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    "textoCompleto" => "<span class="elsevierStyleSections"><p id="par0005" class="elsevierStylePara elsevierViewall">Reaction&#8211;diffusion systems were described by Alan Turing in his 1952 article entitled &#8220;The chemical basis of morphogenesis&#46;&#8221; The mathematical model he proposed explains how different complex patterns can emerge&#46; It is based on 2 or more substances&#44; denoted morphogens&#44; which diffuse through a continuous medium and interact with each other&#46; According to the type of interaction&#44; different patterns form stochastically&#46; The interactions can be represented in simplified form using the following formula&#58;<elsevierMultimedia ident="eq0005"></elsevierMultimedia>where each component of the vector <span class="elsevierStyleItalic">q&#40;x&#44;t&#41;</span> represents the concentration of a substance&#44; <span class="elsevierStyleItalic">D</span> is the diagonal matrix of diffusion coefficients&#44; <span class="elsevierStyleItalic">&#916;</span> denotes the Laplace operator&#44; and <span class="elsevierStyleItalic">R</span> represents local reactions &#40;<a class="elsevierStyleCrossRef" href="#fig0005">Fig&#46; 1</a>&#41;&#46;</p><elsevierMultimedia ident="fig0005"></elsevierMultimedia><p id="par0010" class="elsevierStylePara elsevierViewall">According to the different dynamics of the resulting reactions and their wavelength&#44; there are 6 distinct different potential states&#46; In the fourth case&#44; also known as the Turing pattern&#44; a nonlinear wave is formed in dynamic equilibrium&#44; the wavelength of which is determined by the interactions between substances and their diffusion rates&#46; These Turing patterns emerge independently and tend to regenerate by themselves following perturbations&#46;<a class="elsevierStyleCrossRef" href="#bib0030"><span class="elsevierStyleSup">1</span></a></p><p id="par0015" class="elsevierStylePara elsevierViewall">Turing patterns combine positive and negative feedback systems&#46; An almost infinite number of patterns can be formed as the quantity and type of substances vary&#46; Substances can be simple entities such as molecules&#44; or complex&#44; like cell signaling pathways&#46; Furthermore&#44; they adjust to diffusion in different media as phenomena of chemiotaxis and action potentials&#46;</p><p id="par0020" class="elsevierStylePara elsevierViewall">The distribution of feathers on birds&#44; embryonic development of limbs&#44; and the bronchial tree are examples of Turing patterns in nature&#46;<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">2</span></a> The characteristics of Turing patterns are more evident in 2-dimensional models such as the skin&#46; Examples include the pattern of spots on leopards and the stripes on cebras&#46;<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">2</span></a></p><p id="par0025" class="elsevierStylePara elsevierViewall">Turing patterns have only recently found an application in dermatology&#46; Morphogenesis of hair follicles can be explained by Turing patterns&#44; in which interaction of BMP &#40;bone morphogenic protein&#41;&#44; FGF &#40;fibroblast growth factor&#41;&#44; and WNT &#40;wingless protein&#41; cell signaling pathways give rise to the epidermal and dermal condensate from which the papilla originates&#46;<a class="elsevierStyleCrossRef" href="#bib0040"><span class="elsevierStyleSup">3</span></a> The different morphological patterns of chronic spontaneous urticaria &#40;CSU&#41; can be explained by the activation&#47;inhibition model of histamine&#46;<a class="elsevierStyleCrossRef" href="#bib0045"><span class="elsevierStyleSup">4</span></a> The morphology and rate of appearance of wheals in CSU is different to those produced by intradermal histamine reaction&#46; In CSU&#44; the rate of wheal formation is slower&#44; they last longer&#44; and they can acquire annular or arciform patterns&#44; in contrast to the circular wheals of intradermal reaction&#46;<a class="elsevierStyleCrossRef" href="#bib0045"><span class="elsevierStyleSup">4</span></a> The morphological patterns of psoriasis &#40;annular&#44; circinate&#44; rosacea&#44; large plaques&#41; and evolution can also be explained by Turing patterns and the interaction between pathogenic cytokines tumor necrosis factor&#44; interleukin &#40;IL&#41; 17&#44; and IL-23&#46;<a class="elsevierStyleCrossRef" href="#bib0050"><span class="elsevierStyleSup">5</span></a></p><p id="par0030" class="elsevierStylePara elsevierViewall">Mathematical models such as Turing patterns can explain the phenotype of different skin diseases&#46; The role of the dermatologist is essential in the search for different molecules&#44; cell signaling pathways&#44; and their interactions&#44; which can explain these processes&#46;</p><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0015">Funding</span><p id="par0035" class="elsevierStylePara elsevierViewall">This article did not receive any funding&#46;</p></span></span>"
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RF – What Is the Origin of Morphologic Patterning in Dermatology? An Introduction to Reaction–Diffusion Systems (Turing Patterns)
FR – ¿Cómo se originan los distintos patrones morfológicos en dermatología? introducción a los sistemas de reacción-difusión (Patrones de Turing)
D. Fernández-Nieto
Autor para correspondencia
fnietodiego@gmail.com

Corresponding author.
