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Ecosystems (2010) 13: 841–850DOI: 10.1007/s10021-010-9358-x Ó 2010 The Author(s). This article is published with open access at Springerlink.com Alternative Stable States Driven by Density-Dependent Toxicity Tjisse van der Heide,1,2* Egbert H. van Nes,3 Marieke M. van Katwijk,1 Marten Scheffer,3 A. Jan Hendriks,1 and Alfons J. P. Smolders2 1Department of Environmental Science, Institute for Wetland and Water Research, Faculty of Science, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands; 2Department of Environmental Biology, Institute for Water and Wetland Research, Faculty of Science, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands; 3Aquatic Ecology and Water Quality Management Group, Department of Environmental Sciences, Wageningen University, P.O. Box 8080, 6700 DD Wageningen, The Netherlands Many populations are exposed to naturally occur- we demonstrated that ammonia toxicity in eelgrass ring or synthetic toxicants. An increasing number is highly dependent on the eelgrass shoot density.
of studies demonstrate that the toxicity of such Here, we used the results of these experiments to compounds is not only dependent on the concen- construct a model describing the complex interac- tration or load, but also on the biomass or density tions between the temperate seagrass Zostera marina of exposed organisms. At high biomass, organisms and potentially lethal ammonia. Analyses of the may be able to alleviate adverse effects of the tox- model show that alternative stable states are indeed icant by actively lowering ambient concentrations present over wide ranges of key-parameter settings, through either a joint detoxification mechanism or suggesting that the mechanism might be important growth dilution. We show in a conceptual model especially in sheltered, eutrophicated estuaries that this mechanism may potentially lead to alter- where mixing of the water layer is poor. We argue native stable states if the toxicant is lethal at low that the same mechanism could cause alternative densities of organisms, whereas a high density is stable states in other biological systems as well.
able to reduce the toxicant concentrations to sub-lethal levels. We show in an example that this ef- Key words: alternative stable states; bistability; fect may be relevant in real ecosystems. In an density-dependence; toxicity; ammonia; ammo- earlier published experimental laboratory study, nium; seagrass; Zostera marina.
In their environments, organisms can be exposed toa wide range of naturally occurring or synthetic Received 31 October 2009; accepted 4 June 2010; toxic substances (Moriarty ). Physiological or published online 16 July 2010 population effects of such chemicals are mostly Electronic supplementary material: The online version of this article examined in dose–response studies, where the which is available to authorized users.
dosage of a toxicant is varied on a certain biomass Author Contributions: Tjisse van der Heide and Egbert van Nes con- ceived of or designed study, performed research, analyzed data, contrib- increasing number of studies demonstrate that uted new methods or models, and wrote the article. Marieke van Katwijkconceived of or designed study and wrote the article. Marten Scheffer and toxicity effects may often not only be dependent on Jan Hendriks wrote the article. Fons Smolders conceived of or designed the dose, but also on the biomass of exposed study, contributed new methods or models, and wrote the article.
organisms. In such cases, toxicity may be alleviated *Corresponding author; e-mail: t.van.der.heide@rug.nl T. van der Heide and others by a high organism biomass because the concen- this model can have alternative stable states using tration of a toxicant is reduced to sub-lethal levels realistic parameter settings based on laboratory due to joint uptake or active detoxification. This experiments and literature.
effect has been described for a wide range of bio-logical systems such as heavy metal accumulation in organisms (Duxbury and McIntyre ; Pick-hardt and others ), phytotoxins in microbes Conceptual Models and plants (for example, Weidenhamer and others The basic mechanism of this feedback can be ; Greig and Travisano Pollock and others shown in a very simple model. This model describes ), and for drug treatments of infectious bac- a system with a population of organisms that can- teria or cancer (for example, Brook ; Kobay- not exceed a carrying capacity, for instance due to ashi and others Brandt and others In limited nutrients, food or space. Furthermore, we ecotoxicological studies, this mechanism is often model a toxicant that increases mortality of the referred to as ‘‘density-dependent toxicity'' (for example, Duxbury and McIntyre Kobayashi and others ; van der Heide and others or the ‘‘dilution effect'' (for example, Karimi and others Pollock and others ), whereas it isdescribed as the ‘‘inoculum effect'' in many phar- X describes the biomass of the population, a is the maceutical studies (for example, Brook maximum net growth rate per unit of time and KX Kobayashi and others ; Brandt and others ).
