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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Invest Dermatol. Author manuscript; available in PMC 2009 July 2.
Published in final edited form as:
PMCID: PMC2705329

Complex hair cycle domain patterns and regenerative hair waves in living rodents


Single hair follicles go through regeneration and involution cycles. In a population, hair follicles may affect each other during anagen re-entry, thus forming propagating regenerative hair waves. We review these regenerative hair waves and complex hair cycle domains which were recently reported in transgenic mice. Two non-invasive methods to track the propagating hair wave in large populations of hair follicles in vivo are described. We also reviewed early accounts of "hair growth patterns" from classical literature. We decipher the "behavior rules" that dictate how dynamic hair waves lead to complex hair cycle domains. In general, a single domain expands when a regenerative hair wave reaches a responsive region and boundaries form when the wave reaches a non-responsive region. As mice age, multiple hair cycle domains form, each with own regeneration rhythm. Domain patterns can be reset by physiological events such as pregnancy and lactation. Longitudinal sections across domains show arrays of follicles in a continuum of hair cycle stages. Hair cycle domains are different from regional specificity domains. Regenerative hair waves are different from the developmental wave of newly forming hair follicles. The study provides novel insights into the dynamic states of adult skin and physiological regulation of organ regeneration.

Keywords: pattern formation, skin appendages, regeneration, stem cells, hair cycle

Understanding the regulation of organ regeneration is of fundamental importance in the age of stem cell biology and regenerative medicine. Hair follicles make a great model for this objective because they molt and regenerate repetitively in the adult as part of their physiological process.

When we study the regenerative behavior of an organ, most of the time, we focus on the single organ such as the cycling of a single hair follicle. However, there are thousands hair follicles on the mouse skin, giving another dimension of organ regenerative behavior, one based on population. We became interested in this process when we observed the complex and dynamic hair cycle domains in C.Cg-Msx2tm1Rilm/Mmcd mice (Ma et al., 2003). The propagation of a regenerative hair wave in BomTac:NMRI-Foxn1nu, B6.Cg/NTac-Foxn1nu NE9 and B6129-Foxn1tw mice was also observed (Militzer et al., 2002; Suzuki et al, 2003). We also found that this phenomenon and its relationship with systemic hormone levels have been reported in classical literature in mid-twentieth century. We have learned that it is hair wave dynamics that lead to the formation of complex hair cycle domains. Here we review classical literature and more recent works, extend the study to document the process, and present a simple method that would allow investigators to examine the hair growth pattern on living mice. The study provides novel insights into the dynamic states of adult skins and physiological regulation of organ regeneration.

Hair growth in a population of hair follicles

A single hair follicle undergoes successive growth cycles. The four major stages of the hair growth cycle are: anagen (the period of active growth), catagen (the period of cessation of the growth and regression), telogen (the period of relative inactivity) and exogen (the event of the old hair fiber shedding; Dry E, 1926; Chase HB et al., 1951; Sundberg JP, 1994; Fuchs et al., 2001; Stenn and Paus, 2001; Milner Y et al., 2002). Morphological changes and cellular events associated with the hair growth cycle have been well documented. Signaling pathways operating at different stages of the cycle are the subject of extensive studies. Multiple signaling pathways have been implicated in the regulation of follicular stem cells dynamics, growth activities and the transition between cycle phases including BMPs, WNTs, SHH, FGFs, Neurotrophins, TGFbs, HGF, Interferon gamma, retinoids (reviewed in Fuchs E, 2007; Cotsarelis G, 2006; Plikus et al., 2006).

In a population of hair follicles, hair growth cycles can be mosaic, when neighboring hair follicles proceed through their own cycle stages autonomously. This is observed in vibrissae follicles (Greaves et al., 2004) and pelage hair follicles in the guinea pig (Chase, 1954). At the same time, extraneous stimuli can influence the dynamics of hair cycle progression across the entire animal’s skin, synchronizing anagen entry. The effect of systemic stimuli on the hair growth cycle was recognized. For example, estrogens have profound systemic influence on the hair growth cycle. In many animals, mice included, estrogens such as 17β-estradiol inhibit anagen initiation (Fraser and Nay, 1953). This effect of 17β-estradiol is mediated via estrogen receptors expressed in hair follicles (Ohnemus U et al., 2005). Rapid and profound anagen induction in female mice can be achieved by gonadectomy (Chanda S et al., 2000). Application of extraneous 17β-estradiol extends telogen. Prolactin is another potent systemic modulator of the hair growth (Pearson AJ et al., 1996; Pearson AJ et al., 1999; Nixon AJ et al., 2002; Craven et al., 2006). Commonly, in animals with seasonal hair growth an increase in pituitary prolactin during spring induces new anagen (Dicks P, 1994). Prolactin has also been observed to be produced locally and function in regulating the hair cycle in a non-systemic way (Foitzik K et al., 2003; Craven J et al., 2001).

