A Review of Lens Biomechanical Contributions to Presbyopia

Abstract Purpose: Presbyopia—the progressive loss of near focus with age—is primarily a result of changes in lens biomechanics. In particular, the shape of the ocular lens in the absence of zonular tension changes significantly throughout adulthood. Contributors to this change in shape are changes in lens biomechanical properties, continuous volumetric growth lens, and possibly remodeling of the lens capsule. Knowledge in this area is growing rapidly, so the purpose of this mini-review was to summarize and synthesize these gains. Methods: We review the recent literature in this field. Results: The mechanisms governing age-related changes in biomechanical properties remains unknown. We have recently shown that lens growth may be driven by zonular tension. The same mechanobiological mechanism driving lens growth may also lead to remodeling of the capsule, though this remains to be demonstrated. Conclusions: This mini-review focuses on identifying mechanisms which cause these age-related changes, suggesting future work which may elucidate these mechanisms, and briefly discusses ongoing efforts to develop a non-surgical approach for therapeutic management of presbyopia. We also propose a simple model linking lens growth and biomechanical properties.


Introduction
Presbyopia is caused by aging of the ocular lens which results in the loss of accommodative function. The term presbyopia is derived from ancient Greek and loosely translates to "old man eye." This is a fitting description of the condition since nearly all people can expect to encounter presbyopia as they age. 1,2 Presbyopia is characterized as the loss of accommodative power which presents clinically as the inability to focus vision on nearby objects and a long time to focus. Symptoms are typically noticed some time after the age of forty with complete loss of objective accommodation occurring between the ages of 50-55 years old. 3 Alarmingly, decline in accommodative ability begins in adolescence and can be reduced by up to 50% by age 25. 4 Accommodation is typically entirely lost after about two thirds of a human lifespan, which is a much shorter time course than many other physiologic functions. 5,6 This is significant because symptoms of this age associated pathology can be expected to begin in middle age and without prevention or treatment will hinder patients' vision for an extended portion of life.
Recent work has shown that presbyopia can be entirely explained by age-related changes in the lens. 7 The lens is responsible for approximately 30-35% of the eye's refractive power, and accommodation allows for adjustments ranging from 14 to 18.8 diopters in fully accommodated healthy lenses. 8,9 Changes in the ocular lens can be detected in younger patients even in their twenties. As the lens ages, biomechanical, structural, and chemical changes lead to a loss of accommodative ability and patients are no longer able to mechanically adjust their lens' optical power.

Theories of Presbyopia
Physiologic causes of age-related presbyopia are linked to changes to the lens itself and not due to loss of function in other ocular tissue involved in accommodation. 7,[10][11][12] This is clear from the observation that the lens, in the absence of zonular tension, loses optical power with age. This decrease is sufficient to explain all of the loss of objective accommodation with age. 7 In addition, measurements have found only slight changes in the zonules or ciliary body with age. 2,13 These changes are too small to account for presbyopia. 14 There are two main theories which predict ocular changes that could result in loss of accommodative function in age-related presbyopia. The most well-known explanation is that loss of accommodation is due to changing material properties of the lens, while the second focuses on lens continuous growth as the driving force of lens accommodative dysfunction. Changes in lens properties, such as changing stiffness of the lens interior or lens capsule, could contribute to the loss of accommodation. Property changes may also be optical in nature, including factors such as reduced refractive index, yet would still be classified as a change in material properties of the lens. 15,16 The second field of thought regarding potential growthrelated causes of presbyopia holds the basic assumption that the progressive loss of accommodation is due to changes to the lens size or shape which could arise due to lens growth over time, cellular proliferation, or structural modification to the lens with age. 17 Although lens epithelial cells (LECs), the only proliferative cell in the ocular lens, are relatively metabolically inactive, they do continue to proliferate and differentiate into fiber cells throughout the life of an organism. 18 This continual process of LEC mitosis followed by differentiation into fiber cells increases cell counts within the ocular lens and is responsible for the lens's characteristic onion-like layering ( Figure 1). 19 While it has long been known that the lens is viscoelastic, 20-26 quantitative information on age-related changes to lens viscoelasticity are unavailable. The lens nucleus in particular may be more accurately considered to be a viscoelastic solid, modeled as a spring and dashpot in parallel. Since a long time to accommodate is frequently the driving symptom for clinical presentation 27 and has been associated with qualitative measurements of lens properties, 28 measurement of the lens' viscoelastic properties should be prioritized.
These theories on potential causes of age-related presbyopia are not exclusive, and likely changes to the lens mechanical and optical properties, lens geometry, and continual lens growth may all contribute to the loss of accommodation and onset of presbyopia. Like most biological systems, it is likely that various factors contribute to changes in observed states, and factors such as cellular behavior and mechanical properties could additively or synergistically impact the development of presbyopia. This review will focus on observed biomechanical factors which contribute to presbyopia and will discuss changes to both the ocular lens geometry due to lens growth and to lens material properties over time.

