Activator-Inhibitor - A Model of Biological Pattern Formation

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Activator-Inhibitor - A Model of Biological Pattern Formation
Alternative Title
Aktivator-Inhibitor - Ein Modell zur biologischen Musterbildung
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D 1571
Release Date
Meinhardt, Hans
Production Year

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IWF Technical Data
Film, 16 mm, LT, 151 m ; F, 14 min

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Subject Area
In the development of higher organisms, pattern forming reactions must be involved. In the movie, a yet hypothetical two-component reaction is analysed which is able to generate patterns. Computer simulations made on the basis of two coupled non-linear differential equations show the time course and the regulatory properties of this reaction.
Keywords activator induction, biological inhibitor patterns feedback system development, biological synergetic
Setzen <Verfahrenstechnik> Systemic therapy Deep sea Organic food Inhibitor Nitrosamine
Sand Erosion Process (computing)
Water Activity (UML) Inhibitor Chemical reaction Process (computing) Gene duplication
Systemic therapy Setzen <Verfahrenstechnik> Activity (UML) Concentrate Cell (biology) Gene expression Stratotyp Legieren Inhibitor Nucleic acid sequence Process (computing)
Asymmetric induction Skarn Left-wing politics Activity (UML) Intergranular corrosion Cell growth Radioactive decay Molecule Hyperpolarisierung Cell (biology) Controller (control theory) Active site Inhibitor Derivative (chemistry) Periodate Setzen <Verfahrenstechnik> Gas cylinder Phase (waves) Surface science Filler (materials) Concentrate Chemical property Chemical reaction Systemic therapy Reducing agent Initiation (chemistry) Functional group Acetone Regulatorgen Separator (milk) Thermoforming Gene duplication
Systems biology Initiation (chemistry) Cell (biology) Chemical property Nitrosamine Process (computing)
we would activator inhibitor a model of biological pattern formation as a rule I organism develops from a single fertilized egg the patterns of the adult organism cannot already be present in the egg the patterns must be generated during development pattern formation is not restricted to living systems for instance deep valleys of
formed by erosion despite the fact that the rain is homogeneously distributed over the ground all high sand dunes of
formed despite the fact that the wind redistributes the sound all the time these processes have in common that small perturbations have a strong
positive feedback on their own so that they grow farther self amplification or water catalysis is on its own insufficient to generate a stable pattern the autocatalytic process would spread out into the whole field the order catalysis must be counteracted by a long-range inhibitory effect which restricts the spreading of the reaction we we a
biochemically possible realization of this principle could consist of a substance which positively feeds back on its own production to limit the spreading a 2nd inhibitory substances necessary the inhibitory substance must be activated by the autocatalytic reaction but must feedback negatively on the auto catalysis but what In the following we call the autocatalytic substance the activator and the inhibitory substance the inhibitor H hey we
let's assume a row of cells in which the activator and the inhibitor HI in equilibrium what happens after a local increase of the activator a local activator increase is followed by a corresponding increase of inhibitor since the inhibitor is highly diffusible the inhibitor excess distributes over the field only the perturbation the activator remains higher than the inhibitor consequently the activator concentration will grow further at this position in the rest of the field the activator concentration will decrease thus the perturbation continues to grow the so an activator-inhibitor system is able to generate concentration differences let's regard this process in a
computer simulation at the beginning the activator thick line and the inhibitor broken lines are equally distributed now the local perturbation which initiated the pattern formation on the right a high concentration of both substances builds up the local concentration differences can be used to activate different genetic information at different positions after some time the activator and inhibitor gradient becomes stable the such a simulation of a mathematical expression of the interaction between activator and inhibitor is required the change per time unit of
