Stromal Cell-Derived Factor-1a Autocrine/Paracrine Signaling Contributes to Spatiotemporal Gradients in the Brain

Abstract

Introduction

Stromal cell derived factor-1a (SDF-1a) and its receptor CXCR4 modulate stem cell recruitment to neural injury sites. SDF-1a gradients originating from injury sites contribute to chemotactic cellular recruitment. To capitalize on this injury-induced cell recruitment, further investigation of SDF-1a/CXCR4 signaling dynamics are warranted. Here, we studied how exogenous SDF-1a delivery strategies impact spatiotemporal SDF-1a levels and the role autocrine/paracrine signaling plays.

Methods

We first assessed total SDF-1a and CXCR4 levels over the course of 7 days following intracortical injection of either bolus SDF-1a or SDF-1a loaded nanoparticles in CXCR4-EGFP mice. We then investigated cellular contributors to SDF-1a autocrine/paracrine signaling via time course in vitro measurements of SDF-1a and CXCR4 gene expression following exogenous SDF-1a application. Lastly, we created mathematical models that could recapitulate our in vivo observations.

Results

In vivo, we found sustained total SDF-1a levels beyond 3 days post injection, indicating endogenous SDF-1a production. We confirmed in vitro that microglia, astrocytes, and brain endothelial cells significantly change SDF-1a and CXCR4 expression after exposure. We found that diffusion-only based mathematical models were unable to capture in vivo SDF-1a spatial distribution. Adding autocrine/paracrine mechanisms to the model allowed for SDF-1a temporal trends to be modeled accurately, indicating it plays an essential role in SDF-1a sustainment.

Conclusions

We conclude that autocrine/paracrine dynamics play a role in endogenous SDF-1a levels in the brain following exogenous delivery. Implementation of these dynamics are necessary to improving SDF-1a delivery strategies. Further, mathematical models introduced here may be utilized in predicting future outcomes based upon new biomaterial designs.

Appendix A: Model Components

The tissue was modeled in 2D with a rectangular section of tissue. The injection sub-domain was a rectangle as tall as the tissue but only 200 μm wide and placed in the horizontal (x-direction) center of the tissue. For each transported species, the initial values and reaction terms varied depending upon the geometric location. Equations below include the terms and values for each location. Initial values and reaction terms for soluble SDF-1a transport varied upon delivery method while SDF-1a/CXCR4 complex and unbound CXCR4 transport remained constant between models. Therefore, separate values and terms for soluble SDF-1a transport are listed below for bolus delivery and NP delivery. To create the diffusion only models, maximum reaction velocity was set to zero for both soluble SDF-1a and unbound CXCR4 such that no downstream signaling could occur past SDF-1a and CXCR4 binding.

Soluble, Extracellular SDF-1a Transport for Bolus Delivery

$$\frac{{\partial c_{1} }}{\partial t} + \nabla \cdot \left( { - D_{1} \nabla c_{1} } \right) = R_{1}$$

(A1)

$$D_{1} = D_{c}$$

$$c_{1} ,\;{\text{tissue}} = {\text{blc}}$$

$$R_{1} ,\;{\text{tissue}} = V_{ \hbox{max} } \cdot \frac{{c_{2} }}{{K_{m} + c_{2} }} - k_{deg } \cdot c_{1}$$

(A2)

$$c_{1} , {\text{injection}} = X$$

$$R_{1} ,{\text{injection}} = V_{ \hbox{max} } \cdot \frac{{c_{2} }}{{K_{m} + c_{2} }} - k_{deg } \cdot c_{1}$$

(A3)

Soluble, Extracellular SDF-1a Transport for Nanoparticle Delivery

$$\frac{{\partial c_{1} }}{\partial t} + \nabla \cdot \left( { - D_{1} \nabla c_{1} } \right) = R_{1}$$

(A4)

$$D_{1} = D_{c}$$

$$c_{1} ,\;{\text{tissue}} = {\text{blc}}$$

$$R_{1} ,{\text{tissue}} = V_{ \hbox{max} } \cdot \frac{{c_{2} }}{{K_{m} + c_{2} }} - k_{deg } \cdot c_{1}$$

(A5)

$$c_{1} , {\text{injection}} = {\text{blc}}$$

$$R_{1} ,{\text{injection}} = X \cdot \left( {0.0585} \right) \cdot \left( {0.12} \right) \cdot \left( {t^{\wedge}\left( { - 0.88} \right)} \right) + V_{ \hbox{max} } \cdot \frac{{c_{2} }}{{K_{\text{m}} + c_{2} }} - k_{deg } \cdot c_{1}$$

(A6)

SDF-1a/CXCR4 Complex Transport

$$\frac{{\partial c_{2} }}{\partial t} + \nabla \cdot \left( { - D_{2} \nabla c_{2} } \right) = R_{2}$$

(A7)

$$D_{2} = 0$$

$$c_{2} , {\text{tissue}}, {\text{injection}} = 0$$

$$R_{2} ,{\text{tissue}}, {\text{injection}} = ka \cdot c_{1} \cdot c_{3} - ke \cdot c_{2}$$

(A8)

Unbound CXCR4 Transport

$$\frac{{\partial c_{3} }}{\partial t} + \nabla \cdot \left( { - D_{3} \nabla c_{3} } \right) = R_{3}$$

(A9)

$$D_{3} = 0$$

$$c_{3} , {\text{tissue}}, {\text{injection}} = {\text{crt}}$$

$$R_{3} ,{\text{tissue}}, {\text{injection}} = - ka \cdot c_{1} \cdot c_{3} - \left( {0.1 \cdot k_{ deg } \cdot c_{3} } \right) + Vr \cdot \frac{{c_{2} }}{{\left( {Kr + c_{2} } \right)}} + Vrc$$

(A10)