1
|
Papo D, Buldú JM. Does the brain behave like a (complex) network? I. Dynamics. Phys Life Rev 2024; 48:47-98. [PMID: 38145591 DOI: 10.1016/j.plrev.2023.12.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 12/10/2023] [Indexed: 12/27/2023]
Abstract
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.
Collapse
Affiliation(s)
- D Papo
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, Ferrara, Italy; Center for Translational Neurophysiology, Fondazione Istituto Italiano di Tecnologia, Ferrara, Italy.
| | - J M Buldú
- Complex Systems Group & G.I.S.C., Universidad Rey Juan Carlos, Madrid, Spain
| |
Collapse
|
2
|
Rinaldo A, Rodriguez-Iturbe I. Ecohydrology 2.0. RENDICONTI LINCEI. SCIENZE FISICHE E NATURALI 2022; 33:245-270. [PMID: 35673327 PMCID: PMC9165276 DOI: 10.1007/s12210-022-01071-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/10/2022] [Accepted: 03/27/2022] [Indexed: 11/23/2022]
Abstract
This paper aims at a definition of the domain of ecohydrology, a relatively new discipline borne out of an intrusion-as advertised by this Topical Collection of the Rendiconti Lincei-of hydrology and geomorphology into ecology (or vice-versa, depending on the reader's background). The study of hydrologic controls on the biota proves, in our view, significantly broader than envisioned by its original focus that was centered on the critical zone where much of the action of soil, climate and vegetation interactions takes place. In this review of related topics and contributions, we propose a reasoned broadening of perspective, in particular by firmly centering ecohydrology on the fluvial catchment as its fundamental control volume. A substantial unity of materials and methods suggests that our advocacy may be considered legitimate.
Collapse
Affiliation(s)
- Andrea Rinaldo
- Accademia Nazionale dei Lincei, Rome, Italy
- Laboratory of Ecohydrology ENAC/IIE/ECHO, École Polytechinque Fédérale de Lausanne, Lausanne, Switzerland
- Dipartimento ICEA, Università degli studi di Padova, Padua, Italy
| | - Ignacio Rodriguez-Iturbe
- Department of Ocean Engineering, Texas A&M University, College Station, TX USA
- Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX USA
| |
Collapse
|
3
|
Morgado G, Nowakowski B, Lemarchand A. Fisher-Kolmogorov-Petrovskii-Piskunov wave front as a sensor of perturbed diffusion in concentrated systems. Phys Rev E 2019; 99:022205. [PMID: 30934359 DOI: 10.1103/physreve.99.022205] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2018] [Indexed: 01/17/2023]
Abstract
The sensitivity to perturbations of the Fisher and Kolmogorov, Petrovskii, Piskunov front is used to find a quantity revealing perturbations of diffusion in a concentrated solution of two chemical species with different diffusivities. The deterministic dynamics includes cross-diffusion terms due to the deviation from the dilution limit. The behaviors of the front speed, the shift between the concentration profiles of the two species, and the width of the reactive zone are investigated, both analytically and numerically. The shift between the two profiles turns out to be a well-adapted criterion presenting noticeable variations with the deviation from the dilution limit in a wide range of parameter values.
