Pharmacokinetic model

Assessment of RVG aptitude

Background

The blood brain barrier (BBB) is formed by many components including endothelial cells of the capillary wall, astrocyte and pericytes. It is the largest interface between the blood and the central nervous system and is situated between the blood and the interstitial fluid. Our RVG construct is designed to steer exosome to cross the obstacle Delivering exosome through BBB is an extremely complex process. The affinity of RVG to nicotinic acetylcholine receptor (nAchR) is critical to clathrin and caveolae-mediated transcytosis, which is the main mechanism of guiding exosome through the barrier. To study the ability of our engineered exosomes to pass the BBB, we simplify the whole process into passing endothelial cells and study the aptitude of RVG by modeling the binding properties to the receptor side of the endothelial cell membrane.

CX43, a family member of gap junction proteins, can only help us to deliver exosome if it is open and exchange fusion signal with neuron cell. Here, we present a model demonstrating a macroscopic situation in gap junctions, and thereby ensuring the functionality of CX43 as a cytosolic delivery helper.

Assumption

1. Interacting bonding rupture does not occur during cellular trafficking of endothelial cell, so transcytosis is successful once endocytosis happens
2. Influences of hyperaemia are neglected.
3. endosome can be considered as spheres.
4. Influences resulting from PH、 enzyme and salt concentration in blood are neglected.

Process and Result

The binding of the ligands on the surface of exosomes to the receptors of endothelial cells of capillary wall is affected by the blood flow. Blood flow creates a shearing force at the vessel walls that strains the receptor-ligand bondings and therefore increases the chances of disrupting the interaction. The following equations are given to measure dislodging force, including drag force (Fd) in the direction of blood flow and a rotating force called the torque (T). The two major forces hinder our exosome to be bound and thus transported through the endothelial cell.

Figure 1：drag force(Fd)

Figure 2：Rotation force(T)

The whole forces caused by blood flow could be measured by F_dis = Fd + Tq/2 [11].

The dislodging force (Fdis) to different size of nanoparticle is then tested.

There have been studies showing that exosome with 60nm diameter is most suitable for passing the vivo BBB model [11]. So Fdis of 10^-14 could be used as the force acting on exosome. The probability of forming the interaction and breaking the interaction under shear flow can be given as:

P_bonds=P_form-P_break

P_bonds represents the steady bonds forming during ligand - receptor contact. We set 10 matching receptor-ligand pairs with a series of association constants for one exosome to test the binding status of 0.5s when it comes to exosome-endothelial contact. If RVG-carried exosome has higher affinity, in other words, transcytosis ability than non-RVG exosome, it should adhere to endothelial cell membrane with more steady interaction.

Figure: RVG-carried exosome has the better binding ability under different association constant. Extra steady bonds are always formed on engineered exosome, which increases the probability of successful transcytosis and theoretically proves the aptitude of RVG-carried exosomes to across BBB by receptor-mediated transcytosis. Furthermore, more blood-injected exosome will enter into brain than the rest of the body due to the brain-guiding efficiency of RVG.

Parameters	Definitions	Value	Units	Note
R_d	Receptor-ligand density for exosome/RVG-carried exosome	10⁵/2X10⁵	nm^-2	[11]
A_c	The interfacial contact surface area	225	nm²	Estimated from most-fit exosome
L_D	ligand density	10⁵	nm²
l	distance from the particle center of mass to the cell membrane	35.8	nm
𝑺𝝁	wall shear stress	0.25	Pa	[11]
𝜸	particle aspect ratio	1
kB	Boltzmann constant	1.0X10^-3	min^-1
T	temperature	310.15	K
BN	nanoparticle shared over the number of bonds	5
k0/a	the association constant at zero load per receptor-ligand pair	1000/2000/3000/4000		Tested value
kD	dissociation constant	10^-6
B_RL	bond length	7.2	nm	Estimated from most-fit exosome
𝜹eq	closest distance of the nanoparticle relative to the cell	5.8	nm	[11]
r	Radius of exosome	30	nm	Estimated from most-fit exosome

