation. Importantly, the certificates are obtained by analysing the connection network and the model representing an individual system only. In order to illustrate the strength of our method we apply it to a system of coupled identical Lorenz oscillators and to coupled van der Pol oscillators. (C) 2010 Elsevier B.V. All rights reserved.
Cooper K, Barahona M, 2011, Role-similarity based comparison of directed networks
The widespread relevance of complex networks is a valuable tool in theanalysis of a broad range of systems. There is a demand for tools which enablethe extraction of meaningful information and allow the comparison betweendifferent systems. We present a novel measure of similarity between nodes indifferent networks as a generalization of the concept of self-similarity. Asimilarity matrix is assembled as the distance between feature vectors thatcontain the in and out paths of all lengths for each node. Hence, nodesoperating in a similar flow environment are considered similar regardless ofnetwork membership. We demonstrate that this method has the potential to beinfluential in tasks such as assigning identity or function to uncharacterizednodes. In addition an innovative application of graph partitioning to the rawresults extends the concept to the comparison of networks in terms of theirunderlying role-structure.
Cooper K, Barahona M, 2010, Role-based similarity in directed networks
The widespread relevance of increasingly complex networks requires methods toextract meaningful coarse-grained representations of such systems. Forundirected graphs, standard community detection methods use criteria largelybased on density of connections to provide such representations. We propose amethod for grouping nodes in directed networks based on the role of the nodesin the network, understood in terms of patterns of incoming and outgoing flows.The role groupings are obtained through the clustering of a similarity matrix,formed by the distances between feature vectors that contain the number of inand out paths of all lengths for each node. Hence nodes operating in a similarflow environment are grouped together although they may not themselves bedensely connected. Our method, which includes a scale factor that revealsrobust groupings based on increasingly global structure, provides analternative criterion to uncover structure in networks where there is animplicit flow transfer in the system. We illustrate its application to avariety of data from ecology, world trade and cellular metabolism.
Wu J, Barahona M, Tan Y, et al., 2010, Robustness of Random Graphs Based on Natural Connectivity
Recently, it has been proposed that the natural connectivity can be used toefficiently characterise the robustness of complex networks. Naturalconnectivity quantifies the redundancy of alternative routes in a network byevaluating the weighted number of closed walks of all lengths and can beregarded as the average eigenvalue obtained from the graph spectrum. In thisarticle, we explore the natural connectivity of random graphs both analyticallyand numerically and show that it increases linearly with the average degree. Bycomparing with regular ring lattices and random regular graphs, we show thatrandom graphs are more robust than random regular graphs; however, therelationship between random graphs and regular ring lattices depends on theaverage degree and graph size. We derive the critical graph size as a functionof the average degree, which can be predicted by our analytical results. Whenthe graph size is less than the critical value, random graphs are more robustthan regular ring lattices, whereas regular ring lattices are more robust thanrandom graphs when the graph size is greater than the critical value.
Wu J, Barahona M, Tan Y-J, et al., 2010, Natural Connectivity of Complex Networks, CHINESE PHYSICS LETTERS, Vol: 27, ISSN: 0256-307X
The concept of natural connectivity is reported as a robustness measure of complex networks. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It is shown that the natural connectivity can be derived mathematically from the graph spectrum as an average eigenvalue and that it changes strictly monotonically with the addition or deletion of edges. By comparing the natural connectivity with other typical robustness measures within a scenario of edge elimination, it is demonstrated that the natural connectivity has an acute discrimination which agrees with our intuition.
Delvenne J-C, Yaliraki SN, Barahona M, 2010, Stability of graph communities across time scales, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, Vol: 107, Pages: {12755-12760}-{12755-12760}, ISSN: 0027-8424
The complexity of biological, social, and engineering networks makes it desirable to find natural partitions into clusters ( or communities) that can provide insight into the structure of the overall system and even act as simplified functional descriptions. Although methods for community detection abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We introduce here the stability of a partition, a measure of its quality as a community structure based on the clustered autocovariance of a dynamic Markov process taking place on the network. Because the stability has an intrinsic dependence on time scales of the graph, it allows us to compare and rank partitions at each time and also to establish the time spans over which partitions are optimal. Hence the Markov time acts effectively as an intrinsic resolution parameter that establishes a hierarchy of increasingly coarser communities. Our dynamical definition provides a unifying framework for several standard partitioning measures: modularity and normalized cut size can be interpreted as one-step time measures, whereas Fiedler’s spectral clustering emerges at long times. We apply our method to characterize the relevance of partitions over time for constructive and real networks, including hierarchical graphs and social networks, and use it to obtain reduced descriptions for atomic-level protein structures over different time scales.