Linking Lens Growth and Biomechanics
Volumetric growth of the lens can apply an outward force (away from the optic axis) on the lens capsule and an inward force (toward the optic axis) on the lens nucleus. The capsule, represented by an elastic spring, may be elongated (or, considering higher dimensionality, its surface dilated) by zonular tension and/or the effects of lens growth. The nucleus may be also considered as an elastic spring.
Lens geometry and change to lens geometry during accommodation are key factors that partially determine the lens' influence on vision. Ultimately, the geometry of the fully accommodated lens-both its size and shape-are governed by the biomechanical forces exerted by the capsule on the lens and vice versa. 7 These are known as residual stresses-mechanical stresses which exist when no external loads are applied. 29 The disaccommodated geometry is then determined by imposing zonular tension on the residually loaded (fully accommodated) state. 30 Thus, an accurate definition of the fully accommodated lens' geometry relies on the lens capsule biomechanical properties and residual loading as well as the biomechanical properties and residual loading of the lens itself.
No measurements of lens residual stresses have been reported to date. In addition, measurements of lens properties have assumed linear or quasi-linear constitutive models which are unlikely to capture the complex behavior of the lens under dynamic loading and physiologic deformations. To understand how the residually loaded lens/capsule complex comes about, we present a brief history of lens growth from early development through middle age. A simple LE model of mechanobiological feedback governing lens growth is given in Figure 2.

Early Lens Development
In the earliest stage of embryonic development what will eventually become the ocular lens, and the rest of the eye, starts out as a thick patch of cells known as a placode. A subsection of a cranial placode which is destined to develop into the eye is positioned between the anterior neural plate and surface ectoderm. 31 Due to the invagination process of the lens from surface ectoderm tissue, the resulting organ exhibits an inverted cellular topography with apical surfaces on the interior of the lens capsule and LECs located on the interior of the anterior lens surface. 3 Pax6, a transcriptional factor, is responsible for directing ocular differentiation and growth and forming a lens specific placode. 31 Lens formation can only take place after evagination of the optic vesicle, and is controlled by signaling from both the optic vesicle and periocular mesenchyme. After optic vesicle formation high levels of BMP4 expression initiate lens formation. This dependency on BMP4 has been demonstrated in developing mouse eyes. 31 Eventually a lens pit and lens vesicle are formed from lens progenitor cells. Lens progenitor cells proliferate uniformly until signaling from the optic cup polarize the lens vesicle and initiate lens fiber cell differentiation. Interestingly, a similar process occurs when removed or damaged lenses are regenerated from LECs in the capsular bag, as well as in pathological posterior capsule opacification (PCO). This form of PCO is more common and progresses more rapidly in children, likely due to younger cells being more proliferative and behaving similarly to what is seen in embryonic development. 18,31,32 The lens vesicle is formed with a stalk attaching it to the surface ectoderm. After stalk detachment, three main tissue groups begin to differentiate from the lens vesicle including the lens capsule, lens epithelium, and lens fiber cells. The lens capsule is formed by deposition of fibronectin and laminin from posterior lens pit cells. Initially this is an extracellular extension of the lens basement membrane which goes on to develop into the lens capsule fully encircling the lens vesicle. Integrin linked kinase plays a crucial role in the next phase of lens capsule development as well as organization of collagen IV and laminin in the lens capsule. Fibroblast growth factor (FGF) and bone morphogenetic protein (BMP) signaling pathways help to establish lens polarity and engage primary fiber cell differentiation. 31 After the embryonic lens has formed a recognizable lenslike shape, it continues to develop, and the adult cellular arrangement is sorted out. Primary fiber cells begin to accumulate in the interior of the lens while an anterior epithelial layer is formed. From then onward, LECs continue to proliferate throughout life, although at a significantly reduced rate after birth. LECs then form fiber cells and compact the existing layers of fiber cells toward the lens center. As fiber cells grow and extend from the posterior lens toward the anterior lens, a new layer of fiber cells forms between the epithelial cell monolayer on the anterior lens and the previously deposited layer of fiber cells. This process continues as the layered structure of the lens grows and results in a concentrically layered tissue chronologically dated from the nucleus to the capsule. This arrangement results in a similar pattern to the growth rings of a tree although the growth processes are different. 3 Crystallin proteins are produced in the fiber cells after differentiation from LECs. Over time fiber cells lose the majority of their organelles and cellular machinery and the concentration of crystallin protein within the fiber cells increase. At this point, fiber cells can be thought of as elongated sacks of crystallin proteins, but do maintain biologically active elements mostly on their membranes such as fibrous proteins, anchoring proteins, scaffolding, and molecular channels such as aquaporin 0. [33][34][35] Cellular changes render fiber cells essentially inert, but produce a Figure 2. Hypothesized feedback between zonular tension, volumetric lens growth, and LEC proliferation. In the primate lens, zonular tension is frequently relieved during accommodation. This decreases the net load applied to the lens capsule so that LEC proliferation is decreased, resulting in a smaller lens size relative to non-accommodating species. On the other hand, the zonules in non-accommodating species are presumably under consistent passive tension. The ratio of capsule:lens thickness of non-accommodating species is significantly larger than in primates, suggesting a link between lens growth and capsule remodeling; this remains to be experimentally demonstrated. Volumetric growth of the lens by itself can also alter the magnitude and direction of forces experienced by the lens capsule, potentially inducing LEC proliferation; this too remains to be experimentally demonstrated.
clear lens capable of transmitting light to the back of the eye.
Compaction of fiber cells beginning in the embryonic stage and continuing throughout life produces a dense lens nucleus consisting of embryonic fiber cells, which are some of the oldest cells maintained in the body. 18 The complete structure of the final embryonic lens thus consists of the lens nucleus surrounded by the secondary layer of lens fiber cells and the lens capsule with LECs on the anterior, interior of the capsule. 3 Understanding lens developmental biology is essential in order to understand how the geometry and cellular arrangement of the adult lens is reached. Additionally, cellular behavior of lens cells which can lead to pathologies may be linked to unnecessary continuation of developmental processes, or disoriented cellular function arising at advanced age. Understanding young lens development can illuminate areas of concern in aged lens cellular function.

