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Product Details

ISBN-13: 9781849737982
Publisher: Royal Society of Chemistry, The
Publication date: 03/20/2014
Series: Soft Matter Series , #2
Pages: 238
Product dimensions: 6.20(w) x 9.20(h) x 0.70(d)

About the Author

Ian W. Hamley is Diamond Professor of Physical Chemistry at the University of Reading, UK and holds a Royal Society-Wolfson Research Merit Award. He has previously authored three books on soft matter and block copolymers and edited two texts. His research interests are focussed on soft materials including polymers, colloids and biomaterials.

Che Connon is Reader in Tissue Engineering and Cell Therapy. His research focus is primarily in the area of corneal tissue engineering, seeking to engineer functional replacement and temporary 'bridge' tissues while also developing model systems to study physiological and pathophysiological corneal tissue formation.

Read an Excerpt

Hydrogels in Cell-Based Therapies


By Che J. Connon, Ian W. Hamley

The Royal Society of Chemistry

Copyright © 2014 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-1-78262-205-5



CHAPTER 1

Soluble Molecule Transport Within Synthetic Hydrogels in Comparison to the Native Extracellular Matrix


MATTHEW PARLATO AND WILLIAM MURPHY


1.1 Introduction

Soluble factor signalling and gradient formation are of known biological importance and direct processes such as stem cell differentiation, cellular migration, limb bud development, and neural tube development. Soluble transport within the in vivo environment is complex, involving spatiotemporal interactions and molecular recognition between soluble molecules and extracellular matrix (ECM) components. Because of such complexity, what is known and what can be studied about soluble transport in vivo is limited. Therefore, the use of well-defined in vitro experimental platforms is an attractive option. Because of the similarity of hydrogels to the native ECM, synthetic hydrogels can serve as model systems for the study of soluble transport and gradient formation within the ECM. Synthetic hydrogels are also useful because of their biocompatibility and adaptability for use with a variety of chemistries.

The hydrated polymer chains of synthetic hydrogels slow solute movement just as the macromolecules within the ECM do, thus assisting in the formation of concentration gradients. Furthermore, drug delivery technologies have been incorporated into synthetic hydrogels that serve as well-defined soluble factor sources and sinks within the hydrogel. Other experimental approaches seek to incorporate the ability of the native ECM to specifically bind and release soluble molecules into synthetic hydrogels by the incorporation of proteoglycans or peptides that have high binding affinities for specific soluble molecules. Many methods also exist that exert temporal control over transport within synthetic hydrogels by allowing the hydrogel to degrade over time, be remodelled by cell-secreted enzymes, or respond to external cues such as temperature or pH.

There are many articles and reviews that discuss the first principles of transport within the native ECM and synthetic hydrogels separately; however, the purpose of this chapter is to compare and contrast the two. We endeavour to address some of the critical questions that arise during development of synthetic hydrogels to mimic natural signalling gradients in the ECM, such as: (1) how does transport and gradient formation of soluble molecules within synthetic hydrogels compare to that within the native ECM? (2) What aspects of signalling within the native ECM have been mimicked within synthetic hydrogels and what aspects remain to be explored? and (3) what are the potential consequences of these differences, and how can the synthetic hydrogels be made to more closely mimic the signalling of the native ECM? This chapter is divided into five sections based on the following parameters that influence molecular transport in natural or synthetic ECMs: steady-state diffusion, soluble factor generation and consumption, matrix interactions, temporal dependencies, and convection. Each of these sections is divided into two subsections. The first subsection discusses the topic with regard to the native ECM and the second with regard to synthetic hydrogels. Finally, the chapter concludes with a short discussion of the future directions for synthetic hydrogels that seek to recapitulate various aspects of signalling in the native ECM.


1.2 Steady-State Diffusion

1.2.1 Steady-State Diffusion Within the Native ECM

Soluble factor gradients within the ECM are generated through a variety of mechanisms, but to begin the discussion, a simple case with defined 'source' and 'sink' regions is discussed. In the simplest scenario, defined source and sink regions occur due to one group of cells producing large amounts of soluble molecules while another nearby group does not produce these molecules and instead consumes them. The goal of this section is to understand the basic mechanisms by which soluble factor gradients may form within the native ECM. Additionally, we examine what fundamental properties of both the soluble factor and the native ECM affect this gradient formation.

Within this section, all sources and sinks are assumed to exist at a single point in space to facilitate mathematical descriptions. Therefore, they are referred to as 'point-sources' and 'point-sinks'. They are also assumed to produce or consume molecules instantaneously and without limits. Due to these properties, they are referred to as 'perfect sources and sinks'. Furthermore, we assume that the ECM in which the molecules are diffusing is homogeneous and that all parameters are constant with time (i.e. steady state). Notably, biological scenarios do not feature perfect, point-sources and point-sinks, but this is a useful and widely utilized starting point in discussions of transport in the native ECM. A diagram of this problem is shown in Figure 1.1a. A summary of these assumptions is as follows:

(1) All regions are homogeneous.

