A New Visualization Tool for the Analysis of Labeled Cell Position In-Situ Applied to the Study of Amphioxus Somites.
by Chris Saffran
Columbia University, 2014
A Thesis submitted in Partial Fulfillment of the Requirements for the Degree of
BACHELOR OF ART
in the Department of Biochemistry and Molecular Biophysics.
Abstract
To facilitate the normalization of micrographic data between different specimens in an investigation of somite cell fates in amphioxus, a tool was developed using MATLAB to map imaged expression patterns onto a normalizing field. Internal structures and labeled features were plotted radially in the transverse plane and superpositioned with all other specimens at the same developmental stage. Distinct consensus patterns for all internal structures were observed, and the mean trajectories of migrating cells labeled for ColA were mapped over relative maturational time. Patterns not readily observed in the micrographs were detectable in the resulting visualizations. Several attributes of the migration trajectories were analyzed, and arguments are presented that the momenta of migrating cell cohorts can be used in the analysis of perturbations of the signaling environment in Amphioxus tissues.
1. Introduction
During vertebrate development, structures along the notochord, called somites, differentiate into two heterogeneous compartments with mutually distinct cell fates (Brent and Tabin, 2002). Cells of the dorsal compartment form the dermomyotome and have fates in the dorsal dermis and non-cranial skeletal muscle precursors, while those of the ventral compartment undergo epithelial-mesenchymal transition to form sclerotome, which has fates in the skeletal and connective tissues of the axial skeleton (Scaal and Wiegreffe, 2006). The sclerotome is dynamic and can generate different structures and tissue types. These originate in different subdomains of cells within the sclerotome, and are uniquely induced to different fates by patterning signal gradients produced by the notochord, neural tube, and surrounding tissues (Brent and Tabin, 2002; Scaal et al., 2001). Key among these in regulating amniote somitic cell fates are the Hedgehog (Hh) and and Fibroblast growth factor (Fgf) signaling pathways (Brent and Tabin, 2002). Notably, midline Hh induces the ventromedial subdomain to migrate medially to surround the notochord giving rise to the vertebral body, while lateral Fgf expressed in the myotome antagonizes the ventromedial subdomain, but induces the ventrolateral subdomain to give rise to the ribs and supporting structures (Raymond et, al, 2003).
Given the roll of somites in the formation of the vertebrate axial skeleton during development, an investigation of the somites of chordate ancestors from the time vertebrates first appeared–during the Cambrian era in agnathan fish–may reveal significant insight into how the vertebrate innovation came about. The closest living relative of vertebrates is the invertebrate cephalochordate, amphioxus. Amphioxus, the most basal chordate, develop lateral/medial compartmentalized somites similar to those of their agnathan relatives, and their medial somites also comprise myotome (Ota et al., 2011).
Amphioxus somites are not well studied, however there is no evidence that sclerotome is ever formed, given that adults lack a skeleton. Adults exhibit a segmented body plan involving contractile, myotome-derived structures called myomeres, partitioned by myosepta (Liem et al., 2001). This segmented myomere/myosepta body structure is not only found in modern agnathans but most vertebrate fish. Furthermore, there exists strong evidence that the genome of the shared Cambrian chordate ancestor between vertebrates and amphioxus is well conserved in modern amphioxus, and that the ancestor featured a segmented myomere/myosepta body plan and highly conserved lateral/medial somites (Putnam et al., 1987; Stokes and Holland, 1998). Might the non-myotome amphioxus somites contain precursors to vertebrate sclerotome? Significantly, it is believed these Cambrian amphioxus were the first species to develop somites, and so the somites of modern amphioxus offer not only an excellent, but the best model of the de novo somite (Putnam et al., 1987). It follows, therefore, 1) that the advent of the vertebrate axial skeleton may have its origin in the fates of the non-myotome somitic cells of the Cambrian amphioxus/vertebrate ancestor; and 2) modern amphioxus is the ideal proxy for their Cambrian ancestor in an investigation of ancient somitic cell fates.