is the carrying capacity. Parameter b is a mortality This density-dependent toxicity implies a positive constant which, multiplied with the concentration feedback between population density and toxic of toxicant T represents the mortality rate in substance concentration, because an increase in population X per unit of time. Although the linear biomass alleviates toxicity, which can in turn fur- effect of T in the model may often be an oversim- ther amplify biomass growth. Theory suggests that plification of reality, simulations comparing linear, if such a positive feedback mechanism is strong Monod and Hill functions, showed that basic model enough, it could lead to alternative stable states behavior is not sensitive to the choice of the (also called bistability) and hysteresis (Carpenter function here in the sense that it consistently pro- ; Scheffer and others Scheffer and Car- duced alternative stable states in a wide parameter penter ). This implies that environmental range. Moreover, in many cases the response of changes or disturbances (for example, disease) may organisms to toxicants can well be described by this push the population beyond a critical threshold, simple relation (Hendriks and others ). The causing a collapse (for example, mass mortality) to second equation describes the change in toxic an alternative stable state (Scheffer and others compounds in the system per unit of time.
). Implications of non-linear response and We assume a constant external input or internal threshold behavior in biological systems can be release of the toxicants similar to a chemostat profound. Shifts in populations with positive feed- backs are typically hard to predict and recovery of a However, organisms can also reduce the concen- collapsed system is often difficult.
tration of toxicants in the system: In this study, we examine whether a positive feedback caused by density-dependent toxicity may ¼ ðTin  TÞ p  T f ðXÞ cause alternative stable states. First, we show the basic idea in a simple conceptual model, describing where Tin is the maximum equilibrium concentra- a generalized positive feedback system between a tion of toxicants that can accumulate in the system population of organisms and a toxic compound. We and p is the dilution rate (that is, the fraction of the analyzed two different assumptions of how an volume replaced per time unit). We assume that established population can alleviate toxicity: the the organisms reduce the concentration of toxi- organisms can alleviate toxicity actively (‘‘joint cants as a function of their biomass. This density- detoxification'') or can take up and store a limited dependent alleviation of toxicity is essential for the amount of the toxic substance per organism or unit of biomass (‘‘growth dilution''). Next, we created a We analyzed two different assumptions. In the more realistic model, describing ammonia toxicity first case, organisms can actively transform the toxic in seagrass ecosystems, to further explore our the- compound into a harmless (or even useful) sub- ory for an empirical situation. We analyze whether stance, for instance metabolically or by excretion of Bistability Through Density-Dependent Toxicity compounds that chemically react with the toxicant.
highly dependent on vegetation density, indicating This mechanism can result in decreased mortality if that positive feedbacks between eelgrass and re- the density of organisms if sufficient to reduce duced nitrogen may lead to alternative stable states ambient toxicant concentrations (‘‘joint detoxifica- in sheltered estuaries with high exposure to NHx. In tion''). Here, f(X) is described by d1 X, where d1 is a these systems, high concentrations of NHx may be constant describing the uptake rate of T per unit of caused by for instance discharges of waste or river X. For the second mechanism, we assume that the water and degradation of phytoplankton or macro- toxicant is not converted into a harmless substance, algal mats (van der Heide and others Also, but is stored is the tissues of the organisms (for because ammonium uptake is well studied in eel- example, heavy metal storage in fat tissue). In this grass, model parameters could be reliably estimated case, organisms can only take up a limited amount of based on these studies and results from our own the toxic substance per unit of biomass and detoxi- experimental work.
fication is thus dependent on growth (‘‘growth We based the model on the joint detoxification dilution''). In this case, f(X) is replaced with the term assumption. In the first place because ammonium d2 a X (1 - X/Kx), where d2 describes the uptake of is used as a nutrient by the plants and it is therefore T proportional to growth of X. Notably, net uptake of metabolized. Secondly, an eelgrass shoot may dis- the toxicant in the growth dilution model becomes card excess nutrients by replacing its leaves without zero when carrying capacity is reached. In reality, resorbing the nutrients stored in the leaves that natural mortality and regrowth around carrying are lost (Hemminga and others Moreover, capacity in the population would result in some compared to other vascular plants the lifespan of uptake and release dynamics of the toxicant. For eelgrass leaves is relatively short, suggesting that simplicity, however, we chose not to include a excess nitrogen stored in the leaves may be mortality term in the models, because the general exported from the system through rejection of behavior of the model would remain unchanged.