Although systemic endocrine factors regulating synchronized hair growth have been elucidated, the mechanism of localized hair cycle coordination within neighboring hair follicles is not yet understood. At the same time, a wealth of morphological evidence shows the existence of such localized coordination of hair cycling. Classic literature contains many experimental accounts of what appears to be patterns or waves of hair growth in mouse, rat, hamster, chinchilla and rabbit (Figure 1; Durward and Rundall, 1949; Mottram, 1945; Chase and Eaton, 1959; Whiteley and Ghadially, 1954; Whiteley, 1958). Such waves were defined as “orderly progression in time and space of follicles entering the growth phase, that is, anagen, of their cycles” (Chase and Eaton, 1959). Early observations showed that hair follicles on the trunk of rats cycle in the form of successive waves, spreading from the ventral side of the body to the dorsal over the trunk. This spreading can be visualized as zones of skin, variable in width, with hair follicles in the anagen growth phase (Durward and Rundall, 1949; Mottram, 1945). The width of these zones was shown to decrease with the age (Durward and Rundall, 1949; Butcher, 1936). It was also mentioned that in the head region and around the limbs the pattern of hair growth is more complicated (Durward and Rundall, 1949). Others point out that initial wave-like hair cycle patterns breakdown into “islands of growth, especially on the dorsum” (Chase and Eaton, 1959).

Figure 1
Evidence of hair cycle domain patterns in rodents from classic literature

Observing hair waves on living mice

Despite the presence of well documented accounts of patterned cycling behavior in classic literature, little attention is given to this phenomenon in most of the current studies on the hair cycle. As a standard, hair follicles from the dorsal skin from postnatal days 1 to day 12 are typically used to represent anagen, from day 17 to represent catagen, and from day 21 to represent telogen (Paus, 1998; Ma L et al., 2003). Generally this is correct because hair follicles on dorsal skin during the first month cycle in a nearly synchronized manner. However, dorsal skin in mature and aging mice soon develops more complicated patterns. It would be critical to account for these changing hair cycle patterns while designing experiments related to hair regeneration and cycling, especially because these patterns can also be modulated by physiological events, such as pregnancy (Johnson, 1958b). Classic studies on patterned cycling behavior are controversial and limited to an ambiguous description of the patterning process. Thus, it is important to clearly establish the presence and dynamics of hair cycle patterns in normal rodents as a baseline. Moreover, comparative studies of the altered patterns of hair cycle domains in mutant mice versus control mice may provide new insights into hair cycle control mechanisms. Analysis of these phenomena will help us understand the requirements for hair follicle regeneration in adults. Furthermore, the continuous distribution of hair follicles at different hair cycle stages can be analyzed in longitudinal sections of a single skin strip to facilitate more precise molecular profiling of hair cycle stages. Finally, it will also encourage the development of new models to explain complex hair pattern formation in living mammals.

To identify hair cycle stages of follicles in the living mouse, we need to have non-invasive assays that can reveal recognizable traits of these specific stages. Currently, several methods are available for research of this nature. The first method is based on pigmentation; this method was utilized in most of the classic studies. In pigmented mice, such as inbred C57BL/6J mice, melanin production is restricted to the hair follicles and not to inter-follicular skin. Melanogenesis starts at anagen IIIa, becomes prominent in anagen IIIb, and continues until catagen (so-called: anagen-coupled melanogenesis; Muller-Rover et al., 2001; Figure 2a, 2b). Therefore, hair follicles during most of anagen appear grey or black, while hair follicles in telogen have no pigment and the skin becomes pink. When the mouse is covered by hairs (both anagen and telogen club hairs) the pigment difference among hair follicles is concealed. When hairs adjacent the skin surface are clipped differences in pigmentation of the proximal hair follicles become apparent (Slominski and Paus, 1993). Patchy regions (domains) of black and pink are revealed, corresponding to areas of hair growth and quiescence. These domains are seen on both the dorsal and ventral sides of the body (Figure 3, Figure 4a, Figure 4b). They appear because pelage hair follicle populations in the mouse do not cycle independently, but rather show coordinated hair cycle stages within the same domain and discordant stages among adjacent domains. Interestingly, these domains develop into complex patterns from cycle to cycle as age progresses.