Collapse
Affiliation(s)
- Gabriel Morgado
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.,Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4 place Jussieu, case courrier 121, 75252 Paris CEDEX 05, France
| | - Bogdan Nowakowski
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.,SGGW, Warsaw University of Life Sciences, Nowoursynowska 159, 02-776 Warsaw, Poland
| | - Annie Lemarchand
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4 place Jussieu, case courrier 121, 75252 Paris CEDEX 05, France
| |
Collapse
|
4
|
Giometto A, Altermatt F, Rinaldo A. Demographic stochasticity and resource autocorrelation control biological invasions in heterogeneous landscapes. OIKOS 2017. [DOI: 10.1111/oik.04330] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Andrea Giometto
- Laboratory of Ecohydrology, School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne; CH-1015 Lausanne Switzerland
- Dept of Molecular and Cellular Biology; Harvard Univ.; Cambridge MA USA
- Swiss Federal Inst. of Aquatic Science and Technology, Dept of Aquatic Ecology; Dübendorf Switzerland
| | - Florian Altermatt
- Swiss Federal Inst. of Aquatic Science and Technology, Dept of Aquatic Ecology; Dübendorf Switzerland
- Dept of Evolutionary Biology and Environmental Studies; Univ. of Zürich; Zürich Switzerland
| | - Andrea Rinaldo
- Laboratory of Ecohydrology, School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne; CH-1015 Lausanne Switzerland
- Dipto di Ingegneria Civile; Edile ed Ambientale, Univ. di Padova; Padua Italy
| |
Collapse
|
5
|
Zhang J, Osan R. Analytically tractable studies of traveling waves of activity in integrate-and-fire neural networks. Phys Rev E 2016; 93:052228. [PMID: 27300901 DOI: 10.1103/physreve.93.052228] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2015] [Indexed: 11/07/2022]
Abstract
In contrast to other large-scale network models for propagation of electrical activity in neural tissue that have no analytical solutions for their dynamics, we show that for a specific class of integrate and fire neural networks the acceleration depends quadratically on the instantaneous speed of the activity propagation. We use this property to analytically compute the network spike dynamics and to highlight the emergence of a natural time scale for the evolution of the traveling waves. These results allow us to examine other applications of this model such as the effect that a nonconductive gap of tissue has on further activity propagation. Furthermore we show that activity propagation also depends on local conditions for other more general connectivity functions, by converting the evolution equations for network dynamics into a low-dimensional system of ordinary differential equations. This approach greatly enhances our intuition into the mechanisms of the traveling waves evolution and significantly reduces the simulation time for this class of models.
Collapse
Affiliation(s)
- Jie Zhang
- Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA
| | - Remus Osan
- Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA.,Neuroscience Institute, Georgia State University, Atlanta, Georgia 30093, USA
| |
Collapse
|
6
|
|
7
|
Iomin A, Méndez V. Reaction-subdiffusion front propagation in a comblike model of spiny dendrites. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:012706. [PMID: 23944491 DOI: 10.1103/physreve.88.012706] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2013] [Revised: 06/07/2013] [Indexed: 06/02/2023]
Abstract
Fractional reaction-diffusion equations are derived by exploiting the geometrical similarities between a comb structure and a spiny dendrite. In the framework of the obtained equations, two scenarios of reaction transport in spiny dendrites are explored, where both a linear reaction in spines and nonlinear Fisher-Kolmogorov-Petrovskii-Piskunov reactions along dendrites are considered. In the framework of fractional subdiffusive comb model, we develop a Hamilton-Jacobi approach to estimate the overall velocity of the reaction front propagation. One of the main effects observed is the failure of the front propagation for both scenarios due to either the reaction inside the spines or the interaction of the reaction with the spines. In the first case the spines are the source of reactions, while in the latter case, the spines are a source of a damping mechanism.
Collapse
Affiliation(s)
- A Iomin
- Department of Physics, Technion, Haifa 32000, Israel
| | | |
Collapse
|
8
|
Curtis CW, Bortz DM. Propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:066108. [PMID: 23368005 DOI: 10.1103/physreve.86.066108] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2012] [Revised: 09/17/2012] [Indexed: 06/01/2023]
Abstract
The propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion coefficients is studied. Using coordinate changes, WKB approximations, and multiple scales analysis, we provide an analytic framework that describes propagation of the front up to the minimum of the diffusion coefficient. We also present results showing the behavior of the front after it passes the minimum. In each case, we show that standard traveling coordinate frames do not properly describe front propagation. Last, we provide numerical simulations to support our analysis and to show, that around the minimum, the motion of the front is arrested on asymptotically significant time scales.