Post-natal Changes in Lens Geometry
Post-natal lens geometry is affected by several factors, including refractive error, 36 accommodation state, 7,37-41 and age. 37,[41][42][43] Throughout life the active lens epithelial cells located on the inside of the anterior lens capsule continue to divide. The majority of cellular division in the lens takes place in the germinative zone of the lens capsule which is located just anterior of the equator. 19,44,45 After proliferating cells in the germinative zone move posterior of the equator into a translational zone and begin to differentiate into fiber cells. As cells in the lens continue to divide throughout life, older fiber cells are compacted but the overall size of the lens also increases. [46][47][48][49] Continual fiber cell deposition leads to a gradually increasing lens diameter over the course of an organism's lifetime. Continual overall lens growth beyond a certain functional threshold may be a major cause of accommodative dysfunction observed in presbyopia. Functional accommodation results in a decrease to lens anterior and posterior radii, the anterior surface becomes more hyperbolic, lens thickness increases, posterior surface moves toward the posterior globe, and refractive index increases. 40 Section 2: Changes in Capsule, Material, and Optical Properties

Change to Capsular Properties and Function
In pre-presbyopic lens capsules the thickest regions are in the mid-peripheral regions of the anterior and posterior capsule. 50,51 It was determined that thickness of the anterior peripheral zone increases throughout life, but the thickness of the posterior peripheral zone only increases in pre-presbyopic eyes. In older age groups, likely beyond the onset of presbyopia, the thickness of the posterior peripheral zone was shown to decrease with age. This growth arrangement would result in lens capsule thickness continually increasing across the anterior surface and posterior peripheral zones in pre-presbyopic eyes, but in post-presbyopic eyes, or eyes from older age groups, a discrepancy between anterior and posterior capsule thickness would continuously increase as the anterior capsule thickened and posterior capsule thinned.
As the lens capsule ages the mechanical strength of the capsule decreases. Examination of amino acid concentration has revealed less collagen associated amino acids relative to the total makeup of the lens capsule with time. A reduction in collagen percentage in the lens capsule could signify a reduction in structural elements. 3 Concurrently, as the lens ages the interior mass of fiber cells in the lens cortex and nucleus have been shown to increase in stiffness. 52 In young eyes the cortex is stiffer than the nucleus. However, in the aging eye, the nucleus stiffens dramatically and becomes stiffer than the cortex near the age of typical clinical presentation with presbyopia. 53,54 The lens capsule is the main ocular entity responsible for transmitting force applied by the ciliary muscle through the zonules to the lens and thus is responsible for, or at least crucial to, molding the optical lens and reshaping it during accommodation. 55 The young adult human lens capsule has an elastic modulus that is approximately 2000 times greater than the lens cortex and nucleus contained within it. 3,53 This larger modulus of elasticity is necessary for the capsule to be able to transmit force to the less resistant lens interior, and mold the lens during accommodation. As the lens ages the mechanical properties of the capsule decreases 3,56 while the shear modulus of the nucleus stiffens dramatically. 53,54,57,58 These changes are thought to be one of the main causes of presbyopia currently since the stiffer lens would require more force to deform but the lens capsule is weakened with aging. 3,52 This theory may accurately portray how changes to the lens capsule and interior lens fiber cell mass could reduce accommodative ability and lead to presbyopia, but there are other significant changes to consider as well, such as changes to lens size, geometry, and optic properties. 59

