Identification of alternative topological domains in chromatin
2014

Darya Filippova
Rob Patro
†
Geet Duggal
Carl Kingsford
Identification of alternative topological domains in chromatin

Algorithms for Molecular Biology
9142014RESEARCH Open AccessAlternative topological domainsChromatin conformation captureDynamic programming
Chromosome conformation capture experiments have led to the discovery of dense, contiguous, megabase-sized topological domains that are similar across cell types and conserved across species. These domains are strongly correlated with a number of chromatin markers and have since been included in a number of analyses. However, functionally-relevant domains may exist at multiple length scales. We introduce a new and efficient algorithm that is able to capture persistent domains across various resolutions by adjusting a single scale parameter. The ensemble of domains we identify allows us to quantify the degree to which the domain structure is hierarchical as opposed to overlapping, and our analysis reveals a pronounced hierarchical structure in which larger stable domains tend to completely contain smaller domains. The identified novel domains are substantially different from domains reported previously and are highly enriched for insulating factor CTCF binding and histone marks at the boundaries.

Background

Chromatin interactions obtained from a variety of recent experimental techniques in chromosome conformation capture (3C) [1] have significantly advanced our understanding of the geometry of chromatin structure [2], its relation to the regulation of gene expression, nuclear organization, cancer translocations [3], and copy number alterations in cancer [4]. Recently, dense, contiguous regions of chromatin termed topological domains have been discovered in both mammals [5] and in fruit flies [6]. Topological domains have since been incorporated into many subsequent analyses [7][8][9] due to the fact that they are persistent across cell types, conserved across species, and serve as a skeleton for the placement of many functional elements of the genome [10,11].

3C experiments result in matrices of counts that represent the frequency of cross-linking between restriction fragments of DNA that are spatially near one another. The identification of domains in Dixon et al. [5] employed a Hidden Markov Model (HMM) on these interaction matrices to identify regions initiated by significant *Correspondence: firstname.lastname@example.com † Equal contributors 1 Lane Center for Computational Biology, Carnegie Mellon University, Pittsburgh PA, USA Full list of author information is available at the end of the article downstream chromatin interactions and terminated by a sequence of significant upstream interactions. A defining characteristic of the domains from their analysis is that higher frequency 3C interactions tend to occur within domains as opposed to across domains. This aspect of domains is also reflected in the block-diagonal structure of 3C interaction matrices as shown in Figure 1. In this sense, domains can be interpreted as contiguous genomic regions that self-interact frequently and are more spatially compact than their surrounding regions. However, the single collection of megabase-sized domains may not be the only topologically and functionally relevant collection of domains. On closer inspection of the block-diagonal matrix structure in Figure 1, it becomes clear that there are alternative contiguous regions of the chromosome that self-interact frequently and are likely more spatially compact than their surrounding regions (dotted lines). Some of these regions appear to be completely nested within others, suggesting a hierarchy of compact regions along the chromosome, while others appear to overlap each other. These observations suggest that functionally-relevant chromosomal domains may exist at multiple scales potentially contributing to a hierarchy of domains or a more complex relationship between domains. http://www.almob.org/content/9/1/14 We introduce a new algorithm to efficiently identify topological domains in 3C interaction matrices for a given domain-length scaling factor γ . Our formulation of this problem as a dynamic program allows for an efficient traversal of the solution space to obtain alternative optimal and near-optimal domain sets. Our results suggest that there exist a handful of characteristic resolutions across which domains are similar. Based on this finding, we identify a consensus set of domains that persists across various resolutions. We find that domains discovered by our algorithm are dense and cover interactions of higher frequency than inter-domain interactions. Additionally, we show that inter-domain regions within the consensus domain set are highly enriched with insulator factor CTCF and histone modification marks. We analyze a set of domains from multiple optimal domain sets across scales and establish that the organization of domains is highly hierarchical, suggesting that the generated domains can be used as the basis for understanding the hierarchical organization of the genome and its role in gene regulation. We argue that our straightforward approach retains the essence of the more complex multi-parameter HMM introduced in [5] while allowing for the flexibility to identify biologically relevant domain structures at various scales.

Problem definitions

Given the resolution of the 3C experiment (say, 40kbp), the chromosome is broken into n evenly sized fragments. 3C contact maps record interactions between different sections of the chromosome in the form of a weighted adjacency matrix A where two fragments i and j interact with frequency A ij . Problem 1 (Resolution-specific domains). Given a n×n weighted adjacency matrix A and a resolution parameter γ ≥ 0, we wish to identify a set of domains D γ where each domain is represented as an interval
d i = [a i , b i ], 1 ≤ a i < b i ≤
n such that no two d i and d j overlap for any i = j. Additionally, each domain should have a larger interaction frequency within the domain than to its surrounding regions.

Specifically, we seek to identify a set of non-overlapping domains D γ that optimizes the following objective:
max [a i ,b i ]∈D γ q(a i , b i , γ ),( 1 )
where D γ chosen from the set of all possible domains, and q is a function that quantifies the quality of a domain [ a i , b i ] at resolution γ . Here, the parameter γ is inversely related to the average domain size in D γ : lower γ results http://www.almob.org/content/9/1/14 in sets of larger domains and higher γ corresponds to sets of smaller domains. Since domains are required to contain consecutive fragments of the chromosome, this problem differs from the problem of clustering the graph of 3C interactions induced by A, since such a clustering may place non-contiguous fragments of the chromosome into a single cluster. In fact, this additional requirement allows for an efficient optimal algorithm. Problem 2 (Consensus domains across resolutions). Given A and a set of resolutions = {γ 1 , γ 2 , . . .}, identify a set of non-overlapping domains D c that are most persistent across resolutions in :
max [a i ,b i ]∈D c p(a i , b i , ),( 2 )
where D c is the set of non-overlapping persistent domains across resolutions, and p(a i , b i , ) is the persistence of domain [a i , b i ] corresponding to how often it appears across resolutions.

Algorithms

Domain identification at a particular resolution

Since each row and corresponding column in a 3C interaction matrix encodes a genomic position on the chromosome, we can write the solution to objective (1) as a dynamic program:
OPT 1 (l) = max k<l {OPT 1 (k − 1) + max{q(k, l, γ ), 0}},(3)
where OPT 1 (l) is the optimal solution for objective (1) for the sub-matrix defined by the first l positions on the chromosome (OPT 1 (0) = 0). The choice of k encodes the size of the domain immediately preceding location l. We define negative-scoring domains as non-domains and, as such, only domains with q > 0 in the max term in (3) are retained.

Our quality function q is:
q(k, l, γ ) = s(k, l, γ ) − μ s (l − k),( 4 )
where
s(k, l, γ ) = l g=k l h=g+1 A gh (l − k) γ(5)
is a scaled density of the subgraph induced by the interactions A gh between genomic loci k and l. When γ = 1, the scaled density is the weighted subgraph density [12] for the subgraph induced by the fragments between k and l, which is the upper-triangular portion of the submatrix defined by the domain in the interval [k, l] divided by the scaled length (l − k) γ of the domain. When γ = 2, the scaled density is half the internal density of a graph cluster [13]. For larger values of γ , the length of a domain in the denominator is amplified, hence, smaller domains would produce larger objective values than bigger domains with similar interaction frequencies.

Equation (4) is the zero-centered sum of (5). μ s (l−k) is the mean value of (5) over all sub-matrices of length l−k along the diagonal of A, and can be pre-computed for a given A.

We disallow domains where there are fewer than 100 submatrices available to compute the mean. By doing this, we are only excluding domains of size larger than n − 100 fragments, which in practice means that we are disallowing domains that are hundreds of megabases long. Values for the numerator in (5) are also pre-computed using an efficient algorithm [14], resulting in an overall run-time of O(n 2 ) to compute OPT 1 (n).