Variables	Meaning
P_a	The probability of a spherical nanoparticle adhering to the cell membrane
F_D	Drag force generated by the blood flow
F_s	is the force as a function of aspect ratio
T_s	the torque force as a function of aspect ratio
F_RL	dislodging force per receptor ligand pair
Tq	Torque
P_bonds	The probability to form a stable ligand-receptor bond
Fdis	The total dissociating force

Simulation of exosome in blood simulation

Background

Circulation of the blood is a vital function in human body. The main significance of blood circulation is to guarantee a proper metabolism of every cell in the body. The various tissues of the body get various nutrients， water and oxygen from the blood. Exosome is transported without exception. However, injecting the exosomes into the vein is an efficient but risky approach of delivering exosome to the brain. Excess exosomes in the blood or other parts of the body can be harmful. To ensure a proper delivery of exosome, a pharmacokinetic model is built to simulate the kinetics of exosome circulation in blood after injection.

Process

The formulation is connected with two pharmacokinetic ideas. Firstly, Exosome can be reversibly bounded with blood components, which repress them to enter into main parts of body. Also, Heart acts like a pump which determines the proportion and flow of blood to the body by blood circulation. After considering the two basic ideas above, the following formulas are produced.

Parameters	Definitions	Value	Units	Note
k_blooddis	Exosomes dissociation from blood components	1.7X10^-4	min^-1	IGEM NJU 2017
k_bloodbind	Exosomes binding to blood components	1.0X10^-6	min^-1	IGEM NJU 2017
k_intbrain	Effective fraction of dose available to brain	0.23	min^-1
k_intheart	Effective fraction of dose available to heart	1.0X10^-2	min^-1	IGEM NJU 2017
k_intliver	Effective fraction of dose available to liver	1.0X10^-2	min^-1	IGEM NJU 2017
k_spleen	Effective fraction of dose available to spleen	1.0X10^-3	min^-1	IGEM NJU 2017
k_lung	Effective fraction of dose available to lung	1.0X10^-3	min^-1	IGEM NJU 2017
k_kidney	Effective fraction of dose available to kidney	1.0X10^-2	min^-1	IGEM NJU 2017
k_adipocyte	Effective fraction of dose available to adipocyte	1.0X10^-2	min^-1	IGEM NJU 2017
k_bbb	Effective fraction of dose cross the blood brain barrier	0.4	min^-1
Q_c	Cardiac Output	5.6	L/min	IGEM Slovenia 2012
Q_heart	Blood following through heart tissue	5.6	L/min	IGEM Slovenia 2012
Q_spleen	Blood following through spleen tissue	0.6	L/min	IGEM Slovenia 2012
Q_lung	Blood following through lung tissue	5.6	L/min	IGEM Slovenia 2012
Q_kidney	Blood following through heart tissue	1.7	L/min	IGEM Slovenia 2012
Q_adi	Blood following through adipose tissue	2.8	L/min	IGEM Slovenia 2012
Q_liver	Blood following through liver tissue	1.4	L/min	IGEM Slovenia 2012

Variables	Determination(Units)
DisExo	Dissociated Exosome in blood(ug)
∑E	Sum of exosome entering in tissues except brain(ug)
dFixedExo	Exosome associated with blood component(ug)
dExoB	Exosome after crossing the blood brain barrier(ug)

Results

Figure: distribution of injected exosome

According to the figure, most of the injected exosomes are absorbed by brain and other tissues. Those who bind blood components finally go into other parts of body. Also, the sum of exosome (∑E) entering into other tissues is approaching the 10% of total injected exosome, which is far less than those entering into the brain (ExoB). This result shows the efficiency of our exosome design. Additionally, the remaining amount of exosome in the blood (DisExo and FixedExo) approach zero within 20 hours.

Evaluation

According to our model, RVG could be theoretically helpful to steer exosome on passing BBB. At the meantime, it Increases the proportion of exosomes entering the brain, which lower the risk of causing potential damage to the human body. However, the amount of safe dose of exosome injected into human for curing patient is still remain unknown.