This model tries to prove theoretically the TALE-based scaffold system can improve the multi-enzyme reaction efficiency. (You can go PROJECT page to see more.) The core idea is to calculate reaction rate parameters using time driven stochastic simulation method, and compare these parameters of the TALE-based scaffold system and the none-scaffold system. Furthermore, the effect of the multi-enzyme sites on scaffold is studied.

The models to study reaction efficiency are based on reaction molecular dynamics. The basic point of reaction molecular dynamics is that REACTION EQUALS COLLISION. Michaelis-Menten equation is universally applied to build reaction molecular dynamics models. However, although the Michaelis-Menten equation is derived from the collision behavior characteristics, it presumes that the reactant is UNIFORMLY dispersed in the reaction space and the COLLISION EQUALS CONCENTRATION. Therefore, the Michaelis-Menten equation is improper to simulate the scaffold “aggregation” effect where the reactant is UNEVEN.

Stochastic simulation can directly calculate the behavior of every reactant molecule, which can simulate scaffold “aggregation” effect. The idea of stochastic simulation is to transform a difficult question to a sampling question. In other words, in this article, the stochastic simulation method is applied to calculate and assess scaffold system and none-scaffold system parameters in the form of probability distributions.

Figure 1. The compare between two methodologies.

The stochastic simulation starts from COLLISION while the Michaelis-Menten equation basic on the CONCENTRATION. The transform from COLLISION to CONCENTRATION requires uniform condition.

We simulated multi-enzyme reaction in E.coli. Considering our limited time, equipment and abilities, we adopted the simplifying assumptions below.

Object

The involved objects are E.coli, reactants, scaffold and enzymes (on or off scaffolds). And the enzyme sites are fixed on scaffolds.

Geometry

The simulation is on two dimension. Thus, E.coli, reactants and enzymes are treated as circle, and the scaffolds are treated as lines.

(a) E.coli	(b) Simplified E.coli with scaffold	(c) Simplified E.coli without scaffold
Figure 2. The simplification of E.coli

Motion

The simulation is time driven. Enzymes and scaffolds are fixed in E.coli. The motion of substrates and intermediate products is the composition of the cyclosis and random thermal motion. We neglected the cyclosis here.

The random thermal motion makes them go forward to an uncertain direction. The motion direction and speed in a time step can decide the random thermal motion, where the direction and speed are uniformly distributed. We abandoned the more accurate Maxwell molecular velocity to improve the calculation speed by voiding probability integral of Maxwell distribution.

Interaction

All object are restricted to move within on E.coli. We neglect the non-contact intermolecular force. The substrates and intermediate products can overlap the enzyme and scaffold spot which can simulate the combination during reaction process.

Every collision (overlap) between reactant and enzyme is effective as long as the they match. And every reaction can be finished instantaneously as long as the collision happened.

The smaller blue dots are substrates and the larger blue and red dots are different enzyme. The different enzymes of (b) are linked by scaffold and the scaffold are independently dispersed while those in (c) are independently dispersed.

MATLAB & MacBook Pro 2.8 GHz Intel Core i7

The simulation aims at comparing the scaffold and none-scaffold effect and studying the sites position (on scaffold) effect. The parameters setting below balanced the simulation similarity degree and calculation ability of our equipment. So the reactants, enzyme quantities cell diameter are smaller than the E.coli. But the density of reactants, enzyme is relatively near to the real condition.

	Enzyme Type	Enzymes Distance	Enzymes Diameter
Group 1	2	8	[6,8]
Group 2	2	16	[6,8]
Group 3	2	18	[6,8]
Group 4	3	[12,12]	[6,8,10]
Table.2 The Variable Parameters Setting
					Graphic Note

The multi-enzyme reaction series is:

Note1: Return to V.Parameter Setting to see detailed parameter of the group below.

Note2: All movies are the first 30 time units in 3000 time units.

Group 1

Analysis: Although the substrates are consumed in similar speed. With scaffold the, the intermediate products are transformed to resultant faster than that without scaffold. Thus, the scaffold design improves the reaction efficiency.

Group 2

Analysis: The distance between enzyme sites is larger than group1. But, similarly, the substrates are consumed in nearly same speed. With scaffold the, the intermediate products are transformed to resultant faster than that without scaffold. Thus, the scaffold design improves the reaction efficiency.

Group 3

Analysis: The distance between enzyme sites is enlarged on. Differently, the scaffold design and none-scaffold design have similar reaction efficiency.

Group 4

Analysis: The multi-enzyme reaction series increases than that above. The substrates are also consumed in nearly same speed. But the effect of the scaffold is more obvious than that above.

Group 1/2/3

Figure4. The resultant quantity with two enzymes on one scaffold.

With the distance between different enzymes sites on one scaffold enlarging, the the effect of the scaffold decreasing.

Overall Analysis:

It has same probability between scaffold and none-scaffold design. when the substrate collision with the first enzyme. So, the substrates are consumed in nearly same speed.

While because the scaffolds aggregate the enzymes, when the intermediate products try to collide with the second enzyme, it tends to consume less time between collision with enzyme. So, the scaffold can improve the multi-enzyme reaction efficiency.

However, when the distance between enzyme sites to a extent, the scaffold can aggregate enzymes enough tight, the advantage of scaffold will disappear.

Based on our simulation, we came to the conclusion that:

1. The TALE-based scaffold system can improve the multi-enzyme reaction efficiency.

2. With the multi-enzyme reaction series increasing, the effect of the scaffold is brought out.

3. With the distance between different enzymes sites on one scaffold enlarging, the the effect of the scaffold decreasing. (We did not consider the steric hindrance during modeling, thus this conclusion is not consistent with wet lab.)

In the future, we will go along the road and improve this simple model.

1. Optimizing the simulation algorithm and using more precise parameters.

2. Building 3-dimension model.

Considering non-contact intermolecular force into model (molecular field), which could simulate the steric hindrance.