Remodeling the Lens Capsule
The lens capsule plays a critical role in the development of the ocular lens as well as influencing how lens properties change throughout life. Changes to the lens capsule structure can heavily influence lens behavior, especially with regard to accommodation since the lens capsule is the densest and most stiff structure in the ocular lens. It is also the thickest basement membrane in the body. 3 Electron microscope analysis revealed that the lens capsule is composed of parallel lamellae which are more tightly packed near the outer surface of the lens. The lamellar structure of the lens capsule appears to disappear with age and the capsule becomes more homogeneous. 3 The capsule consists mostly of collagen types I, III, and IV, with collagen IV forming the majority of the basement membrane. Type IV collagen forms a mesh network loosely resembling chicken wire, with crosslinking between the triple helical collagen strands. These cross links are thought to consist largely of 7S domain disulfide cross-link bonds. Collagen IV may also be more flexible than other collagen types like collagen I and II due to having more interruptions between its triple helical segments where crosslinking and molecular binding occurs. Collagen molecules typically interlink through bonding of triple helical domains to form thicker collagen fibrils, and these fibrils can then continue to lace together into thicker rope like fibers or intertwine into a mesh. 3 Interestingly, the composition of specific isoforms of collagen IV does not remain constant throughout an organism's life. Collagen IV can be encoded by six different genes, col4a1-col4a6. Heterotrimers of collagen form from three collagen monomers, and in the lens capsule collagen 4 can be present in three main formations at various stages of development. Collagen IV networks in the embryonic lens consist of only the trimers a1a1a2: a1a1a2 and a1a1a2: a5a5a6. Just after birth a collagen network isoform shift occurs and collagen networks consisting of the trimers a3a4a5: a3a4a5 become more common. The a3a4a5: a3a4a5 network contains a greater number of disulfide cross-links, implying a more stiff behavior. This isoform shift may be due to a change in lens capsule physiologic requirements prior to and after birth. 52 The rapidly growing embryonic lens may need additional flexibility for growth but then could require a shift to a stiffer more highly crosslinked capsule after birth to provide stronger support and a stiffer media through which accommodative forces can shape the lens contents. Prior to birth, ocular accommodation would not be a necessary function, but after an infant begins to utilize their eyes, this shift may be initiated.
Throughout life as the lens continues to grow in size the lens capsule must also grow and more extracellular components of the lens capsule are deposited. The majority of the lens capsule thickens with age due to this process, although the posterior capsule does not change much after birth and weakens with age. 3,60 The lens capsule can be thought of as a collagen network embedded in a matrix forming a soft composite material. Although the collagen basement membrane may have a somewhat organized structure on a molecular level, the overall arrangement of collagen fibers within the larger network in the lens capsule appears to have no organization or patterning. Interestingly, very little is known about the growth of posterior lens capsule after fetal development. The anterior lens capsule is mostly produced and secreted by the anterior epithelial layer, however, there are not metabolically active cells on or near the posterior capsule. Current research suggests that the posterior lens capsule may not continue to grow after birth, and it has been demonstrated that the posterior capsule thickness increases only marginally compared to the anterior capsule. The posterior pole is also the thinnest region of the lens capsule in all age groups. 3 The lens capsule is a very thick (10 mm in the human eye) basement membrane with very low rates of protein turnover. 52 We are not aware of any studies which have elucidated whether or by which mechanism the capsule is remodeled, though certainly any remodeling would necessarily be performed by the LECs. Lens capsule production is thought to occur only in the anterior capsule as LECs secrete capsule proteins in areas of high proliferation. 3,44,61 It is theorized that posterior capsule growth is halted after birth. In other tissues (e.g. blood vessels), cells tend to remodel their extracellular matrix toward some homeostatic biomechanical stress. Since, like the vasculature, the human lens is subjected to tension which varies with time, the LEC remodeling of the capsule may follow a similar mechanism. This tendency would explain the large thicknesses of the capsule of pig and cow lenses (60 mm even in young eyes) as follows. LECs proliferate in response to increased zonular tension in a stretch-and frequency-dependent manner. 62 Approximate conservation of total epithelial cell count implies creation of a lens fiber cell as a result of each LEC proliferation event. 63 Immature fiber cells rapidly expand their volume and surface 64 area while also losing their organelles. 61,[65][66][67][68][69][70][71] Thus, an LEC proliferation event results in an increment in lens volume.