leaves (Hemminga and others In systems with a relatively high dilution rate p, In the model, survival of eelgrass is dependent on dynamics of T are much faster than those of the the concentration of NH3 in the water layer. The organisms. Therefore, we can assume a quasi equation describing the change in eelgrass shoot steady state (that is, dT ¼ 0) without any conse- density per day (dZ/dt) is similar to Eq. quences for the equilibrium density of organisms and the behavior of the model. This assumption Z  m f ðNH3Þ Z simplifies the model to: With r as the maximum net growth rate (day-1), K as the carrying capacity (shoots m-2), and m as the maximum mortality rate (day-1). The toxic effect The conditions for alternative stable states of this of NH3 is described by the function f(NH3). To simple model can be determined analytically for estimate the toxicity effect of NH3 in eelgrass, we the joint detoxification assumption or numerically recalculated and analyzed experimental data of in case of the growth dilution model (online Van der Heide and others ) (online Appendix Appendix 1).
2). Our analyses revealed that toxicity by NH3 ineelgrasses is best described by a Hill-curve (Fig-ure This is an equation that is typically used to Specific Model of NHx Toxicity describe toxicity in organisms. The function ex- presses a sigmoid toxicity effect in the organism in Recent studies have demonstrated that positive response to increasing exposure to a toxicant (Hill feedbacks are important mechanisms in seagrass ecosystems (van der Heide and others , ). This model, based on empirical data, de- scribes a feedback mechanism between the tem- perate seagrass Zostera marina (commonly called Here M describes the fraction of leaf tissue mortality eelgrass), reduced nitrogen (NHx) and potentially in eelgrass after 5 days of exposure to NH3, i is the lethal gaseous ammonia (NH3) in the water layer.
background leaf mortality at zero exposure. HNH is We chose this system as a more realistic analysis for the half-saturation constant (mmol m-3) and n is a our theory because recent research demonstrated dimensionless exponent determining the slope of that susceptibility of eelgrass to NHx toxicity is the curve. To describe the effect of NH3 in our T. van der Heide and others Bifurcation Analysis We analyzed the stability of the equilibria of themodel at varying settings of key parameters. Criticalthresholds were determined by a numerical proce-dure. The key parameter was increased in smallsteps, after which the model was run to stabilize to itsequilibrium. Next, this analysis was also performedbackwards, by decreasing the key parameter in smallsteps. These analyses were combined to constructbifurcation plots of various parameters. We deter-mined unstable equilibria by making the quasisteady state assumption (dT ¼ 0) and plotting equi- libria for different values of the control parameters in Figure 1. Response of eelgrass shoots to ammonia at GRIND for MATLAB.
varying concentrations after 5 days of exposure.
model, we adopted the part of Eq. describing the relative effect of NH3 on eelgrass mortality: Conceptual Models Figure and B shows phase planes of the joint detoxification and growth dilution model, respec-tively, based on the default settings presented in In water, the total NHx concentration is made of the Table Both the graphs show two stable equilibria 3 and ammonium (NH4 ). NH3 and NH4 and one unstable equilibrium (saddle point).
are in equilibrium and the balance between these Whereas toxicant concentrations show a straight- compounds is determined by the pH of the water.
forward decrease with increasing biomass in the The concentration of NH3 in the water can be cal- joint detoxification model, toxicant levels in the culated from the pH and the total concentration of growth dilution model increase again when X nears reduced nitrogen in the water layer: its carrying capacity. This is because the population growth and therefore also the detoxification rate is highest halfway to the population's carryingcapacity. Next, we analyzed the sensitivity of both where ka is the dimensionless dissociation constant models to varying values of the maximum toxicant of NHx in water with a salinity of 16 PSU at 20°C.
in) in a one-dimensional bifurca- x in the water layer is described tion plot (Figure C, D). The results demonstrate by the second differential equation: that both models can have alternative stable states, one without organisms and one with a population that can alleviate toxicity. The systems collapse to a bare state when organism density is pushed belowthe critical threshold (Figure C, D, dashed lines).