Figure 2
Schematic illustration showing two non-invasive methods used to visualize propagating regenerative wave and hair cycle domains in living animals
Figure 3
Propagation hair regenerative wave in the ventral skin
Figure 4
Complex patterns of hair cycle domains

Although less distinctive than the method described above, hair clipping can be used to reveal hair cycle patterns in non-pigmented strains of mice, such as albino Crl:CD1(ICR) mice. This reveals white (anagen) patches on otherwise pink (telogen) skin (Figure 4d). Additionally, hair cycling can be monitored by observing regrowth of white hairs in albino animals after artificial coloring of the coat (Whiteley and Ghadially, 1954), or by the appearance of new orange-pigmented hairs upon intra-peritoneal administration of flavin 9-phenyl-5:6-benzoisoalloxazine dissolved in oil (Figure 1a; Haddow et al., 1945). In mice with an agouti coat, such as C3H/HeJ mice, hair clipping allows distinction not only between anagen and telogen, but also between early and late anagen stages. This is possible do to the fact that in agouti mice hair follicles switch from pheomelanin to eumelanin production during anagen (Bultman et al., 1992). Because the switch between alternative pigments occurs at the same anagen stage in all hair follicles, a black band of anagen hairs enables visualization and monitoring of the timing of the anagen spreading wave (Figure 4e). It is also possible to monitor speed of the anagen spreading wave by artificially ablating melanogenesis in pigmented mice with 8-hydroxyquinoline and measuring width of bands of white hairs (Fig. 1c). Upon application, 8-hydroxyquinoline inhibits melanogenesis (via unknown mechanism) only in the very early anagen hair follicles and for the rest of their hair cycle (Searle, 1972). Late anagen hair follicles are not affected. By modulating frequency of 8-hydroxyquinoline treatment one can lengthen or shorten a time window during which melanogenesis is ablated at the front of the continuously spreading anagen wave.

The second method is based on the recently documented "cyclic alopecia" phenotype described in Ma et al., 2003. This phenotype is characterized by multiple hair growth domains giving the skin an appearance of patterned patchiness. Basic requirements for the “cyclic alopecia” phenotype are: 1) that hair follicles continuously undergo regenerative cycling and 2) that hair shafts dislodge from the follicle at a particular stage of the hair cycle, making affected skin regions alopecic until hair follicles regenerate during the next anagen (Figure 2a, 2c). During recent years, increasing numbers of transgenic mice displaying “cyclic alopecia” phenotype have been reported. Thus far the "cyclic alopecia" phenotype has been documented in C.Cg-Msx2tm1Rilm/Mmcd mice with defective club hair formation (Ma L et al., 2003; Plikus and Chuong, 2004), in B6;129X1-Dsg3tm1Stan/J mice with defective desmosomal attachment of telogen hair to the outer root sheath (Koch PJ et al., 1998), in BomTac:NMRI-Foxn1nu, B6.Cg/NTac-Foxn1nu NE9 and B6129-Foxn1tw with the defect in Foxn1 gene (Militzer K, 2001; Suzuki et al., 2003), in transgenic mice over-expressing gain-of-function allele of Notch1 under the involucrin promoter (B6C3-Tg(IVL- Notch1)IC; Uyttendaele H et al., 2004), in B6-Dsc1tm1Dga (Chidgey M et al., 2001) and in Ppp3r1tm1Grc/ Ppp3r1tm1Grc; +/KRT5-cre mice (Mammucari C et al., 2005).