Lenticular Focus of Presbyopia
Imbalance between lens capsule elasticity and interior lens elasticity as well as other material properties certainly does develop with age and is well documented, however, many other studies demonstrate additional factors are involved which could also contribute to reduced accommodative function. It has been demonstrated that lenticular growth alone accounts for 8-10% of age-related reduction to accommodative power. 59 Changes to relative material properties between the lens capsule, fiber cell cortex, and fiber cell nucleus have all been observed and likely influence how these lens tissues interact mechanically. 3,52,53 It has been suggested that physiologic change outside of the lenticular organ itself such as age-related change in the ciliary muscle or insertion of the iris root could contribute to initiating presbyopia as well, 59 while it has also been suggested that presbyopia is in part a result of continual lens development through life. 72 Other studies specifically conclude that presbyopia is lenticular in origin, and seem to favor the theory that change to lens mechanical properties, especially between the lens capsule, cortex, and nucleus, are mainly responsible for agerelated presbyopia. These studies also conclude that more work is needed to elucidate the impact of change to lens geometry and size and specifically focus on a possible role of loss of zonular tension with age. 73 This study does not directly state that loss of zonular tension is due to lens growth, only that more work is needed in examining potential changes in accommodative ability due to loss of zonular tension. Zonular tension loss could result from changes to the zonules themselves, or potentially from changes to the surrounding and attached tissue. Loosening or growth of the ciliary body may be one potential change that could in theory lead to zonular slacking, however, lens growth is a more likely and simpler explanation. It is known that the lens does continue to grow as it ages, and this theory would agree with the lenticular basis for presbyopia. Other studies and reviews have claimed that change to non-lenticular tissues involved in accommodation is minimal, and do not account for observed changes to visual acuity. 14 Researcher in the field seem to agree that presbyopia is lenticular in nature, and changes to tissues outside of the lens likely have minimal impact on accommodative ability. 6,14,73 Again, lens growth and capsule growth or modification occur as the lens ages mainly due to the activity of LECs or LECs which are in the process of transitioning into fiber cells. LECs and emerging fiber cells are relatively young cells in the growth process of a lenticular cell but contribute to nearly all cellular change which produces an altered cellular environment and can lead to presbyopia with age. Lens growth through LEC proliferation and capsule reformation are driving factors in lens property change during the lifetime of an organism.

Impact of Lens Material Properties
While the development, growth, and morphogenesis of the lens may be governed by the epithelium, it comprises a minute fraction of the total lens volume. The remainder consists of the lens capsule, cortical fiber cells, and nuclear fiber cells. Thus, the material properties of the capsule and fiber cells, such as their refractive index and shear modulus, determine the lens' ability to accommodate.
The lens capsule is the stiffest section of the lens, which directs accommodative forces across and through lens substructures, yet, the underlying fiber cell bundles contribute greatly to overall lens properties. 74,75 Fiber cells are metabolically inactive, but throughout life changes to fiber cell chemical and structural properties can heavily influence lens biomechanics and optical properties. Changes to the biomechanical and optical properties of the lens are likely the dominant contributors to presbyopia, although other factors such as tissue permeability and molecular transport are significant. Structural change at a molecular or cellular level underly these observed mechanical and physiologic changes. The focus of this section will be on change to material properties which impact the optical and biomechanical functions of the lens in the context of presbyopia.

Lens Inhomogeneity Impacts Vision and Research
Restoration of dynamic accommodation by refilling the capsular bag with hydrogels mimicking the young lens properties has been attempted for nearly 60 years, but only with homogeneous material systems. [76][77][78][79][80][81][82][83][84][85] This homogeneity in composition implies homogeneity in material properties as well. The young lens is a wonder of materials engineering: it combines opposing gradients in refractive index and shear modulus. Its refractive index is highest centrally, 16,[86][87][88][89][90][91][92] whereas the shear modulus is very low in the central lens. 53,54,58 These gradients may be essential to accommodation but change significantly with age. 15,74,86,[93][94][95] On the other hand, the shear modulus at the lens center increases by orders of magnitude with age while it remains nearly constant in the cortex. 53,54,57,58 Data directly measuring the shape of this gradient are sparse but suggest that it does not share the broad central plateau observed in the refractive index, instead tending toward a decay from the center to the surface of the lens. 54,57,96 This suggests that different mechanisms govern the optical and mechanical properties of the lens. Measurement of the biomechanical properties of the isolated cytoplasm from the young lens, which is essentially a concentrated crystallin solution, indicate that it behaves as a viscoelastic, shear thinning liquid rather than an elastic solid. 20 Membrane associated proteins account for only around 2% of lens proteins, 97 though their absence can result in altered biomechanical properties in the mouse lens. [98][99][100][101][102] In the lens of middle-aged persons, the oldest fiber cells are the stiffest, suggesting a potential role for age-related modification of proteins. Determination of the cellular and/or molecular mechanisms driving lens stiffening is essential to understanding the evolution of lens biomechanics with age; however, no studies have yet revealed such a mechanism.
Diligent research from biology focused labs, experienced groups working in computational modeling of the lens and eye, functional and structurally minded engineers, clinically oriented physicians, and molecularly concentrated chemists have erected the foundational infrastructure essential for developing an encompassing understanding of presbyopia and the impact of age in the human lens. Still, the driving force of the pathology has not been fully elucidated and science is yet to discover preventative therapies or simple noninvasive treatments which restore or prevent the loss of accommodative function. Synthesis of research in varying but related fields will be necessary to further alleviate the burden of presbyopia. Luckily, direct pathways of pathology progression and lens stiffening have been illuminated such as fiber cell compaction, soluble protein aggregation, soluble protein precipitation, and cytoskeletal remodeling.