Grima R, Yaliraki SN, Barahona M, 2010, Crowding-Induced Anisotropic Transport Modulates Reaction Kinetics in Nanoscale Porous Media, JOURNAL OF PHYSICAL CHEMISTRY B, Vol: 114, Pages: {5380-5385}-{5380-5385}, ISSN: 1520-6106
We quantify the emergence of persistent anisotropy in the diffusion of spherical tracer particles through a nanoscale porous medium composed of a uniform distribution of purely symmetric crowding particles. We focus on the interior of a biological cell as an example of such a medium and find that diffusion is highly directional for distances comparable to the size of some organelles. We use a geometrical procedure that avoids the standard orientational averaging to quantify the anisotropy of diffusive paths and show that the point source distributions are predominantly of prolate ellipsoidal shape as a result of local volume exclusion. This geometrical symmetry breaking strongly skews the distribution of kinetic rates of diffusion-limited reactions toward small values, leading to the result that, for short to intermediate times, almost 80% of the rates measured in an ensemble of heterogeneous media are smaller than the expected rate in an ideal homogeneous medium of similar excluded volume fraction. This crowding-induced modulation may have implications for our understanding and measurement of diffusion-controlled intracellular reaction kinetics and for experimental nanotechnology applications, such as nanoparticle-based bioimaging and drug delivery, where diffusion plays an important role.
Anastassiou CA, Montgomery SM, Barahona M, et al., 2010, The Effect of Spatially Inhomogeneous Extracellular Electric Fields on Neurons, JOURNAL OF NEUROSCIENCE, Vol: 30, Pages: {1925-1936}-{1925-1936}, ISSN: 0270-6474
The cooperative action of neurons and glia generates electrical fields, but their effect on individual neurons via ephaptic interactions is mostly unknown. Here, we analyze the impact of spatially inhomogeneous electric fields on the membrane potential, the induced membrane field, and the induced current source density of one-dimensional cables as well as morphologically realistic neurons and discuss how the features of the extracellular field affect these quantities. We show through simulations that endogenous fields, associated with hippocampal theta and sharp waves, can greatly affect spike timing. These findings imply that local electric fields, generated by the cooperative action of brain cells, can influence the timing of neural activity.
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.
August E, Barahona M, 2010, Solutions of weakly reversible chemical reaction networks are bounded and persistent, Pages: 42-47, ISSN: 1474-6670
We present extensions to chemical reaction network theory which are relevant to the analysis of models of biochemical systems. We show that, for positive initial conditions, solutions of a weakly reversible chemical reaction network are bounded and remain in the positive orthant. Thus, weak reversibility implies persistence as conjectured by Martin Feinberg. Our result provides a qualitative criterion to establish that a biochemical network will not diverge or converge to the boundary, where some concentration levels are zero. It relies on checking structural properties of the graph of the reaction network solely. It can also be used to characterise certain bifurcations from stationary to oscillatory behaviour. We illustrate the use of our result through applications. © 2010 IFAC.
Phoka E, Wildie M, Petersen RS, et al., 2010, How is a sensory stimulus represented in ongoing dynamics in the barrel cortex?, Annual Computational Neuroscience Meeting
Engin Z, Ng J, Barahona M, et al., 2009, An analysis of the Map Seeking Circuit and Monte Carlo extensions, Pages: 2929 -2932-2929 -2932, ISSN: 1520-6149
The Map Seeking Circuit (MSC) has been suggested to address the inverse problem of transformation discovery as found in signal processing, vision, inverse kinematics and many other natural tasks. According to this idea, a parallel search in the transformation space of a high dimensional problem can be decomposed into parts efficiently using the ordering property of superpositions. Deterministic formulations of the circuit have been suggested. Here, we provide a probabilistic interpretation of the architecture whereby the superpositions of the circuit are seen as a series of marginalisations over parameters of the transform. Based on this, we interpret the weights of the MSC as importance weights. The latter suggests the incorporation of Monte-Carlo approaches in the MSC, providing improved resolution of parameter estimates within resource constrained implementations. As a final contribution, we model mixed serial/parallel search strategies of biological vision to reduce the problem of collusions, a common problem in the standard MSC approach.
Drakakis E, Yaliraki S, Barahona M, 2009, Memristors and Bernoulli Dynamics, Berkeley, IEEE CNNA, Publisher: IEEE, Pages: 1-6
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.
Chang HH, Hemberg M, Barahona M, et 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
Alley SH, Ces O, Barahona M, et 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.
Alley SH, Ces O, Templer RH, et 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.
Lazaridis E, Barahona M, Drakakis EM, 2008, Biorealistic Neural Networks, Chaos Conference
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