Analysis of hair cycle patterns can be made more informative by overlapping an anagen hair pigmentation pattern with a static hair distribution pattern. Because each pelage hair follicle is associated with a sebaceous gland (forming what is know as pilo-sebaceous unit), its position on the skin surface can be marked by Oil red fat staining. According to this method, staining of skin is performed prior to its removal from a sacrificed mouse; this is done to prevent background staining of subcutaneous fat. The shaved skin of the sacrificed mouse is then soaked with propylene glycol, followed by incubation with standard Oil red dye. Upon completion of the staining (after 30–40 min.) and washing, the position of individual pilo-sebaceous units is clearly visualized as bright red dots on a pale pink skin. Skin can be then removed and inverted, which allows more precise and informative evaluation of anagen spreading wave dynamics over the static hair pattern (Figure 6a).

Figure 6
Cellular basis of a hair cycle domain

Deciphering principles of hair follicle population behavior

Hair cycle patterns differ at varying stages of an animals’ life. Generally, patterns increase in complexity with age. It is important to know the degree of pattern complexity in mice of different ages to select animals of the appropriate hair cycle stage best suited for the experimental intent. Chase and Eaton (1959) describe the following stages of hair cycle pattern progression in mice based on their analysis of 230 mice for at least the first five hair cycles:

  1. The first hair cycle “occurs as the follicles develop from the epidermis and the order of development is from the dorsum toward the venter (abdomen) and extremities. This is scarcely to be considered a wave”.
  2. The first postnatal hair cycle “proceeds generally as a wave from the venter dorsally and posteriorly”.
  3. The second postnatal hair cycle “proceeds generally from the anterior venter posteriorly, then from the posterior venter anteriorly and dorsally, and then anteriorly on the dorsum after the two posterior lateral portions coalesce”.
  4. The third postnatal hair cycle “essentially duplicates previous on the venter, but on the dorsum there is a new center of activity on the saddle that proceeds posteriorly”. From the second postnatal hair cycle “on, the dorsal spread from the venter stops at the lateral line, except usually in the posterior region”.
  5. By the forth postnatal hair cycle “the waves are weak in males and, instead of waves, there are islands of growth, especially on the dorsum. In females this breakdown of waves generally occurs by fifth postnatal hair cycle”.

Chase and Eaton (1959) further conclude that although the above described pattern of progression is the most common, there are many strain and gender related deviations from the patterning process. Patterns can be “more asymmetrical in some individuals than others. Around the head and legs there are even more extensive individual variations”.

To validate and enrich these classic observations further, we followed the temporal changes of hair cycle patterns in C57BL/6J mice with clipped hairs (n >10). Mice were observed every 48 hours. For comparison, we have also followed the changes of the hair patches in mutant C.Cg-Msx2tm1Rilm/Mmcd mice with cyclic alopecia by observing the same mouse every 24 or 48 hours for a period ranging from 3 to 12 months (n>10). C.Cg-Msx2tm1Rilm/Mmcd mice showed domain pattern changes parallel with those of C57BL/6J mice, although the 'rhythm' of the changes in mutant mice was faster. In general, hair cycle domain patterns undergo an age-dependent progression toward increasing complexity (i.e. hair follicles cycle in smaller and non-synchronized groups). Our long-term study helped us to enrich previously described pattern progression (Chase and Eaton, 1959):