Collapse
Affiliation(s)
- Christopher W Curtis
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
| | | |
Collapse
|
9
|
Propagation of CaMKII translocation waves in heterogeneous spiny dendrites. J Math Biol 2012; 66:1499-525. [PMID: 22588358 DOI: 10.1007/s00285-012-0542-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2011] [Revised: 04/18/2012] [Indexed: 10/28/2022]
Abstract
CaMKII (Ca²⁺-calmodulin-dependent protein kinase II) is a key regulator of glutamatergic synapses and plays an essential role in many forms of synaptic plasticity. It has recently been observed experimentally that stimulating a local region of dendrite not only induces the local translocation of CaMKII from the dendritic shaft to synaptic targets within spines, but also initiates a wave of CaMKII translocation that spreads distally through the dendrite with an average speed of order 1 μm/s. We have previously developed a simple reaction-diffusion model of CaMKII translocation waves that can account for the observed wavespeed and predicts wave propagation failure if the density of spines is too high. A major simplification of our previous model was to treat the distribution of spines as spatially uniform. However, there are at least two sources of heterogeneity in the spine distribution that occur on two different spatial scales. First, spines are discrete entities that are joined to a dendritic branch via a thin spine neck of submicron radius, resulting in spatial variations in spine density at the micron level. The second source of heterogeneity occurs on a much longer length scale and reflects the experimental observation that there is a slow proximal to distal variation in the density of spines. In this paper, we analyze how both sources of heterogeneity modulate the speed of CaMKII translocation waves along a spiny dendrite. We adapt methods from the study of the spread of biological invasions in heterogeneous environments, including homogenization theory of pulsating fronts and Hamilton-Jacobi dynamics of sharp interfaces.
Collapse
|
10
|
|
11
|
Gaudart J, Ghassani M, Mintsa J, Rachdi M, Waku J, Demongeot J. Demography and diffusion in epidemics: malaria and black death spread. Acta Biotheor 2010; 58:277-305. [PMID: 20706773 DOI: 10.1007/s10441-010-9103-z] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2010] [Accepted: 06/28/2010] [Indexed: 01/14/2023]
Abstract
The classical models of epidemics dynamics by Ross and McKendrick have to be revisited in order to incorporate elements coming from the demography (fecundity, mortality and migration) both of host and vector populations and from the diffusion and mutation of infectious agents. The classical approach is indeed dealing with populations supposed to be constant during the epidemic wave, but the presently observed pandemics show duration of their spread during years imposing to take into account the host and vector population changes as well as the transient or permanent migration and diffusion of hosts (susceptible or infected), as well as vectors and infectious agents. Two examples are presented, one concerning the malaria in Mali and the other the plague at the middle-age.
Collapse
Affiliation(s)
- J Gaudart
- LERTIM, EA 3283, Faculty of Medicine, Aix-Marseille University, 27 Bd Jean Moulin, 13385 Marseille Cedex 5, France.
| | | | | | | | | | | |
Collapse
|
12
|
Missel AR, Dahmen KA. Hopping transport in hostile reaction-diffusion systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:021126. [PMID: 19391725 DOI: 10.1103/physreve.79.021126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2008] [Revised: 01/13/2009] [Indexed: 05/27/2023]
Abstract
We investigate transport in a disordered reaction-diffusion model consisting of particles which are allowed to diffuse, compete with one another (2A-->A) , give birth in small areas called "oases" (A-->2A) , and die in the "desert" outside the oases (A-->0) . This model has previously been used to study bacterial populations in the laboratory and is related to a model of plankton populations in the oceans. We first consider the nature of transport between two oases: In the limit of high growth rate, this is effectively a first passage process, and we are able to determine the first passage time probability density function in the limit of large oasis separation. This result is then used along with the theory of hopping conduction in doped semiconductors to estimate the time taken by a population to cross a large system.
Collapse
Affiliation(s)
- Andrew R Missel
- Physics Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
| | | |
Collapse
|
13
|
Missel AR, Dahmen KA. Hopping conduction and bacteria: transport in disordered reaction-diffusion systems. PHYSICAL REVIEW LETTERS 2008; 100:058301. [PMID: 18352440 DOI: 10.1103/physrevlett.100.058301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2007] [Indexed: 05/26/2023]
Abstract
We report some basic results regarding transport in disordered reaction-diffusion systems with birth (A-->2A), death (A-->0), and binary competition (2A-->A) processes. We consider a model in which the growth process is only allowed to take place in certain areas--"oases"--while the rest of space--the "desert"--is hostile to growth. In the limit of low oasis density, transport is mediated through rare "hopping" events, necessitating the inclusion of discreteness effects in the model. By first considering transport between two oases, we are able to derive an approximate expression for the average time taken for a population to traverse a disordered medium.