The former point is supported by the observation that there exist amphioxus orthologs of numerous amniote genes for transcription factors in somitic cells during vertebrate somite differentiation and migration, and it has been confirmed that many of these are expressed in the somites of amphioxus as well (Scaal, & Wiegreffe, 2006). One of these, ColA, a clade A collagen¹, is expressed by non-myotome somitic cells, and is the only clade A collagen in the amphioxus genome (Figure 1) (Meulemans and Bronner-Fraser, 2007). In vertebrates, fibrillar clade A collagens play an important role in the formation of cartilage, tendon and skin, and it is theorized that this family of collagens was the first to be co-opted by ancient chordates along the path that eventually led to the development of mineralized bone (Wada et al., 2006). As the lone clade A collagen in amphioxus, ColA can be labeled with specificity in non-myotome somitic cells at various stages of development to track their position. Whole mount in-situ hybridization of ColA and other amphioxus analogs of amniote patterning signals across a range of developmental stages, followed by sectioning and micrograph imaging is used to study the fates of amphioxus somitic cells.
But while these methods provide useful data, they are static data describing a fluid system. They are limited in terms of resolution as micrographs cannot be quantitatively compared, and the time it takes to identify what is normal or abnormal across a population is hindered by the rate by which the data can be individually analyzed. Therefore the present research focuses on the developing of a tool to enhance the analytical capacity of the investigation into amphioxus somatic cell position.
The principle disadvantage in the study of cell migration and signal expression without access to in-vivo methods is the discontinuity of the data-stream. That is, individual cells or populations of cells cannot be tracked over time. Moreover, there are nontrivial limits to the meaningfulness of information derived by the superposition of results between different specimens at the microscopic scale. This is especially true for amphioxus, which can have significantly varied morphology between individuals (or indeed between different sections of the same individual), and somitic cells only travel micrometer distances. Furthermore variation in maturation rate between amphioxus specimens, in particular in the early to late neurula stages, can also contribute substantially to variation. The majority of data generated by the amphioxus somite investigation are digital imaged microscopy of labeled transcripts and nuclei from sectioned tissues. But without the ability to normalize data across multiple specimens, the information is only resolvable to organs or loosely defined somitic regions, and remains qualitative and susceptible to subjectivity.
The key to contextualizing the generated image data in terms of a common physical body plan is to normalize the various specimen morphologies by mapping them onto a uniformly bounded field—in this case, the unit circle was chosen. In this way meaningful relationships could be observed between expression patterns across different specimens. To accomplish this, the Amphioxus Dynamic Mapping Tool (ADMT) was authored in MATLAB to map data from the images to a vector space using a modified pseudoinverse transform.
It was theorized that if a sufficient amount of micrographic data from specimens of the same developmental stage were mapped with ADMT, consensus patterns would emerge—both with respect to organ structure and mRNA expression. This was indeed born out by experiments in which the position of DAPI-labeled nuclei and ColA expressing cells were mapped. Further, the ColA consensus patterns revealed certain zones of preference, in other words, positions where somite cells were more and less likely to be observed, independent of the boundaries of physical structures. Noteworthy is the fact that these zones are not readily perceptible when observing the parameterized plots sequentially, and are utterly undetectable in the original micrographs. Data was accumulated on five developmental time points to evaluate the center of mass position of the non-myotome (i.e., ColA labeled) somite cells. Ultimately, data at different time points was assembled to generate a model for the movement of these cells over time. Though ADMT is currently configured for use in evaluating amphioxus data, the underlying principles of the ADMT algorithm and derivative applications can potentially be applied to any investigation involving normalization of micrographic data. As will be discussed later, methods for using this analytical tool to enable a more quantitative and holistic insight into cell position behavior are being explored.
2. Materials and Methods:
Images of ColA expression in amphioxus specimens at three stages of development were used in the current investigation: embryonic (24 hour neurula), larval (3, 5, and 6 gill slit), and Adult. In-situ hybridization with RNA to a BCIP/NBT label, was carried out in conjunction with a DAPI fluorescant nuclear stain following a protocol established by Meulemans et. al (2007). The embryos were embedded in a plastic resin (Spurr’s Resin), according to the manufacturer’s instructions (Sigma catalog #EM0300), and the specimens were sectioned at 3μm. Brightfield and fluorescing micrograph pairs of six 24 hour neurula embryos, six 3-gill slit, and 5-gill slit larvae were captured, generally between 60x and 120x at identically corresponding positions and magnifications for one to one overlay to facilitate the identification of the position of the nuclei of ColA expressing cells (Figure 2).