the activator d a over d t and of the inhibitor d h over the T should be described by 2 coupled partial differential equations as the function of a given activator and inhibitor concentration and as function of position the activator should be degraded like all biological molecules the number of activator molecules which disappear per time unit should be proportional to the number of activator molecules present the activator diffuses which is expressed by diffusion constant D a and the 2nd derivative of the position x similar assumptions are made for the inhibitor it decays and it diffuses the diffusion constant D h must be much larger than the diffusion constant of the activator 1 essential is missing the South amplification and inhibition the self amplification must be nonlinear to overcome the normal decay the if the inhibitor reduction on the activator control is also nonlinear the inhibition of the activated production can be linear the following computer simulations have been made with these equations the simulations should demonstrate the types of patterns which can be generated by this into action and what regulatory properties this pattern forming reaction has initiation of pattern formation by random fluctuations small random fluctuations in the order catalysis step-like curve are sufficient for the initiation of the pattern formation again the gradient is formed it's profile is independent of the details in the initiating fluctuations that means the fluctuations which trigger the pattern formation do not contain the pattern itself in a hidden form we regeneration after separation into 2 parts a larger field is separated into 2 parts In the non activated part the inhibitor concentration decreases until a new order catalysis becomes possible a rapid increase of the activator concentration takes place which in turn leads to an increased inhibitor production eventually the same pattern is formed in both parts the this simulation shows that the activator-inhibitor system accounts not only for pattern formation but also for pattern regulation regeneration with polarity reversal again a separation into 2 parts on the left the non-activated side the inhibitor concentration is very low this can after separation provide such an advantage for these cells that they win the competition the results are similar patterns in both parts which are mirror symmetrical in respect to each other induction of a 2nd activator maximum a small activator increase can lead to a 2nd activator maximum precondition is that this perturbation is at some distance from existing maximum the maxima have the tendency to emerge at the greatest possible distance from each other in this simulation a symmetrical pattern is formed despite the fact that the perturbation did not take place at the margin a similar perturbation somewhat closer to the existing maximum can be completely suppressed by the inhibitor which emanates from the existing maximum unspecific induction by inhibitor removal we a decrease in the inhibitor concentration can lead to similar to an activator increase to a 2nd maximum a leakage of inhibitor through war and is thus sufficient to induce a 2nd maximum instead of the normal polar pattern a symmetrical pattern is formed oscillating patterns generated by a long living inhibitor if the inhibitor has a longer lifetime than the activator inhibitor follows too slowly a change in the activator concentration this can lead to oscillations the activator increases the inhibitor is accumulating the activator production breaks down the inhibitor decays a new order catalysis starts the shop maximum is formed due to small differences in the order catalysis what can tactic orientation of a cell we this represents a camel tactics sensitive cell for an unambiguous orientation of the so the cell has transformed a small external concentration differences on its surface into a strong signal the activator-inhibitor system is able to do this at the optimal position arrow a sharp activator maximum is formed this can be used by the cell as the signal for instance to extrude pseudopods the if the direction of the external gradient changes the next peak appears at the new optimal site in contrast on non-oscillating maximum could not be shifted by such small external influences generation of a gradient in a two-dimensional field In the field of the size of the activator range a gradient is formed along 1 axis perpendicular to that axis the concentration of the activator top and of the inhibitor below is constant as a rule the pattern is formed along the largest extension of the field periodic patterns in extended fields after initiation by random fluctuations the maximum appear not had completely regular distances however a maximum and minimum distance is maintained since between 2 remote peaks new peaks would develop while if 2 maxima are too close to each other 1 would be suppressed after growth phase the pattern becomes stable the
resulting pattern will be more regular if initiated by a local perturbations the perturbation grows to a peak of the surroundings becomes suppressed around the inhibited region a ring-shaped ridge appears the reach disintegrates into several regularly spaced peaks formation of regular patterns during growth filler Texas on a growing cylinder the initiation of leaves is simulated here a pair of maximal is formed in 180 degree arrangement on the left is shown the activator on the right the inhibitor distribution the next as of maxima appear at 90 degrees in respect to each previous pair but
with a different choice of parameters at 1st only 1 peak appears further newly-formed cells are inhibited until a critical distance is exceeded the following maximum appears in 190 degree position the process is then repeated a regular pattern of alternating maxima emerges which could be a signal for leaf initiation we have seen that through the interaction of any 2 substances quite complicated patterns can be generated which in their geometry and their regulatory properties have much similarity with those found in real biological systems


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