With NHxin as the NHx concentration of the water A more thorough bifurcation analysis of the joint flowing into the meadow and R as the dilution rate detoxification model shows that the conditions for of the water inside the meadow. Umax is the max- alternative stable states in this model are relatively imum uptake rate of NHx by eelgrass (mmol g dry simple. After reducing the number of model weight-1 day-1) and HNH is the half-saturation parameters to 2 by non-dimensionalization (online constant for NHx uptake (mmol m-3). Finally, Appendix 1), conditions for alternative stable state f(Z) is a function describing the conversion from can be summarized in a simple 2D plot. This plot eelgrass shoot density (shoot m-2) to the amount of shows all parameter combinations at which alter- dry weight biomass per unit of volume: native stable states occur (Figure A). It appears that there are two prerequisites that determine whether the feedback is strong enough to cause alternative stable states. First, the equilibrium Here C is the height of the canopy (m) and DwZ is concentration of toxicant without organisms (Tin) the dry weight of one eelgrass shoot (g).
should be able to prevent colonization of the Bistability Through Density-Dependent Toxicity Figure 2. Analyses of the conceptual models. A and B Nullclines at default settings of the ‘‘joint detoxification'' modeland ‘‘growth dilution'' model, respectively. The closed dots represent stable equilibria in the models, the open dots areunstable saddle points. The separatrix indicates the critical boundary above which the population can survive and developto the equilibrium. C indicates a colonized state, B is a bare state. C and D Bifurcation analyses of the ‘‘joint detoxification''model and ‘‘growth dilution'' model, respectively, with varying values of Tin. Solid lines represent stable equilibria, whereasthe dashed line indicates unstable equilibria. Dots indicate bifurcation points (F fold bifurcation, T transcritical bifurcation),arrows show the direction of change. Note that all parameter settings for the ‘‘joint detoxification'' model and the ‘‘growthdilution'' model were identical, except for parameter b, which were set at 0.2 and 1.5, respectively.
organism [that is, its effect on the organisms (b Tin) Moreover, the qualitative effect of scaled toxicity should be higher than the maximum growth rate of and carrying capacity is remarkably similar.
the population (a)]. The second prerequisite is thatthe effect of a full-grown population (KX) on the Specific Model of NHx Toxicity toxic substances should be strong enough to let the concentration of the toxicant decrease, that is,the refresh rate of the toxic substance (p) should be The eelgrass model was parameterized to describe a less than the maximum effect of the organisms (KX sheltered estuary, where water mixing between the d). Note that this means that the chances for alter- eelgrass meadow and its surroundings is limited native equilibria increase if the turnover rate of the (Table ). Water flowing into the seagrass bed has a toxic substance (p) is low. If these two prerequisites NHx concentration of 100 lmol l-1 NHx, a value are met, there is a range of Tin with alternative comparable to various measurements in the field stable states. With increasing carrying capacity (or (for example, Hauxwell and others ; Brun and decreasing turnover rate), this range increases.
others In these systems pH can vary strongly.
The growth dilution model is too complex for a At night, pH is generally around 8 whereas pH can similar analytical bifurcation analysis. However, we rise up to 9 or even 10 during the day, due to pho- did this analysis numerically, showing very similar tosynthesis of algae and seagrass itself (Choo and results (Figure B). Although the range for bista- others ; Feike and others van der Heide bility in this model is narrower when compared to and others ), hence leading to higher NH3 the joint detoxification model, there is still a rather concentrations. For simplicity, we assumed an large parameter space with alternative stable states.
average pH of 8.5 for our model system.
T. van der Heide and others Variables and Default Parameter Settings of the Conceptual Model Biomass of organism X per liter Concentration of toxicant T Mortality constant; set at 0.2 for model 1 and at 1.5 for model 2 Carrying capacity of X Maximum concentration of T Uptake constant of T Uptake constant of T Note that in this instance, units used in the conceptual model are based upon an organism living in a water body with a constant refreshing rate, for example, (phyto)planktonor fish.