Micrographs corresponding to six sections taken from one 6 gill slit larval specimen, and four sections taken from one adult specimen were obtained from archive, having been generated during an earlier phase of the amphioxus somite investigation. All the images were imported into an image-digitizing application, Analysis Center AC, Version 1.3.1, that enables points on imported images to be converted into ℝ² coordinates. To standardize coordinate assignments of mapped cells, cell position was defined as the coordinate of the cell’s nucleus. By overlaying the brightfield/fluorescing image pairs, the coordinates corresponding to somitic ColA expressing cells (i.e., the migrating, non-myotome somitic cells), and the perimeter cells of the epidermis, notochord, neural tube, and gut were recorded in a series of column vectors (Figures 3a and b).
3. Results
3.1 Constructing the mapping tool
The micrographic data were imported into the Amphioxus Dynamic Mapping Tool (ADMT), an application scripted in MATLAB. The mapping algorithm designed employs a pseudoinverse transform to derive functions corresponding to structural features and expression patterns. This permits parameterization of data according to relative position (Box 1). The migratory fates of non-myotome dorsal-lateral somitic cells that are the focus of the amphioxus somite investigation, and so ADMT was used to transform the position of labeled ColA expressing cells and all visible internal cell structures to Mapped Amphioxus Nuclear Site (MANS) vector space of two spatial dimensions. Note, cell migration patterns and ColA expression patterns are being taken interchangeably here because it has been shown that the ColA expressing cells are migrating during development (as opposed to ColA expression cascading through a tissue of stationary cells) (Meulemans and Bronner-Fraser, 2007). Therefore tracking the expression pattern is a reasonable proxy for tracking the progress of the migrating cells.
To facilitate interpretation of the data output, the MANS vector space has been expanded by a third parameter: time with respect to relative maturation. Using units of relative maturational time, rather than objective units (i.e., seconds) normalizes against varying maturational rates exhibited between different specimens and permits the tracking of migrational velocities within a three dimensional (two spatial plus one temporal) cylindrical field bound by the specimens’ cross-sectional form and the duration of their maturation, which is to say: the boundaries of interest in the amphioxus somite investigation. Setting one MANS space unit equal to one MANS time unit gives the MANS field unit (μ), and permits its use for both distance and velocity in the context of the MANS field. The value assigned to μ is 1/10 the radius of the field, or 1/10 its height.
Box 1. The mapping algorithm.
For each organism, let the set of coordinates corresponding to its epidermis be [x⃑, y⃑ ]e. Then the corresponding function fe(x) = y is derived by the pseudoinverse of some n × m matrix, M, such that
where 𝔓 is a polynomial basis of order n, and χ* is a pseudoinverse transform. Therefore
where f⃑ is a column vector with the property that its elements constitute the coecients of a polynomial of order dim (f⃑ ) - 1 that describes the contour of the epidermis of the organism. That is, for arbitrary, t, the function describing the contour of the epidermis is
Therefore the internal structures within the organism can all be parameterized one cell at a time by computing the ratio of the distance of a cell from the origin (which, for this investigation has been chosen to correspond to the center of the notochord) to the magnitude of the intercept between the slope of the point associated with the cell and the function corresponding to the epidermis. That is, the ratio:
where the coordinate of the cell being parameterized is the ordered pair (a, b).
3.2 Visualization of cell position
Plots of the ADMT transformations of internal organs demonstrated clear consensus patterning at all measured developmental stages, despite the fairly broad variety in the contours of the structures in the original micrographs. Mean value functions were calculated to coalesce the consensus maps into smooth curve plots in order to crystalize visualization of the data.
Consensus patterns are also readily observed corresponding to the internal structures and ColA migration cohorts². Strong ColA expression was observed in the notochord (in particular along its dorsal and ventral aspects), and the lateral and dorsal dermis, which is expected as these structures express ColA. However, somitic expression was also observed in tissues lateral to the notochord and neural tube (Figures 4a through e). Some clustering is expected along regions of tissue differentiation since organ tissues like the notochord and gut are highly specialized with distinct chemical environments, and so cytotactic flux across such borders may be restricted, and indeed consensus patterns did reveal clustering along these borders. However, there was also significant clustering of the left lateral and right lateral ColA migration cohorts in apparently undifferentiated tissues. These patterns revealed conserved zones of preference and inhibition of this type across specimens of each developmental stage, and so appear to give shape to the actual cytotactic migratory path of non-myotome³ somitic cells encoded in DNA of amphioxus.