  1. Synchronous growth all over the body. During the first hair cycle, hair follicles in the dorsal skin appear to cycle synchronously. As a convention, hair follicles in the dorsal skin from postnatal day 1 to approximately day 12 are used to represent anagen and then they gradually enter telogen after day 12. At approximately postnatal day 25, they start to enter the first true postnatal anagen lasting until around day 40. Dorsal skin from these ages is typically used in hair cycle related research of transgenic mice (Paus, 1998; Oro and Higgins, 2003).
  2. Formation of a hair cycle spreading waves (Figure 5b, day 0). In agreement with Chase and Eaton (1959) hair follicles start to form gradient anagen spreading waves.
    Figure 5
    Some basic rules beneath the complexity of dynamic hair cycle domain patterns
  3. Formation of horizontal sectors due to the interruption of the hair cycle spreading wave At this stage (variable number of cycles, > 3) the dorsal skin forms 2 to 4 segment-like discrete domains.
  4. Formation of synchronous lateral domains (Figure 5b, days 30 and 54, Figure 5c). As more hair cycles pass (variable number of cycles, > 4), different horizontal segments start to split into one central and two lateral domains that cycle independently. Interestingly, the two lateral domains usually mirror each other in shape and cycling phases, resulting in a bilaterally symmetric appearance. The central domain is positioned along the midline and cycles independently from its lateral counterparts. Occasionally, it can be in phase with the two lateral domains of the segment anterior or posterior to it, thus forming a V shaped or inverted V shaped zone.
  5. Formation of asynchronous lateral domains (Figure 3b, day 93; Figure 5b, day 115). As the mouse ages, initially synchronous lateral domains within the same segment can become asynchronous.
  6. Further asynchrony of hair cycle domains. Furthermore, each of the lateral domains may further break into two daughter domains. Thus, the hair cycle asynchrony becomes even greater, and the initial symmetry of the lateral domains can get lost.
  7. Hair cycle domains can be altered by systemic physiological conditions such as pregnancy, and local conditions such as skin trauma. For example, pregnancy and prolonged lactation in adult female mice can reset complex hair cycle domain patterns (Johnson, 1958a; Johnson, 1958b). This phenomenon may arise due to the effect of estrogen and / or prolactin levels that are elevated during these physiological states. Both of these hormones are implicated in direct inhibition of anagen induction of anagen initiation in telogen hair follicles (Oh and Smart, 1996; Pearson et al., 1999; Craven et al., 2001; Foitzik et al., 2003; Craven et al., 2006). Resetting occurs following the prolonged telogen associated with pregnancy and lactation (most prominent after repetitive pregnancies). In the post-lactation period there is simultaneous anagen re-entry of most of the hair follicles across the skin regardless of the pre-pregnancy patterning. As a result, most of the hair follicles become synchronized, reminiscent to the status in the first postnatal cycle. Subsequently, new complex hair cycle domain patterns can re-form, unless new pregnancies occur. These data suggest that hair follicles in a hair cycle domain are not permanently 'changed' in their structures or fixed in their 'memory'. Under certain conditions, they can be reset by responding to appropriate signals or can switch between different domains.
    Skin trauma can induce new anagen in telogen hair follicles surrounding the wound (Argyris, 1956). Recently it has been shown that trauma-induced anagen is caused by Map3k5-dependent infiltration and activation of macrophages in the peri-wound area (Osaka et al., 2007). Such trauma-caused centers of new hair growth can propagate anagen induction throughout the adjacent non-wounded skin changing hair cycle domains patterns. Thus, it is important to differentiate trauma-caused and spontaneous anagen induction centers. Hair growth stimulation by wounding can occur after variable intervals and all the way up to 28 days (Argyris and Argyris, 1962), when initial wounding, especially if small, might not be very noticeable. Skin trauma in mice can originate from scratching and fighting. Thus, for long term pattern monitoring experiments it is advisable to keep each mouse separately.
  8. Rate of hair wave propagation can vary While hair follicles from different mice exhibit similar hair cycle domain patterns, the rates (or rhythms) of hair cycles can be different due to the different lengths of anagen and telogen stages in transgenic mice. For example, hair cycle domain patterns in C.Cg-Msx2tm1Rilm/Mmcd mice show similar spatial distributions parallel to that of C57BL/6J mice, but the domains cycle with a faster rhythm (i.e. the total time to complete one full hair cycle is shorter). As a result, C.Cg-Msx2tm1Rilm/Mmcd mice develop complex hair cycle domain patterns at a younger age.

Topographic map of hair cycle domains

As a result nearly all domains cycle at their own pace, introducing a great degree of complexity and creating an appearance of randomly distributed hair patches which become what we call “hair cycle domain patterns”. While the above represents the general trend in more than 25 mice we have observed, it should be noted that variations of this progression are also common. To help describe these patterns, we propose a topographic sector map. We have assigned two longitudinal borders that split the dorsal skin into three large longitudinal sectors. Three horizontal borders were assigned to further divide them into a total of 12 sectors. Similar methods were used for the ventral skin (Figure 4). The proposed mapping includes 12 dorsal sectors, 12 ventral sectors, and 6 cephalic sectors. The sector map helps us describe the observed hair cycle patterns at any given point in their development. However, the sector borders are arbitrarily assigned. While close, they do not coincide exactly with domain boundaries.