Collapse
Affiliation(s)
- Andrew R Missel
- Physics Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
| | | |
Collapse
|
14
|
Fort J, Pérez-Losada J, Isern N. Fronts from integrodifference equations and persistence effects on the Neolithic transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:031913. [PMID: 17930277 DOI: 10.1103/physreve.76.031913] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2007] [Revised: 07/31/2007] [Indexed: 05/25/2023]
Abstract
We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%).
Collapse
Affiliation(s)
- Joaquim Fort
- Departament de Física, Universitat de Girona, 17071 Girona, Catalonia, Spain
| | | | | |
Collapse
|
15
|
Zemskov EP. Wavy front dynamics in a three-component reaction-diffusion system with one activator and two inhibitors. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:046127. [PMID: 16711898 DOI: 10.1103/physreve.73.046127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2005] [Revised: 02/06/2006] [Indexed: 05/09/2023]
Abstract
An analytic description for traveling waves in a one-dimensional reaction-diffusion system with one activator and two inhibitors and with equal diffusion constants is developed using a piecewise linear approximation for the nonlinear activator reaction term. The case of front waves is examined in more detail, the monotonic and oscillating fronts being separately considered. The corresponding wave profiles are constructed, and the speed equation is obtained and discussed. It is found that the fronts in the three-component model propagate faster than the fronts in the two-component system. The front interaction is studied using numerical calculations. The results show that at head-on collisions two oscillating fronts produce a wavy domain, which spreads in space with time.
Collapse
Affiliation(s)
- E P Zemskov
- Nonlinear Dynamics and Chaos Group, Physics Faculty, Moscow State University, 119992 Moscow, Russia
| |
Collapse
|
16
|
Fiałkowski M, Bitner A, Grzybowski BA. Wave optics of Liesegang rings. PHYSICAL REVIEW LETTERS 2005; 94:018303. [PMID: 15698143 DOI: 10.1103/physrevlett.94.018303] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2004] [Indexed: 05/24/2023]
Abstract
Liesegang rings refract and reflect at the interface between the regions of the same gel but of different thickness. The incident and the refracted rings obey a refraction law analogous to the Snell's law of classical optics, with a reverse of the spacing coefficient being a counterpart of the refraction index. The wavelike behavior of the rings at the interface is explained by geometrical arguments derived from the Jablczynski's spacing principle, and is reproduced in numerical simulations based on a three-dimensional minimalistic version of the nucleation-growth model.
Collapse
Affiliation(s)
- Marcin Fiałkowski
- Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Rd., Evanston, IL 60208, USA
| | | | | |
Collapse
|
17
|
Fort J, Campos D, González JR, Velayos J. Bounds for the propagation speed of combustion flames. ACTA ACUST UNITED AC 2004. [DOI: 10.1088/0305-4470/37/29/002] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
18
|
Méndez V, Campos D, Fort J. Dynamical features of reaction-diffusion fronts in fractals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:016613. [PMID: 14995742 DOI: 10.1103/physreve.69.016613] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2003] [Indexed: 05/24/2023]
Abstract
The speed of front propagation in fractals is studied by using (i) the reduction of the reaction-transport equation into a Hamilton-Jacobi equation and (ii) the local-equilibrium approach. Different equations proposed for describing transport in fractal media, together with logistic reaction kinetics, are considered. Finally, we analyze the main features of wave fronts resulting from this dynamic process, i.e., why they are accelerated and what is the exact form of this acceleration.
Collapse
Affiliation(s)
- Vicenç Méndez
- Departamento de Medicina, Universitat Internacional de Catalunya, c./Gomera s/n, 08190-Sant Cugat del Vallés, Barcelona, Spain
| | | | | |
Collapse
|