Enumerating multiple optimal and near-optimal solutions

The set of domains found by the dynamic program in Equation 3 may not be the only set obtaining the maximum value of OPT 1 (·). In fact, there may be multiple optimal solutions and solutions which are near optimal. The domain structures that appear in alternative optimal or near optimal solutions are of interest, especially if they are significantly different, since they represent a potentially diverse array of alternative domains that are only precluded from the initially computed optimal solution as a result of the arbitrary breaking of ties that takes place in the dynamic program. We wish to be able to account for such alternative solutions by enumerating them efficiently and in order of a decreasing solution score. Since Equation 3 will allow 'non-domains' (i.e. intervals on the chromosome with q(k, l, γ ) ≤ 0) to be split arbitrarily without affecting the optimal score, we modified the procedure as shown in Equation 6 to explicitly disallow adjacent non-domains:
OPT 1 (l) = max max k<l {OPT D (k − 1)} OPT D (l),(6)
where the optimal score of l ending a domain is
OPT D (l) = max k<l {OPT 1 (k − 1) + q (k, l, γ )},( 7 )
and the quality function for the domain is
q (k, l, γ ) = q(k, l, γ ) if q(k, l, γ ) > 0 − ∞ otherwise. (8) OPT D (l) = OPT 1 (l) = 0 for l ∈ {0, 1}. In Equation 6
, max k<l OPT D (k − 1) represents the optimal score at l where l ends a non-domain region. This solution to Problem 1 produces a set of domains with the same optimal score as Equation 3, but guarantees that alternative optimal and near-optimal domain sets do not contain non-domains that are adjacent.

To efficiently identify alternative optimal and nearoptimal solutions, we use the fact that the dynamic program in Equation (6) can be conceptually represented as a directed acyclic graph G where each OPT 1 (l) and OPT D (l) http://www.almob.org/content/9/1/14 is connected by an edge to every other term it depends on:
{OPT 1 (k)} k<l and {OPT D (k)} k<l . For each edge e = (k, l)
in G, the weight of e is q (k, l, γ ). Thus, finding a set of domains with an optimal score is equivalent to finding a highest-weight path in G starting from the node representing OPT 1 (n). To find the top-K solutions, we then find the K highest weight paths in G using a standard procedure [15].

Obtaining a consensus set of persistent domains across resolutions

For objective (2), we use the procedure above to construct a set D = γ ∈ D γ . D is a set of overlapping intervals or domains, each with a quality score defined by its persistence p across resolutions. To extract a set of highly persistent, non-overlapping domains from D, we reduce problem 2 to the weighted interval scheduling problem [16], where competing requests to reserve a resource in time are resolved by finding the highestpriority set of non-conflicting requests. To find a consensus set of domains, we map a request associated with an interval of time to a domain and its corresponding interval on the chromosome. The priority of a request maps to a domain's persistence p across length scales.

The algorithm to solve problem 2 is then:
OPT 2 (j) = max{OPT 2 (j − 1), OPT 2 (c(j)) + p(a j , b j , )}(9)
where OPT 2 (j) is the optimal non-overlapping set of domains for the jth domain in a list of domains sorted by their endpoints (OPT 2 (0) = 0), and c(j) is the closest domain before j that does not overlap with j. The first and second terms in (9) correspond to either choosing or not choosing domain j respectively. We pre-compute a domain's persistence p as:
p(a i , b i , ) = γ ∈ δ i where δ i = 1 if [a i , b i ] ∈ D γ 0 otherwise.(10)
Equation (10) is therefore a count of how often domain i appears across all resolutions in for domain sets identified by the dynamic program at a single resolution. It may be desirable to treat multiple highly overlapping, nonequivalent domains as a single domain, however, we con-

Results

We used chromatin conformation capture data from Dixon et al. [5] for human fibroblast and mouse embryonic cells. The 3C contact matrices were already aggregated at fragment size 40kb and were corrected for experimental bias according to [17]. We compared our multiscale domains and consensus sets against the domains generated by Dixon et al. for the corresponding cell type and species. For human fibroblast cells, we used CTCF binding sites from [18]. For mouse embryonic cell CTCF binding sites and chromatin modification marks, we used data by Shen et al. [19].

Ability to identify densely interacting domains across scales

Multiresolution domains successfully capture high frequency interactions and leave interactions of lower mean frequency outside of the domains. We compute the mean interaction frequency for all intra-and inter-domain interactions at various genomic lengths and plot the distribution of means for multiple resolutions (Figure 2(a)). The mean intra-domain interaction frequency (blue) is consistently higher (up to two times) than the mean frequency for interactions that cross domains (red). Compared to the domains reported by Dixon et al., our domains tend to aggregate interactions of higher mean frequency, especially at larger γ . The distribution of mean intra-domain frequencies for Dixon et al. is skewed more to the left than that of the multiscale domains (Figure 2(b)). This difference can be partially explained by the fact that multiscale domains on average are smaller in size (μ = 0.2Mb, σ = 1.2Mb) than domains reported by Dixon et al. (μ = 1.2Mb, σ = 0.9Mb).

Domain persistence across scales

Domain sets across resolutions share significant similarities, even as the distribution of domains and their sizes begin to change (Figure 3). The patterns of similarity are particularly obvious if we plot the domains at various resolutions (Figure 4(a)): many domains identified by our algorithm persist at several resolutions and are aggregated into larger domains at smaller γ , suggesting a hierarchical domain structure. The stability of these domains across resolutions indicates that the underlying chromosomal structure is dense within these domains and that these domains interact with the rest of the chromosome at a much lower frequency.

A pairwise comparison of domain configurations displays regions of stability across multiple resolutions (Figure 4(b)). We use the variation of information (VI) [20], a metric for comparing two sets of clusters, to http://www.almob.org/content/9/1/14 a b

Comparison with the previously identified set of domains in Dixon et al.

At higher resolutions, domains identified by our algorithm are smaller than those reported by Dixon et al. (Figure 3). As the resolution parameter decreases to 0.0, the average size of the domains increases. The composition of the domains we identify is different from that of Dixon et al. as illustrated in Figure 4(a) and captured by the variation of information in Figure 4(b).

We use the consensus domains algorithm to obtain a consensus set of domains D c persistent across resolutions. We construct the set by defining the range of our scale parameter to be [ 0, γ max ] and incrementing γ in steps of 0.05. In order to more directly compare with previous results, we set γ max = 0.5 for human and 0.25 for mouse since these are the scales at which the maximum domain sizes in Dixon et al. 's sets match the maximum domain sizes in our sets.

Our consensus domain set agrees with the Dixon et al. domains better than with a randomized set of domains adhering to the same domain and non-domain length distributions ( Figure 5 and [21]). Comparing to a set of http://www.almob.org/content/9/1/14 random domains also helps to verify that our observations are due to the observed sequence of domains and not the distribution of domain lengths. To shuffle Dixon's domains, we record the length of every domain and nondomain region, and then shuffle these lengths to obtain a randomized order of domains and non-domains across the chromosome. The fact that variation of information is lower between consensus domains and domains reported by Dixon et al. demonstrates that, though the approaches find substantially different sets of topological domains, they still agree significantly more than one would expect by chance.

Enrichment of CTCF and histone modifications near boundaries

We assess the enrichment of transcription factor CTCF and histone modifications H3K4me3 and H3K27AC within the inter-domain regions induced by the consensus domains. These enrichments provide evidence that the boundary regions between topological domains correlate  1-22 (x-axis). We used the variation of information (VI) (y-axis) to compute distances between domain sets for the multiscale consensus set vs. Dixon et al. (blue dots) and the multiscale consensus vs. randomly shuffled domains (red diamonds). http://www.almob.org/content/9/1/14 with genomic regions that act as insulators and barriers, suggesting that the topological domains may play a role in controlling transcription in mammalian genomes [5]. Figure 6 illustrates the enrichment of insulator or barrier-like elements in domain boundaries in both the human fibroblast (IMR90) and mouse embryonic stem cell (mESC) lines. Specifically, we observe that the boundaries between consensus domains are significantly enriched for all of the transcription factors and histone marks we consider. In certain cases -specifically in the case of CTCF -we notice that the CTCF binding signals peak more sharply in the boundaries between the domains we discover than in the boundaries between the domains of Dixon et al.