3.3 Quantitative analysis, and modeling cell movement
Even more interesting is that by observing the images in sequence, it appears there are two separate motivations of non-myotome cells converging on the notochord. The first wave appears to arrive at the 5GS stage, and distinct regions of inhibition and channels of expression can be observed⁴. Resolution of these zonal boundaries is within 1μ2. At 6GS a corona of inhibition approximately 2 to 2.5μ, presumably myotome, was observed around the notochord, thought the regions that had appeared previously as expression channels still maintained slightly increased expression density. This may herald the beginnings myomere development. By metamorphosis into the adult stage, the second wave appears to have taken place, with highly elevated expression density around the notochord and neural tube. Of course, it is important to bear in mind the limitation on interpretation: the direction of migration must be presumed. The second wave could be radiating outward (though this would be inconsistent with the results of other studies). More investigation of the apparent two-stage migration is required, however this observation suggests ADMT can motivate new directions of research.
To explore the quantitative capability of ADMT the centers of mass of the left lateral and right lateral migration cohorts were calculated and their trajectories were quantitatively analyzed (Table 1).
It was observed that velocities⁵ of both cohorts drops at the 5GS stage, then picks up again. Interestingly, the cytotactic momentum continues to drop into the 6GS stage, even after the velocity has begun to pick up. This is related to a decrease in the cohort masses⁶. Might this signify a temporary lapse in the expression of ColA? If so, is the lapse part of the developmental pathway in all amphioxus, or does it derive from an allele possessed by some portion of the population? This also merits further investigation. Plotting the trajectory over time, the proposed points of the migration events can be observed (Figure 5).
4. Discussion
4.1 New insight
Because cell migration factors so heavily in the amphioxus study, amplification of the ability to resolve information corresponding to cytotaxis and its relation to chemical signaling was set as the initial core objective of the ADMT program. The earliest sign of the program’s success was its ability to produce insight to into patterns and sequences of events that were not otherwise detectable. Going a step further, it is theorized that ADMT can be used to provide insight into impossibly complex interactions, to elucidate the effects of genetic modulation.
4.2 Migration determining states
The distribution and concentration of chemical signals and other parameters within a tissue establishes a migration-determining state (MDS) that motivates migration along a particular path through the tissue. Once a set of conditions result in a migration-permissible state (MDS), and a cell is motivated along some path, it follows that if the state does not change, neither the migrational path, nor the rate along which it is traversed, will change because it constitutes the dominant entropy gradient in the cell-tissue system. That is to say that once the migrational velocity of an individual is established, it will only change if some factor changes the conditions of the migration-determining state (Figure 6a).
This is not unlike a particle traveling through space, moving as a result of some condition or combination of conditions (e.g., an electromotive force). The particle will only change its velocity if it is acted upon by another force, in which case it undergoes acceleration, otherwise it continues moving along its vector at rest. A population of migrating cells traveling along an entropy gradient are in a similar situation in that it will require the imposition of some “force” to redirect the pathway (Figure 6b). Unlike the particle, however, this force need not constitute the application of energy, only a change or redirection of energy as either the chemical interactions favoring the existing migrational pathway change in intensity or distribution, or else the permeability of the tissue falls below some critical percolation value such that migration is either slowed, redirected, or halted. In this way, the migration-permissible state behaves as a kind of cytotactic vector field through which migrating cells are traveling, and the migrational pathway is defined by the parameters of this vector field.
Consider now that where this theoretical migration permitting field is constant, the effect on motility will be constant, and so cytotactic momentum will be constant. It is important to bear in mind that the parameters involved are highly complex and, especially in vivo, subject to any number of anomalies. Nevertheless, the effect of chemical signaling must be capable of producing a reliable effect on migrational pathways or biological processes relying on these pathways would fail. Therefore it seems reasonable that the pathway can be characterized as the path along which the center of mass of the population migrates, and that the velocity of this MCCOM times the cohort mass, should be substantially (albeit not wholly) conserved. It follows that changes in this cytotactic momentum reflect changes in the MDS relative to that particular migration. As an important corollary, if the cytotactic momenta of analogous migration cohorts of two different populations of the same species over the same developmental stages are different, the MDSs of the two populations are different. Furthermore, if environmental factors between the two specimen populations are constant (e.g., laboratory conditions), the difference in MDS must be attributable to genetic differences. Therefore the effects of genetic alterations (e.g., knockouts, transgenes, etc.) can be studied quantitatively with respect to a particular migration cohort by calculating the change in cytotactic momentum. It is therefore proposed that analyses of MCCOM trajectories and cytotactic momenta can prove useful tools in the study of biological or biochemical phenomena in amphioxus.
Box 2. Analyzing perturbations of the migration determining state.
