====== Assimilate Transport and Fruit Development ====== //Open {{ :tutorials:advanced:Transport.gsz |Transport.gsz}}// The Transport model extends the [[:Tutorials:Radiation-model-in-crop model7|Flower aging model]] by implementing a physiologically-based system for sugar transport from photosynthetically active leaves through the plant architecture to developing fruits. This creates a more realistic simulation of source-sink relationships in the virtual plant. ===== Assimilate Storage and Transport Parameters ===== The model introduces a new parameter ''as'' (assimilate storage) to track sugar content in different organs (L. 9, 12, 43):


module Internode(super.length, int age, int rank, float as) extends Cylinder(length, 0.1);
module Leaf(super.length, super.width, float al, int age, float as, int rank) extends Box(length, width, 0.01);
module Fruit(float size, int age, float as) ==> Sphere(size).(setShader(RED));

Note that we now track assimilates (''as'') in three types of modules: leaves (where they are produced), internodes (where they are transported), and fruits (where they accumulate). ===== Maintenance Respiration ===== A maintenance respiration constant has been added to simulate the metabolic cost of keeping tissues alive (L. 96):


const float MR = 0.01; //maintenance respiration

This is applied to internodes during growth to simulate sugar consumption (L. 207 ff):


itn:Internode ::> {
		itn[age]++;
		if(itn[as]>0) {itn[as] *= (1-MR); }
		itn[length] += logistic(1, itn[age], 10, itn[as]);
		itn.(setShader(new RGBAShader(itn[as]*15.0, itn[as]*7.5, itn[as])));
	}

Note that internode length is incremented up to a fixed length of 1, however, we vary the speed of elongation as a function of sugar available in the internode, ''itn[as]''. ===== Transport Mechanism ===== The main novelty of the present model is the implementation of a diffusion-based transport system. The transport occurs with a diffusion constant that controls the rate (L. 94):


const float DIFF_CONST = 0.002;

Transport is invoked periodically in the ''grow()'' method - every 24 timesteps to simulate hourly transport (L. 145-149):


if(time % 24 == 0) {
    for(int hour = 0; hour < 24; hour++) {
        transport();
    }
}

===== Transport Rules ===== Three types of transport are implemented using user-defined edge relations: **a) Leaf to Internode Transport, and vice versa ** (L. 256-280):


lf:Leaf <-minDescendants- itn:Internode ::> {
		if(lf[as] > 0.01 && lf[age]>=10) { // Keep minimum for leaf maintenance
        float exportable = lf[as] - 0.01;
        float r = DIFF_CONST * exportable;
        lf[as] -= r;
        itn[as] += r;
		//println("transport from leaf to internode");
		} else
	if(itn[as] > 0.01 && lf[age]<10) { // Keep minimum for internode maintenance
        float exportable = itn[as] - 0.01;
        float r = DIFF_CONST * exportable;
        lf[as] += r;
        itn[as] -= r;
		//println("transport from internode to leaf");
		}
	}

This rule ensures leaves retain a minimum amount (0.01) for maintenance while exporting the surplus. In fact, if you look closely, assimilates can also go the other way, from an internode to a (young) leaf, because the latter is a sugar sink before it has reached its final size and becomes a net exporter of assimilates! **b) Internode to Internode Transport** (L. 260-268):


i_top:Internode <-minDescendants- i_bottom:Internode ::> {
    if((i_bottom[as] - i_top[as])<=0) { 
        float r = DIFF_CONST * (i_top[as] - i_bottom[as]);
        i_bottom[as] :+= r;
        i_top[as] :-= r;
    }
    else if ((i_bottom[as] - i_top[as])>0) { 
        float r = DIFF_CONST * (i_bottom[as] - i_top[as]);
        i_bottom[as] :-= r;
        i_top[as] :+= r;
    }
}

This bidirectional transport follows the concentration gradient between successive internodes. **c) Internode to Fruit Transport** (L. 269-275):


itn:Internode -minDescendants-> fr:Fruit ::> {
    if(itn[as]>0) {
        float r = DIFF_CONST * itn[as];
        itn[as] :-= r;
        fr[as] :+= r;
        println("sugar import into fruit: " + r);
    }
}

This final rule expresses transport in only one direction, i.e. fruits are //absolute sinks// (which is wrong, because young fruit are often green and have been shown to carry out photosynthesis). ===== Fruit Set Decision Based on Sugar Availability ===== The model now makes fruit formation dependent on sugar available in the nearest leaf (L. 169-174):


fl:Flower(t, m), (t >= m && t 
		{float sugar = first((* Leaf *)[as]);
		println("sugar: " + sugar);
		} 
		if(sugar>0.0005) ({noFrts++;} Fruit(0.01,1,0.1,noFrts))
		else (fl);

Note that a ''Flower'' that has not yet become a ''Fruit'', has two more chances to become one. Availability of sugar is calculated by querying ''as'' of the nearest ''Leaf'' before deciding on fruit formation. ===== Fruit Growth Competition ===== Multiple fruits compete for available resources using an age-based weighting system (L. 214-226):


fr:Fruit ::> {
    float totalSugar = sum((* lf1:Leaf *)[as]);
    long fruitCount = count((* fr2:Fruit *));
    
    // Simple age-based competition (younger fruits get more resources)
    float ageWeight = Math.exp(-0.05 * fr[age]);
    float totalAgeWeight = 0;
    for ((* fr2:Fruit *)) {
        totalAgeWeight += Math.exp(-0.05 * fr2[age]);
    }
    
    float sugar = (totalAgeWeight > 0) ? 
        (totalSugar * ageWeight) / totalAgeWeight : totalSugar / fruitCount;

Younger fruits receive proportionally more resources through exponential age weighting, simulating their stronger sink affinity (thereby compensating their smaller size). ===== Visual Feedback ===== Internodes change color based on their sugar content, providing visual feedback of the transport process:


itn.(setShader(new RGBAShader(itn[as]*2000.0, itn[as]*1000, itn[as])));

===== Tasks for Exploration ===== - Run the model and observe sugar flow: Watch how internodes change color as sugar moves through them. - Modify DIFF_CONST: Try values between 0.0001 and 0.01. How does this affect: * Speed of sugar movement? * Final fruit size? * Number of successfully developed fruits? - Change transport frequency: Modify the condition if(time % 24 == 0) to different values (e.g., % 12 for twice-daily transport). What impact does this have? - Adjust maintenance respiration: Change MR from 0.01 to 0.05. How does increased respiration affect fruit development? ===== Biological Relevance ===== This transport model introduces key physiological concepts: • Source-sink relationships: Leaves act as sources, fruits as sinks • Phloem transport: Simplified as diffusion along concentration gradients • Competition for resources: Multiple sinks compete for limited assimilates • Maintenance respiration: Realistic metabolic costs • Sink strength: Younger fruits have stronger sink strength