We also observe that, when compared with the domain boundaries predicted by Dixon et al., our boundaries more often contain insulator or barrier-like elements (see Table 1). Specifically, we normalize for the fact that we identify approximately twice as many domains as Dixon et al., and generally observe a two-fold enrichment in the fraction of boundaries containing peaks for CTCF markers. This suggests that structural boundaries identified by our method are more closely tied to functional sites which serve as barriers to long-range regulation. We also observe a depletion of insulator CTCF elements within our domains when compared to the domains of Dixon et al. This observation is consistent with the assumption that transcriptional regulation is more active within spatially proximate domains since there are fewer elements blocking regulation within these domains. Table 1 also shows similar patterns for histone modifications which suggests that our domain boundaries are enriched for functional markers of gene regulation.

Multiple optimal solutions across scales reveal the hierarchical organization of topological domains

It has been recently hypothesized that chromatin is packed into the nucleus in a hierarchical manner suggesting that smaller, spatially compact domains combine to form larger superdomains that may be functionally similar [2,3,6]. This hypothesis is partially motivated by the fact that the distribution of 3C interaction frequencies better matches a fractal globule model of chromatin organization than an essentially random equilibrium organization of chromatin in the nucleus [22] and by an initial exploration of the hierarchical organization of the Drosophilla genome [6]. By combining alternative optimal and near-optimal domains across scales, we quantitatively determine the extent to which domains at different γ conform to a hierarchical structure empirically identifiable in Figures 4(a) and 7.

We determine the extent to which all identified optimal and near-optimal topological domains are hierarchically organized by combining alternative optimal and near-optimal domains and computing a score characterizing the hierarchy. Specifically, we combine all nearoptimal domains across all resolutions into a single set:
D K = γ ∈ i∈ [1,K] D i γ where D i
γ is the ith optimal solution at resolution γ and K total solutions are found at each resolution. We quantify the extent to which domains in this set are nested by determining the fraction of sufficiently different domain pairs {d i , d j } where either d i or d j is completely contained in the other:
h(D K α ) = 1 |D K α | {d i ,d j }∈D K α δ(d i , d j ),(11)δ(d i , d j ) = 1, if d i ⊂ d j or d j ⊂ d i 0, otherwise,(12)
and D K α contains all pairs of domains {d i , d j } from domains in D K such that α = |d i d j |/|d i ∪ d j | -a fraction of genomic fragments different between two domains d i and d j in relation to the union of all fragments comprising the two domains -is greater than a user-specified value. For our tests, we define two domains to be different if more than 10% of their fragments differ (α = 0.1). If no domain is contained fully in any other domain the score h(·) = 0. If, for every pair of domains, one of the domains is fully contained in the other, the score attains its maximum value h(·) = 1. We empirically observe that randomly generated domains result in h(·) ≈ 0.5.

To determine whether the set of all identified domains we observe is significantly more hierarchical than expected by chance, we randomly shuffle domains while maintaining the same domain and non-domain length distributions as the sets of domains we find [21]. At each resolution, we identify the K = 10 optimal and nearoptimal solutions for all chromosomes in human fibroblast cell line (IMR90) as well as mouse embryonic cells (mESC). The choice of K = 10 is computationally beneficial given that even for such low K, the score for the next optimal solution drops off fast at lower γ , but for γ = 0.5 the optimal score only changes by 0.02% (from 16774.7 to 16771.2) after 50000 solutions are considered. Alternatively, a weaker null hypothesis could be constructed that uses randomly shuffled Hi-C matrix. However, this approach does not control for the distribution of domain lengths -a previously established property of topological domains [5,6]. In addition, it has recently been shown that randomly shuffled Hi-C matrices lack a clear domain structure since they exhibit significantly depleted insulation scores [24]. This weaker null hypothesis is thus not appropriate for determining the significance of hierarchical domain structure. For both organisms, we find that h(·) for the identified set of domains is significantly larger than h(·) for the randomized domains (Benjamini-Hochberg corrected P < 0.001 over all chromosomes). http://www.almob.org/content/9/1/14  Each table entry is of the form e t ≈ r where e is the number of elements containing ≥ 1 of CTCF and histone modifications, t is the total number of elements and r is the approximate ratio e/t. Our method produces more domains, and hence more boundaries, than that of Dixon et al. [5]. However, relative to Dixon et al., our domains are depleted for peaks of interest, while our boundaries are significantly enriched for such peaks.

The mean value of the identified set of domains is ≈ 0.95 as opposed to ≈ 0.70 for 1,000 randomized sets of domains sampled from each resolution. Computing h(·) on the combined set of domains is conservative since it is likely that domains from multiple optimal and nearoptimal solutions can overlap but may not be completely contained in one another within a length scale. This suggests that the multiple optimal and near-optimal domains across scales exhibit a hierarchical structure and that the ensemble of domains can be used as the basis of a more detailed analysis of the hierarchical organization of these genomes.

Discussion and conclusions

In this paper, we introduce an algorithm to identify topological domains in chromatin using interaction matrices from recent high-throughput chromosome conformation capture experiments. Our algorithm produces domains that display much higher interaction frequencies within the domains than in-between domains ( Figure 2) and for which the boundaries between these domains exhibit substantial enrichment for several insulator and barrier-like elements ( Figure 6). To identify these domains, we use a multiscale approach that finds domains at various size scales and generates multiple optimal and near-optimal solutions.

We define a consensus set to be a set of domains that persist across multiple resolutions and give an efficient algorithm that finds such a set optimally.

Our method uses a score function that encodes the quality of putative domains in an intuitive manner based on their local density of interactions. Variations of the scoring Browser [23]. http://www.almob.org/content/9/1/14 function in (4), for example, by median centering rather than mean centering or by optimizing the homogeneity of interaction frequencies instead of total frequencies, can be explored to test the robustness of the enrichments described here.

Our method is particularly appealing in that it requires only a single user-specified parameter γ max . For our experiments, the parameter γ max was set based on the maximum domain sizes observed in Dixon et al. 's experiments so that we could easily compare our domains to theirs. This parameter can also be set intrinsically from properties of the Hi-C interaction matrices. For example, we observe similar enrichments in both human and mouse when we set γ max to be the smallest γ ∈ such that the median domain size is >80kbp (two consecutive Hi-C fragments at a resolution of 40kbp). This is a reasonable assumption since domains consisting of just one or two fragments do not capture higher-order spatial relationships (e.g. triad closure) and interaction frequencies between adjacent fragments are likely large by chance [22].

We compared the fraction of the genome covered by domains identified by Dixon et al. vs. the domains obtained from our method at various resolutions. Dixon et al. 's domains cover 85% of the genome while our sets tend to cover less of the genome (≈ 65% for a resolution that results in the same number of domains as those of Dixon et al.). The fact that our domain boundaries are more enriched for CTCF sites indicates that our smaller, more dense domains may be more desirable from the perspective of genome function. The dense, functionally-enriched domains discovered by our algorithm provide strong evidence that alternative chromatin domains exist and that a single length scale is insufficient to capture the hierarchical and overlapping domain structure visible in heat maps of 3C interaction matrices.