Consider once more the theoretical model of a single cell migrating through a tissue in which the MDS is constant over time—no obstructions, no gradation of cytotactic signals, no barriers, etc. The unperturbed cell can be expected to continue along a linear trajectory. Put another way, the information of the wild type MDS has constrained the migration trajectory to a linear path. Therefore if this path were plotted from the cell’s initial point,Ci at ti, to an arbitrary fate, Cf at tf, the probability that the cell will be on the line C͞iC͞f at an arbitrary time tn (where ti ≤ tn ≤ tf ) is ∼100%⁹. This arises from the fact that for any tn there is only one possible space the cell can occupy next: it is fully constrained (Figure 6a). If, however, the MDS were mutant and comprised different information, that is less wild type information, the trajectory of the cell would be less constrained with respect to the wild type trajectory¹⁰. This results from the fact that with less constraint, the cell now has “options” as to where it might be at tn (Figure 6b). The greater the loss of information, the lower the probability that the position of the cell can be determined at tn in terms of the wild type MDS. Expressing the cytotactic drift potential (range of potentially available positions) at tn corresponding to some loss of information as a circle of radius r, perpendicular to and centered on the wild type trajectory line, this loss of information can be expressed using the Shannon Entropy equation (Shannon, 1948)
where n is the number of spaces of area ε in the circle the cell can occupy, H is the loss of information as a function of ε, and p is the probability that the cell will occupy the i-th space. Note that the relationship between ε and n is
This theoretical model is not be restricted to linear trajectories. A WT cell (let this be cell A) traveling through living tissue may follow a trajectory with numerous twists and turns, but it is every bit as constrained to its path by the MDS as the theoretical one, because the MDS is defined as the combination of factors that cause the cell to migrate exactly how it migrates. The precise nature and quantitative values of these factors are incalculable; all that is known of them is that they combine to result in a particular path for cell A at a particular time. So if cell A were placed back at the initial position and subjected to the exact same MDS (not realistically possible without moving backward in time, these theoretical conditions are only for illustrative purposes), it would travel the exact same path every time¹¹. The MDS can therefore be viewed in terms of call A’s path, i.e., in terms of its result, and be denoted MDSA, such that MDSA provides all the information necessary to calculate the path of cell A over some period of time, 4t. Now let cell B be a similar cell (defining similar cells as being from the same tissue of the same organism with the same cell fate) adjacent to cell A in its tissue of origin. Cell B will not follow the exact same migratory path as cell A moving in tandem over 4t, but rather some approximation of call A’s path (Figure 7a) because MDSA is specific to A during 4t. But of course, the existing conditions can just as easily be viewed as specific for cell B, in which case, cell B would be said to follow the MDSB prescribed path during 4t and cell A would follow the “similar” one—the MDS and the paths remain the same, only the point of view changes (Figures 7b and c). Therefore in either case equivalent graphs of the data can be constructed that generate the variables required for analysis using equation (7). If cells C, D, and E are also similar to A, and placed at the initial point, a mean path can be calculated, and it can be said that cells of that type are constrained to this mean path (Figure 7d through g). The WT MDS cannot by itself by quantified, only mutant MDSs in realtion to it; however, regression analysis can be used to quantify how strongly the WT MDT constrains the WT MCCOM trajectory.
4.3 Perturbation analysis theory
Investigating the comparison of trajectories of two analogous migration cohorts, it is helpful to think of the parameters of the MDS (i.e., the elements of the matrix directing the migration—signaling factors, extracellular biomolecules, etc.) as containing information. From this perspective, interactions between migrating cells and the information-rich molecules and structures of the matrix can be viewed as transfers of information. It follows that these transfers of information control the momentum of the MCCOM, and so a loss⁷ of wild type information will result in a deviation of wild type cell trajectories. And so while the MDS itself can never be determined because it has far too many parameters—it can only be said to exist—perturbations in the MDS can be observed and measured when such changes produce measurable effects (Figure 8a through g) in the migration of groups of analogous cells⁸ (Box 2).
Developing a clear picture of how the patterning signal gradients of the Hh and Fgf pathways interact with migrating somitic cells in amphioxous, and the transcription factors they express, will require a sophisticated method for evaluating not only whether a particular signal affects migration, but to what degree. Certainly a great deal can be comprehended from visual, qualitative observations of micrographs of labeled transcription factors. The object here is to expand upon this: to enable meaningful superpositioning of data and help visualize it in a context that better models migration over time, and to help identify certain perturbative effects of signal gradient and transcription factor modulations that are too subtle to visually identify independently, but which might aggregate significantly (Box 3).