Mechanical and Optical Gradients
Protein structure is not the only property which changes through the lens along a radial gradient. Fiber cells closer to the interior have a greater concentration of proteins due to a reduction in water content. More insoluble protein accumulates here while soluble protein and water both associate more with the cortex or exterior lens. 20,33,103,104 The refractive index of the central lens remains approximately constant, but the diameter of this "central plateau" region increases steadily with age, corresponding roughly with the maximally compacted nuclear fiber cells. 46 These compacted fiber cells are relatively dehydrated, implying an increase in the concentration of crystallin proteins and, therefore, the refractive index. 70,91,[105][106][107][108][109][110] The mechanism by which this gradient is maintained involves an osmotic pressure gradient, [110][111][112] which biomechanically necessitates a corresponding hydrostatic pressure gradient. 113 Aquaporins and connexins are required for maintenance of this functional gradient 114,115 and may necessitate the microcirculation of ions and water. [116][117][118][119][120] A non-continuous refractive index also manifests in the lens along this gradient. The gradient refractive index (GRIN) of the lens is thought to result in a minimal refractive power at the lens periphery and maximum refractive index in the center of the lens. Changes to the lens geometry and position during accommodation can result in modification to the GRIN. Cellular a-crystallin concentration influences refractive index on this gradient. 40,104 Fiber cell compaction and lens water content plays a key role in maintaining the ocular GRIN. 46,86,92 Age-related modification to lens proteins, fiber cell networks, and tissue structures within the lens cortex and nucleus almost certainly lead to additional modifications to the GRIN as well as lens mechanical properties.
Previous studies have demonstrated a shear thinning viscoelastic behavior of crystallins in the lens substance. Shear thinning behavior allows for accommodation associated geometric change from relatively weak forces applied through the zonules from the ciliary muscle. In a young healthy lens, the nucleus deforms more than the cortex during accommodation. 39,121 It has been noted that in young lenses the central regions are less stiff than peripheral regions, and in aged post-presbyopic lenses the nuclear material becomes stiffer than more cortical tissue. This exchange occurs as central lens tissues stiffen faster than peripheral tissues, although both tissues stiffen with age. 53,54 It is thought that age associated change to crystallin and connective proteins in the lens may interact with cytoskeletal elements or cell-to-cell binding cites. Agglomeration between degraded proteins within fiber cells, or on the membranes of fiber cells could serve to stiffen individual fiber cells as well as the overall lens tissue. Protein precipitation in a fiber cell can stiffen the cell itself. This would be inconsequential as long as cells were capable of sliding past each other, but if this process is paired with cell-to-cell binding, overall lens stiffening could occur.

Altered Structure, Altered Function
Alterations to fiber cell content and intercellular fiber cell binding are likely key contributors to age-related stiffening of the lens cortex and nucleus. Many previous studies have demonstrated some alteration to molecular structure and organization within fiber cells and linked these changes to age associated lens remodeling. Previous works demonstrate cytoskeletal protein binding, 39,40,96,99 crystallin protein degradation and localization, 82-84 modification to lens water content in older fiber cells, 85,87,91 active and intermixed cell junctions, 92,95,99 and nuclear mechanical stiffening with age. 29,32,73 Increased gamma crystallin content in the lens nucleus may contribute to nuclear stiffening in older eyes when compared to the softer cortex. 85 Existing studies have suggested that the lens behaves as a crosslinked gel rather than a collection of fibers. 95,96 Researchers have predicted that in young lenses cytoskeletal elements provide necessary support, but crosslinking could occur with age resulting in a stiffer lens. Cytoskeletal elements even form "paddleprotrusions" at tricellular junctions enhancing cell-to-cell cohesion. 100,101 Additionally, it has been shown that nuclear fiber cells contain only membrane bound cytoskeletal elements. 102 Without internal cytoskeletal elements nuclear fiber cells may be expected to be rather compliant, which contradicts observed nuclear stiffening with age. 32,34,73,75 This may suggest a link between binding of membrane bound proteins with complimentary cytoplasmic protein aggregation.