(2) The source region is a perfect, point source.

(3) The sink region is a perfect, point sink.

(4) All parameters are constant with time ('steady state').


To analyse this situation, Fick's first law of diffusion is applied (eqn (1.1)) This law states that the mass flux, J, of a solute through a region of space is proportional to the rate of change of the solute's concentration with respect to position, dC/dx. We assume that at the position x = 0, the solute is produced in a way that maintains a constant concentration, [C.sub.0] and this assumption is used to develop the boundary condition (eqn (1.1), BC 1).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.1)

Eqn (1.1) shows the diffusion and gradient formation within a homogenous region from Fick's first law. Here C is the concentration of the soluble factor, J is the mass flux of the solute, x is position, and D is the diffusion coefficient. Here a linear relationship is demonstrated that is dependent on initial concentration of the molecules at the source ([C0), mass flux (J), and the solute diffusion coefficient (D). The ratio of J/D is the slope of the linear concentration gradient (Figure 1.1b), and C0 is the y-intercept. This problem can also be solved by Fick's second law of diffusion. However, this law is applicable with non-steady state problems because it assumes non-constant mass flux, so it is discussed in Section 1.4.1 where temporal dependencies are discussed in detail.

In general, solutes that are small in size when compared to pores in the ECM diffuse quickly, and those that are large diffuse more slowly, because that larger solutes interact with the matrix more often than smaller solutes. This slowing of molecular movement is referred to as 'sieving action'. Many models exist to approximate the size of a molecule, and a commonly utilized model is the Stokes–Einstein relationship (eqn (1.2)). This model assumes a spherical molecule with a density close to that of water (1 g mL-1). Molecular radii calculated from this relationship are referred to as hydrodynamic radii (represented by the variable a) because this model is based on hydrodynamic diffusion theory. Though derived for a solute diffusing freely in a homogenous solution, this model can also be related to diffusion coefficients of solutes in hydrogels. One of the best-known models was derived by Brinkman, which relates diffusion coefficients in a gel, such as the native ECM (represented by the variable [DECM), to that in water (represented by the variable D0) based solely on hydrodynamic radius, a, and a fitted system parameter, κ.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.2)


Eqn (1.2) shows the Stokes–Einstein relationship for relating the diffusion coefficient, D, to molecular radius, a. In this relationship, an approximately spherical molecule is assumed with a density, ρ which is close to that of water (1 g mL-1). The notation used here is as follows: R is the universal gas constant, T is temperature, μ is the solution viscosity, N is Avogadro's number, and MW is the molecular weight. Diffusion coefficients within the ECM, DECM can be compared to those found in dilute water solutions, D0 through this relationship developed by Brinkman where κ is a fitted system factor and a is again molecular radius.

Eqn (1.2) presents a method predicting how various biomolecules of different hydrodynamic radii diffuse through the ECM (Figure 1.4c and d). Even when all other variables are held constant, molecular size alone can dramatically affect the slope of the gradient.

Many examples of Fick's first law are found in in vivo situations, and studies of the transport of solutes into cancerous tissue provide illustrative examples of such relationships. For instance, some types of tumours are known to retain a large amount of fluid, increasing their interstitial volume and thus increasing the diffusion coefficients of solutes. The change occurs because the increased volume lowers the concentration of macromolecules that compose the ECM, thus allowing for faster movement of solutes because there are fewer solute interactions with the matrix. In contrast, within other types of tumours diffusion is severely hindered because of increased ECM protein secretion around the tumour tissue. Creation of more material around a site increases the concentration of the macromolecules that comprise the ECM, and transport by diffusion is slowed because of an increased number of interactions between solutes and matrix. Additionally, digestion of the tumour ECM by enzymes enhances diffusion into the tumour tissue, due in part to the corresponding decrease in ECM concentration. From these studies, it is clear that transport within the native ECM is dependent on ECM network parameters in addition to solute properties.


1.2.2 Steady-State Diffusion Within Synthetic Hydrogels

As in the native ECM, gradients can form within synthetic hydrogels through multiple mechanisms; however, numerous examples of gradients forming primarily through sieving action can be found in the literature. When analysing gradient formation in synthetic hydrogels, the same assumptions that were made in the previous section are made here. Notably, the assumption that the hydrogel is a homogeneous, porous network of inert macromolecules is more appropriate for synthetic hydrogels than for the native ECM.

Prediction of the diffusion coefficients of solutes within synthetic hydrogels has been modelled using hydrodynamic theory and the Stokes–Einstein relationship (eqn (1.2)). Specifically, the diffusion coefficient within hydrogels, Dgel, versus that of free solution, D0 is commonly modelled with the following relationship:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.3)


Eqn (1.3) shows the Stokes–Einstein relationship specifically for the hydrogel diffusion case. Here a is the hydrodynamic radius, B is a system coefficient, and c is the polymer concentration of the hydrogel (expressed in units of volume fraction). Dgel is the diffusion coefficient within the hydrogel and D0 is the diffusion coefficient of the solute in free solution.