Box 3. Applied perturbation analysis.
To apply MDS perturbation analysis to a change in MDS for analogous migration cohorts, the drift component of the cytotactic momentum, rρ, may be substituted for r, however it is also necessary to consider any changes in area of the migration cohorts. Letting AWT be the wild type cohort cross sectional area and Am be that of an analogous mutant cohort, we can evaluate their difference
where x and y are the lateral and dorsoventral axes in the transverse plane, and s⃑ is a vector value function describing the area bounded by the respective WT or mutant cohort. Since the value for ε is constant, fixing the relationship between rρ and n as suggested by equation (8), we can sum the drift entropy with the entropy related to the change in cohort sectional area to determine a coecient of perturbation, ϖ:
where
and
ϖ is unitless and theoretically constant. In practice, ϖ will vary as more data on the MCCOM trajectories involved is accumulated, however determinations of ϖ will converge as more data is amassed. Once it stabilizes to within the minimum resolution of other experimental measurements within an investigation, it can therefore be treated as a constant perturbation coecient associated with a particular genetic modulation.
4.4 Needed refinements
Exploration of the capabilities and advantages of ADMT are in the early stages and not nearly enough data has been mapped to fully realize its potential. Nevertheless, results thus far are promising: the consensus maps of amphioxus emerged quickly, nuanced expression patterns were detected that were otherwise indiscernible, and the evaluation of MCCOM paths and momenta appeared to agree with what is known and understood about amphioxus development. That said, certain issues exist. Much more image data needs to be amassed, and many more developmental stages need to be represented. Moreover, as new data is collected it will be important to format ADMT’s input protocol such that the position of each section to be mapped is recorded. The current data are taken arbitrarily from a local region near the midline of each specimen, and so treat the organism as constant along its anteroposterior axis (Figure 9a). It is the case that (as far as is known) the cell fates of amphioxus somitic cells involve migration along the transverse plane. But a far greater understanding of signaling is likely to be enabled by developing an amphioxus map with a third spatial dimension such that the MANS field will occupy a four dimensional cylinder (including the time dimension, Figure 9b). However, this will mean even more data will be required to achieve ADMT’s full potential. This is because rather than merely requiring a few dozen micrographs per developmental stage per targeted factor or signal; a complete 4-cylinder dataset will require a few dozen micrographs per 3-micron section per developmental stage per targeted factor or signal. This raises another problem: the time it takes to upload micrograph data is fairly time consuming and so realizing the goal of mapping the whole organism could be prohibitively laborious.
One possible solution being explored is the automation of image capture and mapping by ADMT. As it stands, the process of mapping images involves separately reading the images into a digitizer program, plotting cell coordinates, then feeding the coordinates into ADMT. It is hoped that by using the right label and imaging protocol, the ADMT code can be revised to recognize features on its own, issue the initial coordinates, then map them to the MANS field. This will have the added effect of substantially enhancing the quantitative nature of the output, as the current method involves the investigator manually selecting the cell positions in the digitizer, which can degrade accuracy of results.
However, once a sucient number of images are mapped, ADMT can use consensus of morphology to categorize new images in the appropriate developmental stage. This will help standardize the relative maturation time coordinate. As it stands, the time coordinate is fixed according to known developmental stage, and so two specimens exhibiting different rates of maturation but who are in the same developmental stage are assigned the same time coordinate. But because the tissues change significantly and characteristically between stages, if an image is input that shows characteristics between two stages for which ADMT has sucient information, it can place the organism’s time coordinate at an appropriate position between these values. Only then will the time component of μ be fully normalized.
4.5 The future of ADMT
That said, these early results ADMT have demonstrated its capacity for the realization of the objectives: to resolve informational analysis of amphioxus somitic cell migration image data to a higher level of clarity, to increase quantitative analytical capabilities of the amphioxus investigation, and to reveal nuanced data unavailable when considering micrographic data sequentially or without normalized superposition. And while the study of amphioxus somites was the instigating force that drove the development of ADMT, it can be adapted to many other investigations involving the analysis of section micrographs of in-situ hybridization labeled targets. And so it is hoped that as an information resolving and hypothesis-generating tool, ADMT will contribute meaningfully to efforts to determine the role of chemical signaling in amphioxus somitic cells, and to other important discoveries as well.