Crystallin Proteins: Concentration, Organization, and Degradation
Of all cells in the body lens fiber cells have the highest concentration of protein intracellularly. High protein densities allow the fiber cells to create a refractive index in the lens greater than that of water. The refractive index of the lenses in mammals is 1.41 compared to that of water which is 1.3333. 72 This difference is necessary since the lens is surrounded by the aqueous and vitreous humor, and the difference between refractive indexes of adjacent tissues grants the lens its refractive power. In fish, the lens is the main focusing member of the eye since the cornea is in contact with water instead of air. This results in fish lenses expressing even greater refractive indices of 1.65. 72 Such refractive power is made possible by the development of fiber cells in the lens, loss of organelles in the fiber cells, and finally the arrangement of a high concentration of crystallin proteins within the lens fiber cell.
One study linked an increase in a specific lens protein, aA-crystallin, with increased fiber cell cytoplasmic refractive index, but also noted that an increase in the associated protein concentration made the lens susceptible to protein change with age. aA-crystallin protein is a common lens crystallin, and specifically an increase in aspartic acid found in the aA-crystallin protein yielded these results. 103 It appears that since such a strong refractive index must be achieved to allow for lens function, the highly concentrated but necessary protein structures which achieve this refractive index may set the lens up for chemical instability with extended age. Consideration of how change to lens proteins may influence lens function through various routes of influence is essential since the fiber cells of the lens contain such great concentrations of protein, these proteins are known to significantly impact lens mechanical properties, refractive index, and optical properties.
The outstanding clarity of a healthy ocular lens arises both from crystallin protein concentration and crystallin protein organization within the fiber cells and aggregate lens tissue. Alpha, beta, and gamma crystallin proteins are three of the most common lens crystallin proteins and can be found in the eyes of all vertebrate species. These species are non-homogenously distributed throughout the lens and each have additional subfractions. The alpha and beta crystallins mostly consist of oligomers while the gamma proteins are mostly monomeric. Many species have additional crystallin proteins that serve unique needs in vision or have additional biological function in the lens. 20,97,103,108 Specific crystallin proteins are concentrated in different areas of the lens and significant change to protein expression can be measured between the nuclear and cortical fiber cells when sampling along the radial axis of a lens. Crystallin proteins in the lens are known to break down and can form truncation products after exposure to thermal stress or as a function of age. Additionally, some proteins are only found in cortical fiber cells, suggesting that these proteins may completely degrade with age. 33 Intact a-crystallin appears to be more common toward the exterior of the lens and in the cortex. Differing isoforms and degradation products associated with a-crystallin are more prevalent toward the center of the lens. 103,104 The apparent gradient of intact to degraded crystallin protein from the exterior to interior of the lens may be explained by the concentric lens growth pattern as LECs differentiate into fiber cells which stack on existing layers compacting their substrate. Aged proteins thus accumulate toward the lens nucleus as fresh protein is deposited in new cortical fiber cell layers. 122 This is not the only potential factor which could lead to a protein degradation gradient through the lens, nor is this phenomenon exclusive to a-crystallin. Numerous factors could alter protein stability in the lens at varying depths. Exposure to reactive oxygen species which can cause protein crosslinking 1 may be more likely in cortical cells. Diffusion may be altered spatially within the lens. Microcirculation, which can import beneficial chemicals such as antioxidants and glutathione 123 may be reduced in the lens interior. Cells may be subject to greater strain applied by the capsule during accommodation at different lenticular locations.

Cytoskeletal Elements and Interactions
During fiber cell compaction and water loss fiber cell protein concentration increases. This process occurs over time and results can be seen in more nuclear lens cells. 46,124 At higher concentrations lens proteins are more likely to interact and could bind together more frequently. Additionally, degraded protein products and insoluble protein fractions, which are more prevalent in nuclear portions of the lens, are known to associate with cytoskeletal elements of fiber cells. Truncated crystallin protein elements, small peptides associated with beta and gamma crystallin fragments, and insoluble protein fractions all interact tightly with fiber cell cytoskeletal elements, intermediate filament proteins, and membrane associated proteins. 33 Membrane associated processes of fiber cells, such as organized control of sodium ion flow in and out of the cell, create microcirculation gradients within the lens. These gradients can be utilized to control water content in the fiber cell, cell volume, protein concentration, and thus other properties like GRIN. Oncotic pressure between concentric fiber cell layers is also generated by control of cellular colloidal contents which is determined by the cytoplasmic makeup of each fiber cell. This oncotic pressure influences cellular water content as a result of cellular protein content. In this case, the concentration of protein leads to water loss, not the other way around. 124 Beaded filament proteins are a significant component of the lens fiber cell cytoskeleton. Phakinin and filensin are two major intermediate filaments in the lens. Originally identified as cytoskeletal protein 49 (CP49) and cytoskeletal protein 95 (CP95), CP49 and CP95 are now known to be the same beaded filament found specifically in fiber cells. The protein CP49 and CP95 was renamed filensin. 124,125 Components of filensin and a-crystallin proteins have been observed binding together. This interaction may be part of a pathway by which lens proteins become insoluble with age, bind membrane proteins and potentially fiber cells together, prevent gelling between intermediate filament networks, or alternatively increase overall lens stiffness through fiber cell to fiber cell connections. 33,124,125 The interaction between lens crystallin proteins, beaded filament proteins, cytoskeletal elements, protein connexins, ion channels, and other molecular components of fiber cells is complex. Multiple pathways link these proteins to physiologically significant mechanical, chemical, and optical functions. Examination of filensin knock out mice has revealed that lenses without filensin intermediate filaments are more elastic than wild type lenses and smaller than wild type. This finding suggests that higher proportions of strain energy are lost in the less elastic wild type lenses. This could potentially be lost as heat, which might contribute to crystallin protein breakdown through cyclic exposure to accommodative forces as it was also demonstrated that thermal stress can result in crystallin breakdown over time. 33,126,127 Other studies confirm that biomechanical properties and fiber cell arrangement are maintained by filensin and anchoring membrane proteins which colocalize with aquaporin 0. Aquaporin assists with microcirculation in the lens and water balance as a membrane water channel. Ankyrin-B, a membrane connective protein maintains the organized hexagonal structure of fiber cell bundles. Lenses without ankyrin-B exhibit significantly decreased elastic moduli as well. It is thought that the cytoskeletal element periaxin maintains fiber cell organization which allows for lens clarity. Periaxin and ankyrin-B together maintain tensile strength between fiber cells in the lens. 34,35,98,125,128 Furthermore, studies have shown that some connexin proteins found in the lens are mechanosensitive. These results show another way in which accommodative biomechanical force can alter lens cellular behavior and lens chemistry. 129,130 It is overwhelmingly apparent that multiple proteins expressed in the ocular lens are essential to proper lens function, overlap in complex webs, and that age associated degradation has great potential to interfere with the balance of these systems.
Just as LEC proliferation drives initial lens growth, biomolecular function maintains mechanical properties within the lens fiber cell mass. Alterations to the functional proteins of the fiber cells accumulate with age and result in material property changes and modifications of fiber cell functions which are essential for preserving the physiologic faculty of a healthy lens.