The Stokes–Einstein relationship is a simple representation of the sieving action of a synthetic hydrogel, but this model is limited based on its dependence on a fitted parameter, the system coefficient B. A more broadly useful and predictive model minimizes its dependence on fitted parameters and maximizes its dependence on parameters that can be measured by the experimenter. Based upon thermodynamics first principles of hydrogel networks, the molecular weight between crosslinks, Mc, can be predicted based upon average polymer molecular weight, Mn, and volume fraction of polymer in the network, v2,s (eqn (1.4)):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.4)


Eqn (1.4) shows the molecular weight between crosslinks of a hydrogel based upon thermodynamic first principles. Here Mc is the molecular weight between crosslinks, Mn is the average polymer molecular weight, v is the specific molar volume of the polymer, V is the molar volume of water, χ is the Flory interaction parameter between the polymer and the solvent, v2,s is the swollen volume fraction of polymer, and [v.sub.2,r] is the relaxed volume fraction of the polymer.

Once the molecular weight between crosslinks is known, the average physical distance between crosslinks, [??], can be determined based on known polymer parameters and the molecular weight between crosslinks, Mc.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.5)

Eqn (1.5) shows the distance between crosslinks, [??] based on the swollen volume fraction of the polymer, v2,s, the Flory characteristic ratio, Cn, the molecular weight between crosslinks, Mc, the average distance of one bond in the polymer backbone, l, and the molecular weight of polymer repeat unit, Mr.

This physical length can be used to determine the diffusion coefficient of a solute through the hydrogel network. Comparing the molecular radius, a, to the distance between crosslinks in the hydrogel, [??] one can calculate the amount by which the movement of the solute is slowed. Lustig and Peppas incorporated this principle into a solute diffusion model based on free volume theory:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.6)


Eqn (1.6) shows the ratio of the diffusion coefficient within a hydrogel, Dgel, to the diffusion coefficient within free solution, D0, based on molecular radius, a, and the average distance between crosslinks, [??] Here, Y is the lumped free volume parameter, and v is the volume fraction of the polymer. This relation simplifies at low volume fractions since the exponential term becomes approximately 1.

An example of diffusion from a source within synthetic hydrogels was described by Peret et al. when protein-releasing microspheres were encapsulated within a small section of a hydrogel to create a localized source (Figure 1.2). In this work, the rest of the hydrogel acted as a sink for molecules released from the localized source. The gradients that formed in these hydrogels were dependent upon source concentration and the hydrodynamic radii of the diffusing molecules. Both of these dependencies can be predicted from equations described thus far in this chapter. Another study by Cruise et al. demonstrated trends in the diffusion of proteins through hydrogel networks that were similar to those seen by Peret et al. In this work, the permeability of poly(ethylene glycol) (PEG) hydrogel networks to proteins of various sizes was controlled solely by adjustments to hydrogel network properties.


1.3 Soluble Factor Generation and Consumption

1.3.1 Soluble Factor Generation and Consumption Within the Native ECM

Though the relationships discussed in previous sections can be used to generally explain gradient formation in the ECM, they make unrealistic assumptions about soluble factor generation and consumption. For instance, cells are only capable of producing soluble molecules at specific rates, which Savinell et al. established to be on the order of thousands of molecules per cell per second. Additionally, the number and distribution of cells producing a particular soluble factor is also a matter to consider, as well as any feedback mechanisms that may influence the production rate. The same statements can be made about soluble factor consumption. Although there are in vivo situations where soluble molecules are produced or consumed regardless of all other variables, this is rare. Therefore, a much better description of soluble factor production and consumption are the following functions (eqn (1.7)), which account for cell number at the source, N, as well as soluble molecule concentration, C, and time, t:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.7)


Eqn (1.7) shows that the soluble factor concentration is dependent on the rate at which the soluble factor can be produced (top) or consumed (bottom) by the point-sources and sinks. P' and E' represent functions that relate soluble factor production and consumption to cell number, N; concentration of that factor, C; and time, t, to soluble factor concentration.


(Continues...)

Excerpted from Hydrogels in Cell-Based Therapies by Che J. Connon, Ian W. Hamley. Copyright © 2014 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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Table of Contents

Soluble Molecule Transport Within Synthetic Hydrogels in Comparison to the Native Extracellular Matrix; Biocompatibility of Hydrogelators Based on Small Peptide Derivatives; Recombinant Protein Hydrogels for Cell Injection and Transplantation; The Instructive Role of Biomaterials in Cell-Based Therapy and Tissue Engineering; Microencapsulation of Probiotic Bacteria into Alginate Hydrogels; Enzyme-Responsive Hydrogels for Biomedical Applications; Alginate Hydrogels for the 3D Culture and Therapeutic Delivery of Cells; Mechanical Characterization of Hydrogels and its Implications for Cellular Activities; Extracellular Matrix-Like Hydrogels for Applications in Regenerative Medicine;

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