We provided the first quantitative analysis testing the hypothesis that the domain structure across scales is significantly hierarchically organized, suggesting that the domains we identify can be used as the basis for studying the hierarchical organization of genomes and how this structure impacts gene regulation. By incorporating multiple optimal and near optimal solutions into this analysis, we provide evidence that the observed hierarchical structure persists not only across scales but across a variety of plausible high-scoring domain sets. However, multiple optimal solutions are not necessary to quantify the hierarchical structure of the domains since single optimal solutions across scales can already reveal a hierarchical structure. There are many more near-optimal solutions at higher values of γ since the domain sizes tend to be smaller. For this special case, it would be desirable to develop a method that more concisely characterizes these larger solution spaces, and this is an interesting direction for future work. The quantitative evidence of the hierarchical structure of topological domains also motivates the development of novel methods for domain discovery that directly account for such hierarchy in the models they assume and the functions they optimize.

The method for discovering topological domains that we have introduced is practical for existing datasets. Our implementation is able to compute the consensus set of domains for the human fibroblast cell line and extract the consensus set in 24 minutes when run on a personal computer with 2.3GHz Intel Core i5 processor and 8Gb of RAM. Computing optimal and near-optimal solutions adds only a small overhead to overall running time: when computing 20 top optimal and near-optimal solutions per each γ setting (with γ 0.0-0.9 with a step of 0.05) the computation finishes in 25 minutes 34 seconds.

A preliminary version of this manuscript appeared in the 2013 Workshop on Algorithms for Bioinformatics [25].

Figure 1
1Interaction matrix for a portion of human chromosome 1 from a recent Hi-C experiment by Dixon et al. [5]. Each axis represents a location on the chromosome with a step of 40kbp. Densely interacting domains identified by the method of Dixon et al. are shown in red. Alternative domains are shown as dotted black lines on the upper triangular portion of the matrix. Visual inspection of the lower triangular portion suggests domains could be completely nested within another and highly overlapping when compared to Dixon et al.'s domains. This motivates the problem of identifying alternative domains across length scales.

servatively identify exact repetitions of a domain across resolutions since this setting serves as a lower bound on the persistence of the domain. If m = |D|, then pre-computing persistence takes O(m| |) time, and c(j) is precomputed after sorting the intervals by their endpoints. The limiting factor when computing OPT 2 (m) is the time to compute c(j), which is of order m log m. Thus, the overall algorithm runs in O(m log m + (n 2 + m)| |) time taking into account an additional O(n 2 | |) time for computing D.

Figure 2
2Our approach identifies densely interacting domains across scales. (a) Our algorithm discovers domains with mean frequency value for inter-and intra-domain interactions (solid lines) at or better than that of Dixon et al. domains (dotted lines). Each solid line represents domains at different resolution γ in human fibroblast cells. (b) Multiscale domains identified in human fibroblast cells by our dynamic program tend to have higher mean frequency than those of Dixon et al. (distributions are plotted after outliers > μ + 4σ were removed). compute the distance between two sets of domains. To capture the similarities between two domain sets D and D and the inter-domain regions induced by the domains, we construct new derivate sets C and C where C contains all domains d ∈ D as well as non-domain regions (C is computed similarly). To compute entropy H(C) = c i ∈C p i log p i , we define the probability of seeing each interval c i = [a i , b i ] in C as p i = (b i − a i )/L where L is the length of the chromosome. When computing the mutual information I(C, C ) = c i ∈C c j ∈C p ij log[p ij /(p i p j )] between two sets of intervals C and C , we define the joint probability p ij to be |[a i , b i ] ∩[a j , b j ] |/L.

Figure 3
3Domain sizes and count across resolutions. The domain sizes increase and the domain count decreases as the resolution parameter drops. Above: plotted are maximum (red), average (blue), and minimum (green) domain size averaged over all chromosomes for the domains on human fibroblast cells (IMR90). The magenta line shows the average domain size for domains reported by Dixon et al. Below: the number of domains increases for higher values of resolution parameter. The magenta line displays domain count for Dixon et al. We then compute variation of information on these two new sets: VI(C, C ) = H(C) + H(C ) − 2I(C, C ). Chromosome 1, for example, has three visually pronounced groups of resolutions within which domain sets tend to be more similar than across (γ = [0.00-0.20], [0.25-0.70], and [0.75-1.00] -see Figure 4(b)).

Figure 4
4Domain persistence across scales. (a) Domains identified by our algorithm (black) are smaller at higher resolutions and merge to form larger domains at γ close to 0. Visual inspection shows qualitative differences between consensus domains (red) and domains reported by Dixon et al. (green). Data shown for the first 4Mb of chromosome 1. (b) Variation of information for domains identified by our algorithm across different resolutions for chromosome 1 in human fibroblast cells.

Figure 5
5Comparison of Dixon et al.'s domain set with the multiscale consensus set for chromosomes

Figure 6
6Enrichment for chromatin marks and histone modifications in domain boundaries. Enrichment of CTCF binding (a) in IMR90 and (b) in mESC and histone modifications (c), (d) in mESC around domain boundaries for our consensus set of persistent domains (left, blue), and for those identified by Dixon et al. (right, blue). Green lines represent the presence of CTCF at the midpoint of the topological domains. http:

Figure 7
7Domain sets at various resolutions. 10 best optimal and near-optimal solutions for resolutions γ = 0.5, 0.35, 0.15, 0.10 for a portion of human fibroblast chromosome 20 (IMR90). Variations in the domain assignments within a single γ and across resolutions correspond with visually identifiable, hierarchical regions of dense Hi-C interactions. All histone mark tracks were obtained from IMR90 cells. Plotted with WashU EpiGenome

Table 1
1Chromatin marks and histone modification enrichments within and between domainsSignal
Domains ([5])
Domains (Here)
Boundaries ([5])
Boundaries (Here)

CTCF (IMR90)

2050

2234 ≈ 0.92

3092

5365 ≈ 0.58

423

2136 ≈ 0.20

2126

4861 ≈ 0.44

© 2014Filippova et al.;  licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
AcknowledgementsThis work has been partially funded by National Science Foundation (CCF-1256087, CCF-1053918, and EF-0849899) and National Institutes of Health (R21AI085376, R01HG007104). C.K. received support as an Alfred P. Sloan Research Fellow. D.F. is a predoctoral trainee supported by NIH T32 training grant T32 EB009403 as part of the HHMI-NIBIB Interfaces Initiative.Availability and requirementsA C++11 implementation of the algorithms and instructions for compilation and use are available at http://www. cs.cmu.edu/~ckingsf/software/armatus/.Competing interestsThe authors declare that they have no competing interests.
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Sensory epithelia of the fish inner ear in 3D: studied with high-resolution contrast enhanced microCT

Tanja Schulz-Mirbach
Martin Heß
Brian D Metscher
Sensory epithelia of the fish inner ear in 3D: studied with high-resolution contrast enhanced microCT
M E T H O D O L O G Y Open Access
Introduction: While a number of studies have illustrated and analyzed 3D models of inner ears in higher vertebrates, inner ears in fishes have rarely been investigated in 3D, especially with regard to the sensory epithelia of the end organs, the maculae. It has been suggested that the 3D curvature of these maculae may also play an important role in hearing abilities in fishes. We therefore set out to develop a fast and reliable approach for detailed 3D visualization of whole inner ears as well as maculae.Results: High-resolution microCT imaging of black mollies Poecilia sp. (Poeciliidae, Teleostei) and Steatocranus tinanti (Cichlidae, Teleostei) stained with phosphotungstic acid (PTA) resulted in good tissue contrast, enabling us to perform a reliable 3D reconstruction of all three sensory maculae of the inner ears. Comparison with maculae that have been 3D reconstructed based on histological serial sections and phalloidin-stained maculae showed high congruence in overall shape of the maculae studied here.Conclusions: PTA staining and subsequent high-resolution contrast enhanced microCT imaging is a powerful method to obtain 3D models of fish inner ears and maculae in a fast and more reliable manner. Future studies investigating functional morphology, phylogenetic potential of inner ear features, or evolution of hearing and inner ear specialization in fishes may benefit from the use of 3D models of inner ears and maculae.