The nullclines of this model at default parameter settings are presented in Figure Similar to theconceptual model, the graph shows one unstableequilibrium and two stable points. Depending onthe initial conditions, the meadow will either de-velop towards carrying capacity or collapse to abare state. A bifurcation analysis on the NHx con-centration of the water flowing into the eelgrassmeadow (NHxin) reveals that alternative stablestates are present over a wide range of realisticconcentrations, from 75 to over 158 lmol l-1(Figure B). We analyzed the interactive effects ofNHxin, pH, and dilution rate R, because theseparameters are often variable in the field. Resultsdemonstrate that the effect of the NHx concentra-tion of the incoming water is highly dependent onboth pH and the dilution rate of the water insidethe meadow (Figure B). The analysis showsthat alternative stable states are present at pH val-ues higher than 7.9 (Figure A). Below pH 7.9, thetoxicity of NHx is too low as only little NHx ispresent as toxic NH3. Therefore, the meadow tol-erates extremely high concentrations of NHx in theincoming water. Sensitivity to NHx exposure in-creases strongly with rising pH levels, as the NH + NH3 equilibrium shifts towards NH3. At pH 10,alternative stable states exist between NHx con-centrations of 10 and 55 lmol l-1 in the waterflowing into the meadow. Figure demonstratesthe interactive effects of NHxin and water dilution Figure 3. Two-dimensional plots of the scaled conceptual rate R. No alternative stable states are present when models (see online Appendix 1). On the axes are the two the concentration of NHx is below 75 lmol l-1, combined parameters: the scaled toxic load a ¼ bT because these concentrations are not lethal for the the scaled carrying capacity of X, which is b ¼ d K eelgrass plants at pH 8.5 (compare the first pre- ‘‘joint detoxification'' model and c ¼ d a K for the ‘‘growth requisite of the conceptual model). The effect of dilution'' model. The figures give all parameter combina-tions where we get alternative stable states. (C colonized, NHx becomes dependent on both NHx input con- C/B alternative states, B bare only, F (solid line) fold bifur- centrations and the turnover rate R, when NHx cation, T (dashed line) transcritical bifurcation).
concentrations of the incoming water rise above Bistability Through Density-Dependent Toxicity Variables and Default Parameter Settings of the Eelgrass Model Eelgrass shoot density mmol m-3 (=lmol l-1) Reduced nitrogen concentration mmol m-3 (=lmol l-1) Ammonia concentration Maximum net growth rate Maximum mortality rate Carrying capacity mmol m-3 (=lmol l-1) Half rate constant for toxic effects of NH Hill-curve exponent in NH3 toxicity curve Dissociation constant for NH3/NH4 mmol m-3 (=lmol l-1) NHx concentration of water coming into the meadow Dilution rate of the water in the meadow Maximum uptake rate per g dry weight mmol m-3 (=lmol l-1) Half rate constant for NH Dry weight per shoot (1) Olesen and Sandjensen ((2) Bostro¨m and others ), (3) Choo and others ) and Feike and others ((4) Khoo and others ((5) Hauxwell andothers ) and Brun and others ((6) Thursby and Harlin ((*) recalculated from original data of van der Heide and others ), (+) unpublished results, (±)estimated.
Figure 4. Analyses of theeelgrass model.
A Nullclines of the modelat default settings.
B Bifurcation analysis ofthe model with varyingNHx concentrations in theincoming water (NHxin).
See Figure for themeaning of symbols used.
the 75 lmol l-1 threshold. Alternative stable states actively broken down by the exposed organisms.
exist far beyond NHx concentrations of 500 lmol l-1 The population can maintain itself, provided that its for NHxin when R drops below 1 day-1.
biomass is sufficient to reduce toxicant concentra-tions to a level where organism growth may equalize or exceed mortality. Growth dilution is a mechanism where the toxicant is not broken down, We show in both a conceptual and a more realistic but is stored in the organism's tissues. Because these model that ‘‘density-dependent toxicity,'' a positive tissues are only able to store a limited amount of feedback mechanism between a population of toxicants, they will become saturated. In this case, organisms and a toxic compound may lead to reduction of the toxicant is dependent on popula- bistability in biological systems. Organisms may tion growth rather than the biomass present in the alleviate adverse effects of the toxicant by actively lowering ambient concentrations through either Our eelgrass model suggests that density-dependent ‘‘joint detoxification'' or ‘‘growth dilution.'' Joint toxicity may indeed be important in real ecosystems.
detoxification is a mechanism where the toxicant is Although the model is somewhat more complicated, T. van der Heide and others toxicant levels may be low due to detoxificationmechanism, whereas the toxicant load may actually bevery high. Therefore, ecosystem monitoring shouldfocus on determining the toxicant load in such cases.