While hair cycle domain patterns undergo progressive temporal changes, their configuration is relatively stable and can be tracked from one cycle to another over the course of an extended period of time (at least 83 days; Figure 5a). However, the precise shape and size of a single hair cycle domain is not identical over the course of several growth cycles. The domain boundaries can shift from one cycle to the next, suggesting that these boundaries are not static. Indeed we did not find any anatomical structures corresponding to domain boundaries. In fact, one particular hair follicle can belong to domain “A” in one cycle, and to domain “B” in the following cycle.

Cellular basis of the hair cycle domain

A skin specimen containing a hair growth pattern is in and of itself very informative. Longitudinal sections spanning the entire length of an anagen spreading wave show a continuous array of hair follicles in sequential hair cycle stages (Figure 6b; Suzuki et al., 2003). Such histological preparations can be used for temporal molecular profiling of hair cycle stages and can enable identification of transient signaling events within any signaling pathway.

The hair cycle domains discussed above represent the transient status of hair cycle stages, and not permanent anatomical differences. There are also regional differences between various parts of the skin, known as regional specificity. Regional specificity implies that different skin regions such as the scalp, beard, eyebrows, face, lips, palms, nails, mammary glands, sweat glands, etc have different characteristics. Epidermal precursors (or stem cells) are initially multi-potent and competent of forming all the above structures. During development, special domains of the dermis send specific messages to the epidermis. Through a series of epithelial-mesenchymal interactions, these different skin domains with special structures and functions gradually emerge. The integument diversifies to endow different functions to different parts of the skin (Widelitz et al., 2006; Chung et al., 2006). Conversely, hair cycle domain boundaries are transient, and can be reset by local or systemic hormone events.

The regenerative hair wave discussed above should also be distinguished from the developmental wave. During skin development, hair primordia form as the result of mechanisms which may involve activators and inhibitors (Nagorcka and Mooney, 1985; Sick et al., 2006; Maini et al., 2006). The new hair primordia are laid out in a temporal order, suggesting that the formation of new hair primordia may also be facilitated by the adjacent newly formed primordia. In the B6.129P2-Fzd6tm1Nat mice, hair primordia distributes in the shape of multiple whorls (Guo et al., 2004; Wang et al., 2006), suggesting the involvement of the WNT pathway in this process. In humans, this phenomenon is most clearly manifested in the occipital hair whorl patterns (Plikus and Chuong, 2004). However, once a follicle is born and the patterns are set in development, these arrangements can not be changed. On the other hand, the regenerative hair wave we have discussed here involves hair follicles with different hair cycle statuses and is transitory.


We hope that the experimental evidence reviewed here will facilitate further recognition of the complexity of the hair cycle in the field of hair research. It can be used as a guide for the planning of hair cycle experiments in adult animals. Simple, yet powerful techniques of monitoring and studying hair cycle patterns, such as whole mount pilo-sebaceous units staining with Oil red, can be easily adopted into any experimental design. We also want to advocate the use of transverse sections through hair cycle domains to capture all stages of hair cycle instead of just one. This method is much more advantageous over having to collect multiple skin samples from different discrete hair cycle stages. Our method allows to observe the continuum of hair cycle stages and not to overlook brief events, such as transient expression of signaling molecules. Furthermore, researchers performing hair cycle studies in transgenic mice should recognize that hair growth pattern dynamics can be dramatically altered in mutant animals,

In the future, it will be most interesting to study the interactive behavior of a population of organs. Here, we have observed that the regenerative behavior of thousands of hair follicles is coordinated. We are interested in computer simulation models that can be used to describe these complex wave patterns. We would like to learn how physico-chemical principles can be applied to explain this regenerative behavior. What are the molecules which mediate wave propagation? What are the molecular pathways which receive or do not receive such propagation signals, leading to the complex wave patterns? How do the principles described here help elucidate patterning behaviors in the biological and non-biological world? How do wave patterns behave in different animals? How do the wave patterns changed by systemic physiology help animals adapt to the external environment, either as an individual during its life span or as a species during evolutionary adaptation? These are challenging questions waiting to be answered.


This work is supported by grants from NIAMS (CMC). We thank Dr. John Sundberg, Dr. Ralf Paus, Dr. Vladimir Botchkarev, Dr. Kurt Stenn, Dr. Angela Christiano and Dr. Valerie Randall, Dr. George Cotsarelis, Dr. Sarah Millar and Dr. Anthony Oro for their helpful discussions and insights.


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