Introduction

Inner ears in modern bony fishes (Teleostei) are composed of three semicircular canals and three otolithic end organs. Sensory epithelia of the canals, called cristae, are solely overlain by a gelatinous matrix, the cupula. In each of the end organs, the sensory epithelium (macula) is overlain by a massive calcium carbonate biomineralisate, the otolith. Maculae are characterized by orientation patterns of ciliary bundles of the sensory hair cells, i.e. the morphologically and physiologically polarized ciliary bundles form differently oriented groups on the macula. The orientation of a ciliary bundle is determined by the position of its eccentrically placed kinocilium relative to the stereocilia.

Teleosts show several different orientation patterns, and these patterns have been interpreted with regard to or correlated with acoustic abilities (e.g. sound source localization) of fishes (e.g., [1]). For evaluation of patterns, maculae are flattened during preparation for further analysis using scanning electron or confocal microscopes (e.g., [2]). This in turn means that orientation patterns are obtained, shown, and compared between species in a purely two dimensionally way irrespective of the natural curvature of the maculae in the ear. As has already been stated by Platt and Popper (1981) [3], orientation patterns should preferably take into account the three dimensional structure of sensory epithelia. Until now, the reliable reconstruction of maculae in their original 3D curvature was difficult and has to our knowledge only rarely been performed (zebrafish: [4]; Atlantic molly, Poecilia mexicana: [2]). These reconstructions based on histological serial sections were labor-intensive and results were in part uneven as maculae were prone to distortion or artifacts such as disruption during dehydration or embedding procedures.

The non-destructive imaging method of x-ray microcomputed tomography (microCT) was used in a recent study on cichlid ears [5] and in an investigation of 3D utricular and saccular macula in mammals [6]. These studies indicate that a rather fast 3D reconstruction should be possible using microCT. However, iodine stained samples of cichlids [5] did not provide a sufficient contrast to discriminate otolith, otolithic membrane, maculae, and innervating nerve fibers of the VIII th cranial nerve. The aim of our study therefore was to establish a fast and more reliable method to three-dimensionally reconstruct whole inner ears of fishes with special focus on the reconstruction of the 3D curvature of maculae.

Our results indicate that reliable 3D reconstructions of inner ears including otoliths and maculae can be obtained by using high-resolution microCT imaging of specimens stained with phosphotungstic acid.

Methods

Study animals

We chose two species from two different orders within the teleosts, the cyprinodontiform black molly Poecilia sp. (Poeciliidae, live-bearers; four specimens) and the perciform slender lion head cichlid Steatocranus tinanti (Cichlidae; two specimens) from local aquarium stores because inner ear morphology including otoliths and/or sensory epithelia of S. tinanti and of the closely related species Poecilia mexicana, respectively, have been investigated in previous studies [2,5] and could thus be used for comparative purposes.

PTA staining

Specimens were anesthetized and euthanized with an overdose (approx. 0.02%) of MS 222 (ethyl 3-aminobenzoate methanesulfonate; Sigma-Aldrich). Subsequently, scales on the head and in the region of the shoulder girdle were removed and the abdomen was ventrally opened to facilitate penetration of the fixative and the staining solution. Fishes were then fixed in 10% buffered formalin (buffered in 0.1 M cacodylate buffer, pH = 7.2) for up to five days at 4°C. Cacodylate buffer was used instead of phosphate buffer as with the latter phosphate crystals often grow during fixation nearby or on the surface of otoliths (pers. observ. TSM). Based on our previous experience of weak staining of inner ears for microCT with Lugol's solution (aqueous iodine/iodide staining) and on comparative studies on different staining agents for microCT investigations [7,8], we chose phosphotungstic acid (PTA; Sigma-Aldrich P4006) because it has been observed to stain other sensory epithelia well such as olfactory epithelia in fishes ( [7]; unpublished observations). Prior to staining, a microCT scan was performed using the unstained samples still in aqueous fixative solution.

One black molly specimen ( Figure 1A-C) was dehydrated through an ascending ethanol series (30%, 50%, 70%) and then transferred to 0.3% PTA in 70% ethanol for six days. After staining it was returned to 70% ethanol for scanning and storage. The other samples were dehydrated to methanol (50%, 75%, 100%, at least 1 hour each) and were stained in 1% PTA in 100% methanol for four days. Samples were transferred back to methanol for scanning and storage.

To check the effects of dehydration and staining, one individual of each species was scanned as (1) nondehydrated and unstained, (2) dehydrated and unstained, and (3) dehydrated and stained sample to test whether otoliths were partly dissolved or affected (e.g. growth of phosphate crystals) by the staining using PTA in methanol. A first scan was made of each specimen while in the fixative solution. Subsequently, specimens were dehydrated through an ascending methanol series (50%, 75%, 100%; at least one hour per step and overnight in 100%). Prior to staining, a second scan was performed using the unstained and dehydrated sample to check for potential effects of dehydration, i.e. shrinkage and/or distortion. Fishes were then transferred to 1% PTA in 100% methanol for four days. The staining solution was then changed to 100% methanol, in which the sample was scanned.

Testing the dehydration and staining on two spare black molly specimens (33 and 35 mm SL, 5 and 6 mm lateral body thickness) showed that overnight staining (approx. 18 hours) in 1% PTA in methanol was insufficient for full penetration and contrasting of the internal structures, and 48 hours of staining provided some contrast of the peripheral body, but not the central portions (data not shown). Four days of staining proved consistently adequate for fish specimens of this size, and this was adopted a general minimum staining time.

MicroCT

Scans of inner ears with special focus on sensory epithelia were performed with a MicroXCT high-resolution microCT system (Xradia, MicroXCT-200, Zeiss X-Ray Microscopy, Pleasanton, CA) with a tungsten microfocus X-ray source and variable secondary optical magnification. These scans were made with an anode voltage setting of 40 kV at 4-8 W, with an exposure time of 5-8 seconds and 2x2 pixel binning for projection images every 0.25°. Reconstructed image stacks had isotropic voxel sizes of 9.4 μm (unstained), 5.4 μm (stained), or 2.0 μm (stained, high-resolution scan) for the black molly ( Figure 1A-C) and 10 μm (stained) and 4 μm (stained, high-resolution scan) for S. tinanti ( Figure 1D-F).

Scans checking potential artifacts of dehydration or staining were always performed using the same isotropic voxel size of 10 μm for both specimens (one specimen per species) and all three conditions (non-dehydrated and unstained; dehydrated and unstained; dehydrated and stained).

3D reconstructions

3D renderings of inner ears including otoliths, sensory epithelia such as maculae and cristae, and the posterior part of the brain were performed in AMIRA® v. 5.4.1 (Visage Imaging GmbH, Berlin, Germany).

Mainly a threshold-based segmentation was applied and, if necessary this labeling was refined or corrected using the brush tool. This means that after setting a threshold which corresponds a certain grey value, only voxels with values greater than or equal this threshold were assigned to the respective LabelField of the structure of interest (otolith, brain, etc.). For the reconstruction of otoliths and organs, initially every 5th to 10th image was labeled, with subsequent interpolation of structures on intervening images. Using the interpolate function may save time and is important to obtain rather smooth surfaces right away [9].   [9] recommended initial labeling of every third image; as otoliths and most of the organs labeled in our samples changed gradually across slices, we found labeling of every 5th (otoliths, labyrinth, sensory epithelia) to 10th (brain) image sufficient to yield a first good approximation of the respective structure. Subsequently, we checked every image for potential interpolation errors such as still unlabeled portions of the respective structure or labeled regions belonging to another organ. These errors were corrected using the brush tool by labeling or removing erroneously labeled parts where necessary.