Finally, it should also be noted that when such anecosystem collapses, it may not only affect the com-munity structure directly. After the collapse manyassociated species may now also experience toxicityeffects because toxicant levels will increase dramati-cally.
Although we studied only one example, density- dependent toxicity is most likely an importantmechanism in a wide range of biological systems.
Joint detoxification has also been reported in forexample isoetid macrophytes. In these vegetations,ammonium toxicity can be prevented becauseammonium concentrations in the pore water areactively lowered, not only by uptake, but also bydensity-dependent oxidation of ammonium tonitrate due to high radial oxygen loss of the roots(Smolders and others ). Toxic effects of sulfidein salt-marshes (Webb and others Webb andMendelssohn Goodman and others Pedersen and othersor sulfate-rich freshwater wetlands (Lamersand others ; Armstrong and Armstrong ;van der Welle and others may be preventedin a similar way. In these systems, sulphide can be Figure 5. Two-dimensional bifurcation analyses of the oxidized to harmless sulfate if oxygen loss by the eelgrass model. A Bifurcation analysis with varying pH root system is sufficiently high.
and NHx concentrations in the incoming water (NHxin).
possible mechanism B Bifurcation plot with varying dilution rates of the dependent toxicity, growth dilution, may for water in the meadow (R) and NHx concentrations in the instance reduce toxic effects of heavy metals; tox- incoming water (NHxin). Solid lines represent fold bifur-cations, whereas the icants that cannot be broken down. The dilution dashed lines indicate transcritical bifurcations. B indicates a bare state; C/B indicates effect increases tolerance of microbes to heavy the area where alternative stable states occur. Left of the metal exposure (Duxbury and McIntyre In dashed lines (indicated with C), eelgrass presence is the aquatic ecosystems, accumulation of toxic metals in only stable state.
the trophic chain of food webs has been shown tobe reduced with increasing concentrations of phy- its essence is identical to our conceptual joint detoxi- toplankton (Pickhardt and others or even fication model. Sudden die-off events caused by high with increasing nutritional quality of the algae reduced nitrogen (NHx) loads, combined with a high (stoichiometric dilution) (Karimi and others pH may be prevented by joint uptake if shoot density of Although our analyses suggest that the mecha- the meadow is high enough. This mechanism fails if nism presented in this study may lead to alternative shoot densities are pushed below a certain threshold, stable states in many biological systems, it should be resulting in a shift to a bare state. This illustrates noted that dynamics in our models are described in that density-dependent toxicity can have important a simplified manner. This implies that the models implications for toxicity research and management in may disregard or oversimplify processes that might ecosystems. For toxicity research in laboratory and in reality be important. These can include factors field studies, our results indicate that it may be very that weaken the positive feedback as well as pro- important to choose realistic population densities in- cesses that enhance it. In general, processes stead of working with standardized biomass or densi- strengthening the feedback may include symbiosis ties. Moreover, our simulations also show that it is not or natural selection leading to more resistant indi- sufficient to measure ambient toxicant levels to viduals (Brook ), whereas factors weakening it assess ecosystem health. At high population densities, can include limitation of resources (for example, Bistability Through Density-Dependent Toxicity nutrients, water) (Weidenhamer competi- tion with other species (Weidenhamer or Armstrong J, Armstrong W. 2001. An overview of the effects of disease (van der Heide and others More phytotoxins on Phragmites australis in relation to die-back.
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What is zopiclone?Zopiclone is a drug with very similar effects to benzodiazepines (like diazepam, temazepam). It is pre-scribed by doctors for the treatment of insomnia (difficulty sleeping), and in the recommended dose brings on sleep for periods of 6 to 8 hours. However, this leaflet is about the use of zopiclone as a ‘street drug' and the risks and likely problems this may cause for drug users.

Diabète type 2 principes de ttt

CONSEILS ET PRINCIPES DE TRAITEMENT POUR UN DIABÈTE DE TYPE 2 Le diabète est une maladie chronique, il n'y a pas de « petit - Les ongles doivent être coupés régulièrement en diabète ». C'est une maladie qui expose à des complications évitant toute blessure (préférer des soins de pédicurie +++). Ne mettez pas vos pieds en danger : ne marchez pas pieds nus,