Section 5: Potential Therapeutic Treatments for Presbyopia
Pharmacological approaches for treating the symptom of presbyopia (i.e. lack of near focusing ability) using eye drops have made a recent resurgence. Since the biophysical mechanism governing this massive stiffening at the center of the lens remains unknown, but clearly plays a key role in the age-related loss of accommodation, most pharmacologic approaches for managing presbyopia rely on miosis rather than accommodation and have been recently reviewed. 1 Attempting to manage presbyopia via miosis is a centuriesold approach 131 and has several significant pitfalls. 132 Thus, there exists a clear need for improved therapeutic approaches targeting the underlying cause of presbyopia to restore dynamic accommodation. 133 Disulfide bonds have therefore been targeted by the only pharmacologic approach to improving near vision by altering lens biomechanical properties. 134,135 Lens crystallin protein oxidation leading to intramolecular disulfide formation from thiols is one proposed biomolecular mechanism of age-related stiffening. 136 However, while intermolecular disulfides could lead to altered lens elasticity, intramolecular crosslinks cannot directly cause increased elastic stiffness since they do not result in the transmission of elastic stresses between neighboring molecules. 137,138 Thus, reducing intramolecular disulfides is unlikely to restore accommodation since it does not address the biophysical mechanism of lens stiffening. For example, if elasticity is decreased due to hydrophobic bonding of lens crystallins after intramolecular disulfide formation, reducing these disulfides is unlikely to restore youthful elasticity. On the other hand, intermolecular disulfide bonds have been found to contribute to cataract and could directly alter elasticity, though this has not been demonstrated in pre-cataractous lenses. Thus, there is a clear need to determine the biophysical mechanism driving lens stiffening within the age range relevant to the development of presbyopia.
To date, the experimental evidence for this lens stiffening mechanism is found in two studies using mouse lenses. First, Garner and Garner 134 compressed mouse, presumably with the capsule intact (though this is not stated in the article). Lenses from 8-month-old mice were cultured for 12 hours with a lipoid acid choline ester (LACE), resulting in LACE dose-dependent increase in equatorial diameter upon loading with a single cover slip. Then, lenses from an in vivo LACE treatment protocol were compressed using a computer-controlled system incremented displacement while recording the applied load. Many key details of this experiment were omitted, so rigorous biomechanical interpretation is impossible; however, the study reported decreased stiffness in LACE-treated lenses.

Conclusions
The molecular and cellular contributions to presbyopia remain unknown and the use of pharmacological approaches to altering lens stiffness are speculative. Still, such approaches may prove fruitful and will certainly be useful in investigating the molecular mechanism of lens nuclear stiffening. Considerable biophysical investigation of these mechanisms will be needed to inform development of pharmacologic interventions aiming to alter lens stiffness.
An alternative approach which has not been investigated would attempt to modulate the mechanotransduction pathways involved in lens growth. We have shown that YAP signaling is involved in this process, 62 though it is involved in many other signaling pathways in the eye and lens so it is probably unsuitable as a target for modulating lens growth. [139][140][141][142][143] Additional research into the mechanotransduction pathways involved in lens growth therefore warrant further investigation.
The lens research community has identified many key components which are influential in the aging process of the ocular lens and development of presbyopia. Although much has been discovered in the relatively short period in which lens biomechanics have been brought to light, much remains to be uncovered, paths are left to be followed, threads untwisted, and information synthesized. Careful incorporation of research across a wide range of fields impacting ocular health will be a requisite step forward. Ongoing research shows promise for novel discovery. Careful analysis and quantification of mechanical properties and viscoelastic properties of ocular tissue would be incredibly beneficial, especially in improving the accuracy of computation models. Further insight into the roles of reactive oxygen species, growth factors, enzymes, and other bioactive molecules and their influence on lens growth throughout life is necessary to improve clinical treatments and perpetuate ocular health in an aging population. Finally, determining the precise biophysical mechanisms which govern lens stiffening and presbyopia will be a necessary advancement toward creating effective preventative care.

Disclosure statement
No potential conflict of interest was reported by the author(s).