Subsequently, every otolith and organ was separated from the 'master' LabelField file into single LabelFields and saved as separate files. In the case of checking potential artifacts of dehydration or staining, the 'master' LabelField was directly used for surface rendering without prior separation of single LabelFields. Surface rendering was performed with the SurfaceGen module. If necessary surfaces of each labeled object were reduced to 100,000 surfaces. This was followed by the smoothing of surfaces using the SmoothSurface module (20 iterations; unconstrained smoothing).

Interactive 3D models

In order to give a full 3D impression of reconstructed structures, we created interactive figures in which all organs can be interactively accessed (free choice of perspective and organ composition) and thus provide a better understanding of the spatial relationship of maculae to each other as well as the amount of their curvature. Interactive 3D pdf models were created using Adobe Acrobat 9 pro extended (Adobe Systems, San Jose, CA, USA) and Deep Exploration 5.5 (right hemisphere) modifying the procedure described by Ruthensteiner and Heß (2008) [10].

Validation of 3D reconstructions

The right inner ear of one black molly and the left inner ear of one S. tinanti were dissected out, semicircular canals were removed, and end organs were captured in (antero-)medial or ventral (utricle of the S. tinanti specimen) views while taking a stack of 8-13 images at different focal planes for each view using a Leica MZ 16 F stereomicroscope equipped with a ProgRes® C5 camera, applying the ProgRes® MAC CapturePro 2.7.6 image capture software (Jenoptik AG, Germany). To combine the in-focus areas of the source images to an extended-focus 2D-image, we created a montage image using the "Do stack" tool in CombineZM (Image Stacking Software by Alan Hadley, UK).

Moreover, we compared the 3D reconstructed macula sacculi and macula lagenae of the specimen studied here with the respective maculae of Poecilia mexicana described in detail in a previous study by TSM and MH [2,5].

Evaluation of ciliary bundle orientation in 2D

To validate 3D reconstructed maculae of S. tinanti and to illustrate one possible application of 3D models of sensory epithelia, we first determined orientation patterns of ciliary bundles of the maculae of S. tinanti in 2D. In the case of the black molly, orientation patterns of ciliary bundles of the closely related P. mexicana were available from a previous study [2]. In both species, the macula utriculi showed the strongest threedimensional curvature. We therefore chose this macula type to project the 2D orientation patterns of ciliary bundles onto the respective 3D models.

Immunohistochemistry: To identify orientation patterns, ciliary bundles of the maculae in eight specimens of S. tinanti (SL: 43-83 mm) were stained according to the method introduced by Lu and Popper (1998) [11] with TRITC-labeled phalloidin (Sigma-Aldrich, St. Louis, MO, U.S.A.) for stereocilia and anti-bovine α-tubulin mouse monoclonal antibodies (Molecular Probes®, Invitrogen, Darmstadt, Germany) and Alexa Fluor 488 conjugated anti-mouse secondary antibodies (Molecular Probes®, Eugene, OR, U.S.A.) for kinocilia. Prior to staining, the fresh heads were fixed for 1-2 hours in 10% buffered (0.1 M phosphate buffer) formalin solution at room temperature. Inner ears were dissected out in fixative, otoliths removed, and then sensory epithelia were washed four times in 0.1 M phosphate buffer with 0.01% sodium azide at 20 minute intervals at room temperature on a slowly moving shaker. All further steps (unless specified otherwise) were performed at room temperature on a shaker, and after every staining/antibody step tissue samples were washed four times with phosphate buffer with sodium azide at 20 minute intervals. Inner ears were incubated in blocking solution for 1 h and then incubated overnight in anti-bovine α-tubulin mouse monoclonal antibodies (1:200 dilution in 0.1 M phosphate buffer with sodium azide). Sensory epithelia were incubated in Alexa Fluor 488 anti-mouse antibodies (1:200 dilution in 0.1 M phosphate buffer) for 1.5 h at 37°C and in TRITC-labeled phalloidin (1:100 dilution in 0.1 M phosphate buffer) for 4 to 5 h. After the staining procedure, samples were stored at 4°C for one day, after which the sensory epithelia were mounted on a slide with an anti-fading medium, VectaShield® (Vector Laboratories). In this medium, the sensory epithelia were carefully flattened and then covered with a cover slip, sealed with nail polish, and stored at 4°C.

Confocal imaging: Samples were investigated with a Leica TCS SP2 inverse confocal laser scanning microscope (CLSM) using a Leica HCX PL APO UV 40x oil dipping objective (NA = 1.25) and with the 488 nm argon-gas-laser line and the 543 nm He-Ne laser. Overlapping image stacks of each macula were photographed at a z-step size of 1 μm and a pixel size of 183 nm x 183 nm. The image stacks were reduced to one image by applying the brightest point projection tool in Image J v. 1.46r. Brightest point projected images were used for creating one map of the stained stereocilia of each macula in Adobe Photoshop CS4®. Orientations of ciliary bundles were determined as described by Lu and Popper (1998) [11].

Projection of 2D orientation patterns on the 3D models of the maculae

In AMIRA® v. 5.4.1 created and rendered surfaces were opened in Adobe Photoshop CS4® Extended as wavefront (obj) files. Then arrows indicating the orientation of groups of ciliary bundles were drawn on the dorsal face of the 3D models of the macula utriculi of S. tinanti and Poecilia sp., respectively.

Results and discussion

Effects of dehydration and staining

The overlays in Figure 2 show that dehydration and staining led to a discernible shift of otoliths in the black molly mainly towards the brain (Figure 2A-B). Dehydration resulted in an inward tilt of saccular and lagenar otoliths whereas the utricular otoliths were still in place ( Figure 2A). Staining seemed to affect the utricular otoliths that both shifted slightly into right lateral position ( Figure 2B). In S. tinanti effects of dehydration and staining were weak resulting in a faint posterior shift of utricular and lagenar otoliths ( Figure 2C-D). Thus, PTA staining seems to affect inner ears to different amounts depending on the fish species under study. The stronger effect in the black molly may be explained by the fact that the bony lamella partly surrounding the medial portions of the saccule and lagena in S. tinanti is almost completely absent (see Figure 3A). Such effects must be taken into account when interpreting the spatial relationship of the maculae to each other; while it is unlikely that the curvature of the maculae themselves is affected because the overlying otoliths which stabilize the maculae displayed the same morphology irrespective from the treatment applied ( Figures 1A vs.   High-resolution contrast enhanced microCT imaging allows accurate reconstruction of the maculae in the black molly. Accuracy of reconstruction of the macula lagenae was especially improved by using the image stack scanned with higher resolution (B vs. A). Comparison with the dissected right ear (D) shows that end organs, maculae (especially the macula sacculi), and otoliths were reliably reconstructed. Note that in (B) the semicircular canals and the utricle are incompletely reconstructed because the field of view during scanning had to be restricted to achieve the higher resolution. For a better comparison with (B), semicircular canals including the ampullae were removed from the iodine stained, dissected ear (D). (C) shows the reconstructed otoliths of the specimen prior to staining. c, cristae of the anterior (ca, green), horizontal (ch, yellow), and posterior (cp, blue) semicircular canals; lot, lagenar otolith (yellow); ml, macula lagenae (dark brown); ms, macula sacculi (yellow orange); mu, macula utriculi (light brown); sot, saccular otolith (purple); uot, utricular otolith (red). Iodine stained otoliths all have a yellowish appearance while maculae and the overlying as well as surrounding otolithic membranes are orange red. Scale bars, 500 μm. only bone, pharyngeal teeth and otoliths can easily be identified while after staining (C, F) diverse other tissues and organs such as brain, muscles, and the membranous labyrinth are now clearly visible. All scans were performed using the same isotropic voxel size of 10 μm for both specimens and all three conditions. Scale bar, 1 mm. samples allow the identification of diverse tissues, e.g. brain, muscles, and the membranous labyrinth (shown by the saccule and parts of the semicircular canals) ( Figure 5C, F).