, D. Ortega-Quijano, P. Boixeda
Servicio de Dermatología, Hospital Universitario Ramón y Cajal, Universidad de Alcalá de Henares, Instituto de investigación Sanitaria del Hospital Ramón y Cajal (IRYCIS), Spain
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    "textoCompleto" => "<span class="elsevierStyleSections"><p id="par0005" class="elsevierStylePara elsevierViewall">Reaction&#8211;diffusion systems were described by Alan Turing in his 1952 article entitled &#8220;The chemical basis of morphogenesis&#46;&#8221; The mathematical model he proposed explains how different complex patterns can emerge&#46; It is based on 2 or more substances&#44; denoted morphogens&#44; which diffuse through a continuous medium and interact with each other&#46; According to the type of interaction&#44; different patterns form stochastically&#46; The interactions can be represented in simplified form using the following formula&#58;<elsevierMultimedia ident="eq0005"></elsevierMultimedia>where each component of the vector <span class="elsevierStyleItalic">q&#40;x&#44;t&#41;</span> represents the concentration of a substance&#44; <span class="elsevierStyleItalic">D</span> is the diagonal matrix of diffusion coefficients&#44; <span class="elsevierStyleItalic">&#916;</span> denotes the Laplace operator&#44; and <span class="elsevierStyleItalic">R</span> represents local reactions &#40;<a class="elsevierStyleCrossRef" href="#fig0005">Fig&#46; 1</a>&#41;&#46;</p><elsevierMultimedia ident="fig0005"></elsevierMultimedia><p id="par0010" class="elsevierStylePara elsevierViewall">According to the different dynamics of the resulting reactions and their wavelength&#44; there are 6 distinct different potential states&#46; In the fourth case&#44; also known as the Turing pattern&#44; a nonlinear wave is formed in dynamic equilibrium&#44; the wavelength of which is determined by the interactions between substances and their diffusion rates&#46; These Turing patterns emerge independently and tend to regenerate by themselves following perturbations&#46;<a class="elsevierStyleCrossRef" href="#bib0030"><span class="elsevierStyleSup">1</span></a></p><p id="par0015" class="elsevierStylePara elsevierViewall">Turing patterns combine positive and negative feedback systems&#46; An almost infinite number of patterns can be formed as the quantity and type of substances vary&#46; Substances can be simple entities such as molecules&#44; or complex&#44; like cell signaling pathways&#46; Furthermore&#44; they adjust to diffusion in different media as phenomena of chemiotaxis and action potentials&#46;</p><p id="par0020" class="elsevierStylePara elsevierViewall">The distribution of feathers on birds&#44; embryonic development of limbs&#44; and the bronchial tree are examples of Turing patterns in nature&#46;<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">2</span></a> The characteristics of Turing patterns are more evident in 2-dimensional models such as the skin&#46; Examples include the pattern of spots on leopards and the stripes on cebras&#46;<a class="elsevierStyleCrossRef" href="#bib0035"><span class="elsevierStyleSup">2</span></a></p><p id="par0025" class="elsevierStylePara elsevierViewall">Turing patterns have only recently found an application in dermatology&#46; Morphogenesis of hair follicles can be explained by Turing patterns&#44; in which interaction of BMP &#40;bone morphogenic protein&#41;&#44; FGF &#40;fibroblast growth factor&#41;&#44; and WNT &#40;wingless protein&#41; cell signaling pathways give rise to the epidermal and dermal condensate from which the papilla originates&#46;<a class="elsevierStyleCrossRef" href="#bib0040"><span class="elsevierStyleSup">3</span></a> The different morphological patterns of chronic spontaneous urticaria &#40;CSU&#41; can be explained by the activation&#47;inhibition model of histamine&#46;<a class="elsevierStyleCrossRef" href="#bib0045"><span class="elsevierStyleSup">4</span></a> The morphology and rate of appearance of wheals in CSU is different to those produced by intradermal histamine reaction&#46; In CSU&#44; the rate of wheal formation is slower&#44; they last longer&#44; and they can acquire annular or arciform patterns&#44; in contrast to the circular wheals of intradermal reaction&#46;<a class="elsevierStyleCrossRef" href="#bib0045"><span class="elsevierStyleSup">4</span></a> The morphological patterns of psoriasis &#40;annular&#44; circinate&#44; rosacea&#44; large plaques&#41; and evolution can also be explained by Turing patterns and the interaction between pathogenic cytokines tumor necrosis factor&#44; interleukin &#40;IL&#41; 17&#44; and IL-23&#46;<a class="elsevierStyleCrossRef" href="#bib0050"><span class="elsevierStyleSup">5</span></a></p><p id="par0030" class="elsevierStylePara elsevierViewall">Mathematical models such as Turing patterns can explain the phenotype of different skin diseases&#46; The role of the dermatologist is essential in the search for different molecules&#44; cell signaling pathways&#44; and their interactions&#44; which can explain these processes&#46;</p><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0015">Funding</span><p id="par0035" class="elsevierStylePara elsevierViewall">This article did not receive any funding&#46;</p></span></span>"
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