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Hydrodynamic radii of ranibizumab, aflibercept and bevacizumab measured by time-resolved fluorescence anisotropy

Abstract

**Purpose:** To measure the hydrodynamic radii of intravitreal anti-VEGF drugs ranibizumab, aflibercept and bevacizumab with \(\mu\)s time-resolved fluorescence anisotropy.

**Methods:** Ruthenium-based dye Ru(bpy)\(_2\)(mcbpy-O-Su-ester)(PF\(_6\))\(_2\), whose lifetime of several hundred nanoseconds is comparable to the rotational correlation time of these drugs in buffer, was used as a label. The hydrodynamic radii were calculated from the rotational correlation times of the Ru(bpy)\(_2\)(mcbpy-O-Su-ester)(PF\(_6\))\(_2\)-labelled drugs obtained with time-resolved fluorescence anisotropy measurements in buffer/glycerol solutions of varying viscosity.

**Results:** The measured radii of 2.76\(\pm\)0.04 nm for ranibizumab, 3.70\(\pm\)0.03 nm for aflibercept and 4.58\(\pm\)0.01 nm for bevacizumab agree with calculations based on molecular weight and other experimental measurements.

**Conclusions:** Time-resolved fluorescence anisotropy is a relatively simple and straightforward method that allows experimental measurement of hydrodynamic radius of individual proteins, and is superior to theoretical calculations which cannot give the required accuracy for a particular protein.

**Keywords:** Hydrodynamic radius, fluorescence, phosphorescence, time-resolved anisotropy, rotational diffusion

**Abbreviations**

AMD

= Age-related Macular Degeneration

BSA Bovine Serum Albumin

DLS Dynamic Light Scattering

FCS Fluorescence Correlation Spectroscopy

FRAP Fluorescence Recovery After Photobleaching

MW Molecular Weight

NMR Nuclear Magnetic Resonance

PBS Phosphate Buffered Saline

PLIM Phosphorescence Lifetime Imaging

SANS Small-Angle Neutron Scattering

SAXS Small-Angle X-ray Scattering

VEGF Vascular endothelial growth factor

There are many diseases that manifest in the posterior segment of the eye. These include age-related macular degeneration (AMD), retinal vein occlusion, and diabetic retinopathy and maculopathy. Together they account for the majority of blind registrations in the developed world.(Bunce 2010) Many of these diseases are treated with regular injections of drugs into the vitreous cavity, with the inconvenience of regular clinic review, cost of repeated injection, discomfort, and small but repeated risks of complications.(Edelhauser 2010) Given the many downsides of regular intravitreal injections, the drug industry is actively investigating novel methods of delivering drugs to the posterior segment, including sustained release intravitreal devices,(Callanan 2008) transscleral drug delivery,(Ambati 2002, Ambati 2000, Ambati 2000a) topical drug delivery (eye drops),(Tanito 2011) oral (McLaughlin 2013) and others such as iontophoresis.(Molokhia 2009)

Topical drug delivery has many potential advantages, including self-administration, reduced cost, sustained drug levels, potentially fewer clinic visits, and the elimination of the risks associated with eye injections. Whilst desirable, topical drug delivery to the posterior segment is greatly impeded by the external ocular barriers to diffusion. This is compounded by the fact that many of the drugs used to treat posterior segment disease have a high molecular weight (MW), including ranibizumab (Lucentis, 48 kDa), aflibercept (Eylea, 97 kDa), and bevacizumab (Avastin, 150 kDa).

Many factors, such as the molecular size and shape, will influence how intravitreal drugs cross the vitreous, and retina, to reach diseased macular and choroidal tissue.(Foulds 1985, Gisladottir 2009, Srikantha 2012) It is well known that increasing MW reduces diffusion across biological tissue,(Maurice 1977, Pitkänen 2005, Geroski 2001) and other studies have shown that the molecular radius is a better predictor of tissue penetration than MW.(Ambati 2002, Ambati 2000, Geroski 2001, Bohrer 1984, Ohlson 2001, Venturoli 2005)

It is possible to estimate the radius of a protein from the MW. Erickson uses the fact that all proteins have approximately the same density, 1.37 g/cm\(^3\), to calculate the protein volume from the MW.(Erickson 2009) Assuming a smooth spherical shape, this yields a minimum possible radius \[R_{min} \text{(nm)} = 0.066 \cdot \text{MW}^{1/3} \label{eq:Erickson}\]

However, proteins have a rough surface, are often not perfectly spherical, and their charge can affect their diffusion in solution. The hydrodynamic radius \(R_h\), defined as the radius of a hard sphere that diffuses at the same rate as the solute, takes these effects into account. The hydrodynamic radius is important in predicting transretinal penetration.(Jackson 2003, Ambati 2000)

Small-angle scattering studies using X-rays (SAXS) or neutrons (SANS) (Svergun 2013) as well as dynamic light scattering (DLS) (Dynamic Light Scatter..., Hong 2009) and nuclear magnetic resonance (NMR) techniques (Wilkins 1999) have been used for measuring \(R_h\). Empirical relationships have been defined between \(R_h\) and the number of amino acids \(N\) (related to the MW by \(N = \frac{\text{MW}}{110 \text{ Da}}\)), for example, by Wilkins *et al.* (Wilkins 1999) \[R_h^W (\text{\AA}) = 4.75\cdot N^{0.29} \label{eq:Wilkins}\] and Dill *et al.* (Dill 2011) \[R_h^D (\text{\AA}) = 1.45\cdot(2.24\cdot N^{0.392}) = 3.248\cdot N^{0.392} \label{eq:Dill}\]

These formulas were obtained by global analysis of hundreds of proteins, and fitting to a scatter plot of \(R_h\) against MW. While they give a good indication of the expected size, there is a big variance in the measured \(R_h\) as a function of MW. This can be explained by the deviation of these models from the protein’s actual properties, which are due to molecular shape, charge and surface roughness.

Time-resolved fluorescence anisotropy measurements can determine the molecule’s rotational mobility which depends on the molecular volume and the viscosity of the environment surrounding the molecule.(Lakowicz 2006) The sample is excited with a pulse of polarised light, and the fluorescence is collected in parallel and perpendicular polarisation directions as a function of time. The anisotropy \(r(t)\) of a molecule undergoing rotational diffusion in the solution can be obtained from the measured intensities \(I_\parallel\) and \(I_\perp\) by \[r(t)= \frac{I(t)_\parallel-GI(t)_\perp}{I(t)_\parallel+2GI(t)_\perp} \label{eq:anisotropy}\] where \(G\) is a correction factor that compensates for different transmission and detection efficiencies in the parallel and the perpendicular directions.(Suhling 2014) If the sample solution contains spherical molecules of homogeneous size, the anisotropy decay follows a single-exponential function \[r(t) = r_0\cdot e^{-\frac{t}{\phi}} \label{eq:1expfit}\] where \(r_0\) is the initial anisotropy at \(t=0\) and \(\phi\) is the rotational correlation time. If the rotating unit is not spherical, a more complex multi-exponential model is required.(O’Connor 1984)

\(\phi\) can thus be obtained by fitting eq \ref{eq:1expfit} (or the more complex model) to the experimental anisotropy decay. \(\phi\) is related to the volume \(V\), and thus the effective radius, of the rotating molecule by the Stokes-Einstein-Debye equation (Van Holde 1998) \[\phi = \frac{\eta V}{kT} \label{eq:SED}\] where \(\eta\) is the solvent viscosity, \(k\) is the Boltzmann constant and \(T\) is the absolute temperature.

Although time-resolved anisotropy measurements are a well established tool in molecular biology, only a few studies report applications in ophthalmology.

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