Reliability of 3D reconstructed maculae

PTA staining allowed for a good 3D reconstruction of sensory epithelia, especially regarding the macula sacculi and the macula utriculi, when comparing with the maculae of the dissected inner ears (black molly: Figure 4A-B vs. D; S. tinanti: Figure 6A vs. B-C). In S. tinanti, the 3D reconstructed maculae showed high congruence with those stained with TRITC-labeled phalloidin ( Figure 6A vs. D-F). The result was refined and improved in the black molly using higher resolution images for the reconstruction of the macula lagenae ( Figure 4A vs. B) and of the lateral portion of the macula utriculi, namely the lacinia (Additional file 1, inner ear in lateral view). A comparison between the reconstructed macula sacculi of the black molly (Poecilia sp.) and that of P. mexicana (studied by Schulz-Mirbach et al. 2011 [2]) showed several similarities such as the dorsal bulge in the anterior portion of the macula and the overall shape of the anteriormost part ( Figure 7A, C) that is not overlain by the saccular otolith. The macula lagenae was also similar in its overall shape and curvature to the maculae lagenae from P. mexicana; the ventral portion, however, was distinctly narrower in the herein reconstructed macula ( Figure 7B, D-E).

In order to derive reliable results for the 3D reconstruction of the maculae, it is necessary to incorporate prior knowledge of the shape of sensory epithelia and the inner ear anatomy of the species under study based on dissections or scanning electron microscopic investigations. Moreover, we carried out macula labeling in the 3D images with the aid of the borders of the furrows of the otolith housing the macula (in the case of the saccular and lagenar otoliths; Figure 3A-B), in part by using otolith dimensions (utricular otolith), and sites of innervation by the VIII th cranial nerve. Although histological serial sections have the advantage that single cells can be identified, determination of macula delimitations is still difficult because of the smooth transition between macula and nonsensory epithelium ( Figure 3C). In addition, as otoliths have to be dissolved during sample preparation for histology, the organic remains of the otolith can only in part be used as guideline for the identification of macula dimensions. In the case of the macula utriculi, delimitations of this sensory epithelium were easier to identify (Figure 8).

Projection of 2D ciliary bundle orientation patterns on the 3D models of the maculae

In both species the bowl-shaped macula utriculi and its laterally situated lacinia shows the advantage of the projection of the 2D orientation pattern of ciliary bundles on the 3D models. Orientation patterns can be studied from different perspectives following the 3D curvature of the macula (Figure 9). 3D models of maculae as obtained by our approach and subsequent projection of 2D evaluated orientation patterns of ciliary bundles of sensory hair cells onto the 3D reconstructed maculae (see Figure 9), may be especially Figure 7 Validation of the 3D reconstructed maculae based on microCT imaging. 3D reconstructed macula sacculi (A) and macula lagenae (B) of the herein studied black molly are compared with a corresponding reconstruction from the Atlantic molly Poecilia mexicana in a previous study [2]. Reconstructions of the maculae of P. mexicana (C-E) based on histological serial sections (thickness of sections: 1 μm). The shape of the respective macula types of black molly and Atlantic molly show a high degree of similarity, especially with regard to the macula sacculi, indicating the reliability of 3D reconstructed sensory epithelia based on microCT imaging. Similar features of the maculae sacculi are marked by the arrow and circle. The yellow area in (C) represents reconstructed non-sensory epithelium surrounding the macula sacculi. All maculae are shown in lateral view with their dorsal side up and anterior to the right. Scale bars, 100 μm. important in comparative studies investigating several species of the same group with regard to their inner ear morphology and hearing abilities. Buran et al. (2005) [12] found distinctly out-of-plane curved maculae lagenae in one out of four studied elopomorph species. Ramcharitar et al. (2004) [13] reported strongly curved maculae sacculi in a sciaenid species (Bairdiella chrysoura); the authors [13] assumed that this may have an impact on the hearing abilities. Future application of microCT imaging on stained specimens in such studies will therefore have an impact in two ways: (i) peculiarities such as strongly curved maculae can be illustrated and compared qualitatively in 3D by the authors and the readers using interactive 3D models, and (ii) 3D datasets offer the possibility for a quantification of the amount of curvature of maculae, evaluation of the angle between the macula or otoliths to the sagittal plane, or to perform other 3D morphometrics (e.g., [14,15]), or even functional modeling of the sensory organs.

Further future applications

So far, PTA contrasting for microCT has less frequently been used compared to iodine-based stainings for example. PTA staining provided good results for studying vertebrate  embryos and thus is of great value for developmental studies [16,17].

Once the specimen is stained, microCT scans can be performed using different resolutions. Scans at "lower" resolutions (ca. 5-10 μm voxel sizes) may help to gain additional insights for example on the position and distance of inner ears to the swim bladder which is an important aspect in fish hearing; a small distance or even a connection between swim bladder and inner ears is likely to enhance auditory abilities (for an overview see [18]). High-resolution scans on the same specimen then allow for deciphering details of inner ear anatomy that yield not only information on the 3D curvature of maculae, but also on the in situ position and orientation of the maculae relative to each other and on the amount of overlap between macula and the corresponding otolith (see also Additional file 1, Additional file 2). The latter information may be of particular interest because parts of the macula not overlain by the otolith are hypothesized to be stimulated in a different way than the overlain regions, which is suggested to have physiological implications for hearing in fishes such as sound source localization [19].

Finally, as the method produces highly informative datasets in a rather short time, these can be used by scientists interested in the diversity of inner ear morphology in fishes asking taxonomical, phylogenetic, or ecomorphological questions. Evangelista et al. (2010) [20] have already performed a quantitative comparison of inner ears in sharks and rays, concluding that variation in ears could best be explained by taking into account phylogeny as well as feeding strategy; however, the study was based on 2D measurements. Measurements taken from 3D models of inner ears comparing different taxa may elucidate certain specializations in inner ear morphology and hearing abilities found in some species. In phylogenetic studies on inner ears in primates, such 3D morphometric analyses based on CT imaging have already successfully been applied (e.g., [21,22]).

Successful 3D reconstruction of fish inner ears has recently been performed using thin-sheet laser imaging microscopy (TSLIM) [23] (see also [24,25]). Though TSLIM provides excellent resolution similar to histological sections, a decalcification step during sample preparation is necessary. In the case of fish inner ears this means that otoliths have to be dissolved, i.e. information about otolith morphology and the relationship between otoliths and corresponding maculae is lost. A combination of both non-destructive methods [24], however, might further improve the success of 3D reconstruction of fish ears and their components.

Conclusions

Our study shows that high-resolution contrast enhanced microCT imaging of PTA stained fish provides a powerful method to obtain reliable 3D images of fish inner ears including the maculae in a less labor-intensive way compared to most previous studies illustrating fish inner ears and/or maculae in 3D based on histological methods [2,4,26]. We suggest that future studies will benefit from using such 3D models of fish inner ears and maculae in comparative investigations focusing on functional morphology, hearing specializations and morphometric analyses. As dehydration and staining can differently affect inner ears of different species, any analysis of inner ears in 3D should include an investigation of the effects on the species under study.

Additional files

Additional file 1: Voxel size in MicroCT imaging considerably affects accuracy of the 3D reconstruction of the lacinia (B: 2 μm isotropic vs. A: 5.4 μm isotropic). The white arrow indicates the reconstructed lacinia of the macula utriculi. Brain (orange); c, cristae of the anterior (ca, green), horizontal (ch, yellow), and posterior (cp, blue) semicircular canals; lot, lagenar otolith (yellow); mu, macula utriculi (light brown); sot, saccular otolith (purple); uot, utricular otolith (red). Scale bars, 500 μm. The interactive 3D models can be accessed by clicking onto the figures (Adobe Reader Version 7 or higher re-quired). Rotate model: drag with left mouse button pressed; shift model: same action + ctrl; zoom: use mouse wheel (or change default action for left mouse button). For selection or deselection (or changed transparency) of components in the model tree, switch between prefab views or change surface visualization (e.g. lighting, render mode, crop etc.). Deactivate 3D content via context menu (right mouse click).

Additional file 2: Interactive 3D model of the left inner ear of Steatocranus tinanti. c, cristae of the anterior (ca, green), horizontal (ch, yellow), and posterior (cp, blue) semicircular canals; lot, lagenar otolith (yellow); ml, macula lagenae (dark brown); ms, macula sacculi (yellow orange); mu, macula utriculi (light brown); sot, saccular otolith (purple); uot, utricular otolith (red). Scale bars, 1 mm. For activation of the inactive model see Additional file 1.

Figure 1
1Comparison of volume renderings based on tomographic reconstructions of the posterior part of the fish head of a black molly (A-C) and S. tinanti (D-F), including the ears of the same specimens before (A, D) and after phosphotungstic acid staining (B-C, E-F). Without contrast enhancement, only bones and otoliths can be visualized (A, D). Phosphotungstic acid distinctly enhances tissue x-ray contrast enabling 3D reconstructions of the inner ears including the sensory epithelia (maculae and cristae) (C, F). Brain (orange): Ce, cerebellum; dM, dorsal medulla; Hy, hypophysis; H, hypothalamus; TO, tectum opticum; ears (transparent blue): c, cristae (green, yellow, blue); lot, lagenar otolith (yellow); sot, saccular otolith (purple); uot, utricular otolith (red). Scale bars, 1 mm.

Figure 2
2Effects of dehydration and staining on inner ears illustrated by the position of the otoliths. In dorsal view, 3D reconstructed utricular (red), saccular (purple), and lagenar otoliths (yellow) show a discernible shift in the black molly (A-B) provoked by dehydration and staining while in S. tinanti (C-D) the treatment effects are small. Scale bars, 1 mm.

Figure 3
3Transverse tomographic (A-B) and histological sections (C) displaying the Poecilia saccule, its otolith and the corresponding macula. The histological section (C) is from the inner ear of Poecilia mexicana. The higher resolution tomographic section in (B) shows that the nerve (VIII), otolith, and macula of the saccule could effectively be discriminated. For identification of the delimitations of the macula, the clearly visible sulcus of the otolith in the tomographic sections could be used; the sulcus is the furrow on the medial face of the saccular otolith housing the macula sacculi. Despite better discrimination of the macula from overlying otolithic membrane and the underlying basal lamina in the histological section, delimitations are still difficult to identify because of the gradual transition of the macula into non-sensory epithelium and the few organic remains of the dissolved otolith. In the insert in (B) and in (C) the sulcus is indicated by a dotted line and the macula is red labeled. Ce, cerebellum; ms, macula sacculi; VIII, part of the VIII th cranial nerve innervating the macula sacculi. Scale bars, 500 μm.

B-C and D vs. E-F; 2A, C vs. B, D; 4A-B vs. C). Moreover, all reconstructed maculae of the black molly and S. tinanti showed a continuous undistorted curvature (Additional file 1, Additional file 2). A comparison of unstained, unstained and dehydrated vs. PTA stained tomographic sections displays a clear enhancement of the tissue contrast in both species when performing the staining. While in the unstained sections only bone, pharyngeal teeth and otoliths are clearly visible (Figure 5A-B, D-E), the sections of the PTA-stained

Figure 4
4Figure 4 High-resolution contrast enhanced microCT imaging allows accurate reconstruction of the maculae in the black molly. Accuracy of reconstruction of the macula lagenae was especially improved by using the image stack scanned with higher resolution (B vs. A). Comparison with the dissected right ear (D) shows that end organs, maculae (especially the macula sacculi), and otoliths were reliably reconstructed. Note that in (B) the semicircular canals and the utricle are incompletely reconstructed because the field of view during scanning had to be restricted to achieve the higher resolution. For a better comparison with (B), semicircular canals including the ampullae were removed from the iodine stained, dissected ear (D). (C) shows the reconstructed otoliths of the specimen prior to staining. c, cristae of the anterior (ca, green), horizontal (ch, yellow), and posterior (cp, blue) semicircular canals; lot, lagenar otolith (yellow); ml, macula lagenae (dark brown); ms, macula sacculi (yellow orange); mu, macula utriculi (light brown); sot, saccular otolith (purple); uot, utricular otolith (red). Iodine stained otoliths all have a yellowish appearance while maculae and the overlying as well as surrounding otolithic membranes are orange red. Scale bars, 500 μm.

Figure 5
5Enhancement of tissue contrast by performing PTA staining. In transverse tomographic sections of the unstained (A, D) or unstained and dehydrated samples (B, E) of both species (A-C, black molly; D-F, S. tinanti)

Figure 6
6High-resolution contrast enhanced microCT imaging allows accurate reconstruction of the maculae in S. tinanti. Comparison with the dissected left saccule, lagena (B; anteromedial view), and the utricle (C; ventral view) and the phalloidin-stained maculae (D-F) shows that end organs, maculae (especially the macula utriculi), and otoliths were reliably reconstructed (A). For a better comparison, semicircular canals including the ampullae were removed from the iodine stained, dissected saccule and lagena (B). ca, anterior semicircular canal; ch, horizontal semicircular canal; cp, posterior semicircular canal; lot, lagenar otolith; ml, macula lagenae; ms, macula sacculi; mu, macula utriculi; sot, saccular otolith; uot, utricular otolith.(A-B): Scale bars, 500 μm; (C-F): Scale bars, 250 μm.

Figure 9
9Projection of the 2D orientation patterns of ciliary bundles onto the 3D models of the macula utriculi. (A-B) Macula utriculi of S. tinanti in dorsal (A) and medial (B) views. (C) Macula utriculi of the black molly in medial view. Especially the strongly curved lacinia illustrates the value of orientation patterns shown in 3D. a, anterior; d, dorsal; l, lateral.

Figure 8
8Transverse tomographic section displaying the utricle, its otolith, and the corresponding macula of S. tinanti. In (A) the section is shown without labeling and in (B) the same section is illustrated indicating the delimitations of the macula utriculi. The macula utriculi can clearly be distinguished from the part of the VIII th nerve innervating the macula. Scale bar, 500 μm.
http://www.frontiersinzoology.com/content/10/1/63
AcknowledgementsWe thank Prof. Dr. I. Lichtscheidl (CIUS, Core Facility Cell Imaging and Ultrastructure Reesearch, Vienna, Austria) and her working group for their support with confocal microscopy and Prof. Dr. F. Ladich (Department of Behavioural Biology, Vienna, Austria) for providing the specimens of S. tinanti. This study was funded by the German Academic Exchange Service (TSM).Competing interestsThe authors declare that they have no competing interests.Authors' contributions TSM, MH, and BM conceived and designed the study. BM carried out the microCT imaging. TSM performed the 3D reconstructions and dissections. MH created the interactive 3D models. All three authors equally contributed to and wrote the manuscript. All authors read and approved the final manuscript.
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Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color figure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution. Schulz-Mirbach, Frontiers in Zoology. 1063Sensory epithelia of the fish inner ear in 3D: studied with high-resolution contrast enhanced microCT. Submit your manuscript at www.biomedcentral.com/submitCite this article as: Schulz-Mirbach et al.: Sensory epithelia of the fish inner ear in 3D: studied with high-resolution contrast enhanced microCT. Frontiers in Zoology 2013 10:63. Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color figure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit