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Computer aided alignment and quantitative 4D structuralplasticity analysis of neurons

Ping-Chang Lee1,2, Hai-yan He1,3, Chih-Yang Lin4, Yu-Tai Ching2, and Hollis T. Cline3

2Department of Computer Science, National Chiao Tung University, Hsin Chu, Taiwan3The Dorris Neuroscience Center, The Scripps Research Institute, La Jolla, CA, USA4Chung Hua University, Department of Bioinformatics, Hsinchu, Taiwan

AbstractThe rapid development of microscopic imaging techniques has greatly facilitated time-lapseimaging of neuronal morphology. However, analysis of structural dynamics in the vast amount of4-Dimensional data generated by in vivo or ex vivo time-lapse imaging still relies heavily onmanual comparison, which is not only laborious, but also introduces errors and discrepanciesbetween individual researchers and greatly limits the research pace. Here we present a supervised4D Structural Plasticity Analysis (4D SPA) computer method to align and match 3-Dimensionalneuronal structures across different time points on a semi-automated basis. We demonstrate 2applications of the method to analyze time-lapse data showing gross morphological changes indendritic arbor morphology and to identify the distribution and types of branch dynamics seen in aseries of time-lapse images. Analysis of the dynamic changes of neuronal structure can be donemuch faster and with greatly improved consistency and reliability with the 4D SPA supervisedcomputer program. Users can format the neuronal reconstruction data to be used for this analysis.We provide file converters for Neurolucida and Imaris users. The program and user manual arepublically assessable and operate through a graphical user interface on Windows and Mac OSX.

1. INTRODUCTIONThe structures of neuronal dendrites and axons proscribe the connectivity neurons makewithin circuits and are therefore critical determinants of circuit function and plasticity(Halavi, Hamilton et al. 2012). Axonal and dendritic arbor structures change dramaticallyover time under natural circumstances, for instance, during development, aging, as a resultof circuit plasticity or disease, and under experimental conditions, such as sensorydeprivation or enhanced activity. Technical advances in vivo neuronal labeling methods andin vivo microscopy techniques, such as confocal and multi-photon laser scanning (Helmchenand Denk 2005; Wilt, Burns et al. 2009), have greatly facilitated imaging and acquisition oftime-lapse data of changes in neuronal structure over time. These data have demonstratedthat dynamic changes in neuronal structure can occur over the time-course of minutes todays to months (Cline 1999; Chen, Lin et al. 2011). Although 3 dimensional reconstructionof neuronal structure can be accomplished with computer assistance, analysis of dynamicstructural changes in time-lapse image data sets remains a great challenge because of the

1These authors contributed equally.Information Sharing AgreementThe software and user manual described in this work will be publicly accessible online at http://people.cs.nctu.edu.tw/~percycat/4DSPA/The authors declare that they have no conflict of interest.

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http://people.cs.nctu.edu.tw/~percycat/4DSPA/

difficulty of comparing two complex 3D neuronal arbors required to identify structuraldifferences between them (He and Cline 2011).

To analyze detailed changes of 3D neuronal structures over time is a difficult task, partlybecause cumulative changes in the locations of individual branches can occur as a result ofmodest 3D shifts in positions or orientations of lower order branches, or because minordifferences in the position of the animal during in vivo imaging may shift the orientation ofthe neuron in the image. Most 4D analysis of neuronal structural dynamics from time-lapseimaging data is done by manual comparison of 2D or 3D reconstructions. To analyze thechanges between two 3D reconstructions of neurons manually takes an expert hours to alignand match the two reconstructed 3D complete dendritic arbor structures. Manualidentification of the numbers and distribution of dynamic branches, categorized as retracted,newly added, transient, and stable, over a set of multiple images (Haas, Li et al. 2006;Bestman and Cline 2009) is laborious and greatly slows down research in the field (He andCline 2011). A computer method that assists in comparing 3D neuronal structures wouldaddress the weaknesses of manual analysis.

Recent work reported that computer-assisted automatic analysis of neuronal structures fromtime-lapse images could be achieved in cultured neurons (Al-Kofahi, Radke et al. 2006).This advance was facilitated by the 2D structure of cultured neurons and their relativelysimple neuronal morphology. In this paper, we present a supervised 4D neuronal StructuralPlasticity Analysis (4D SPA) computer method that computes precise changes in thepositions and lengths of all neuronal branches in the arbor between two images or time-points and presents the data as an image superimposed on the 3D reconstruction of theneuron. The method is based on the identification of stable branch points, or ‘significantpoints’ in a pair of images, which are used as reference points to facilitate the alignment ofthe dendritic structures. We then decompose the neuronal arbor into subsets of branches, orsubtrees, with each branch defined as the process extending from a significant point to thebranch tip. Similarities between two branches at sequential time-points were then calculated,generating a suggestion list of potentially matched branches, which was then evaluated bythe analyst. This method takes advantage of both the computer algorithm and humanexpertise to significantly reduce the time to identify matched branches in the sequentialimages and increases the reliability of the analysis results.

2. METHODS2.1 Data Preparation

Neurons from the optic tectum of Xenopus laevis tadpoles were labeled by expression ofGFP (green fluorescent protein) and time-lapse images were acquired with a two-photonlaser-scanning microscope, at either 4 hour or 24 hour intervals. Reconstruction of the entiredendritic arbor of the neurons was done by the computer-aided filament tracing function inthe 3D image analysis software Imaris (Bitplane, USA) and the full filament data set wasexported and converted into a text file for dynamic analysis using the 4D SPA method. Anexample of a 3D image of a GFP-labeled neuron and the reconstructed dendritic arbor isshown in online resource Video 1. In the input txt file, the branches are represented as datapoints defined by their 3D location (coordinates) and is organized block-wisely. Each blockstarts with a line defining the branch index (P #) and the number of nodes in that branch (N#). The first point is the starting point of the branch, either the soma or the branching point,and the last point in the block is the tip. The first point in the first block of the file representsthe soma position. The detailed description of the input data format can be found in themanual of the 4D SPA (available through supplemental online resources). To facilitate usageof the SPA program, we made converting tools for reconstructed filament files generated

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from two of the most commonly used reconstruction software programs (Imaris andNeurolucida), which are also available through supplemental online resources.

2.2 Computer-aided comparison MethodA flow diagram of the program is shown in figure 1. The traced neuron, denoted N, ispresented as a three-dimensional tree rooted at the soma, s. The tree structure data iscomposed of a series of vertices. The vertices in N are categorized into 3 sets: tips, regularpoints and branch points. The tips are the unbranched ends of branches in N denoted ti, 1 ≤ i≤ n, where n is the number of tips. The branch points are vertices that have out degree,number of points directly connected to this point on the path away from the soma, greaterthan 1. All the other vertices are regular points in the neuronal structure. They have outdegree equal to 1.

Branches are defined as following: For a pair of points u and v among all points in N, ifthere is a direct path b = < u, p1, p2,…,pk, v >, in which p1, p2,…,pk, are points in between u

and v, the path length . We also use <u,v> to denote the path b.If u is the soma or a branch point and v is a tip, then the path b is called a “branch” in N. Toestimate the length of each branch, which will be used to compute the similarity between apair of branches in two images, we resample points on the path between the branch pointand the branch tip by arbitrarily counting the length between neighboring points as 1.

To facilitate comparison of the reconstructions of neuronal trees imaged at different timepoints, we need to define reference points or ‘significant’ points. Within the neuronal tree,each branch point can be considered as the root of a subtree (Figure 2a). The size of asubtree is defined as the number of branch tips in that subtree. The “average tree size” ofneuron N is then calculated by dividing the sum of the size of all subtrees within neuron Nby the total number of branch points. A branch point, v, is defined as a “significant” point if1. The size of any subtree, rooted at v is greater than the average tree size of the neuron; and2. One of the following criteria is also satisfied:

1. There are more than 2 subtrees rooted at v.

2. There are only two subtrees rooted at v and the sizes of both subtrees are greaterthan 3.

Empirically, significant points defined above are usually stable over time and would exist inthe dendritic trees of the same neuron at two consecutive time-points, thus can be used asreference points for alignment of the arbors (Figure 2). In the following matching process,we firstly consider the branches emanating from a significant branch point bi to a tip tiwhere bi is the closest significant point to ti on the path from ti to the soma. If there is nosignificant branch point along the path from ti to the soma, then the soma is used as thestarting point.

2.3 Branch attributesEach branch b = < bi, ti > has 3 attributes, the length, L(b), the parent, and the position. Theparent is either itself (the default value) or another branch b’ = < bj, tj > that b attaches to.The position of b is deemed as undefined if the parent is itself. If the parent of b is b’, thenthe position of branch b is defined as L(< bj, bi >) /L(b′). The parent and position of b aredenoted as parent (b) and position (b) respectively. As mentioned earlier, the default parentof each branch is itself at the beginning of the matching process. During the matchingprocess, the starting points of some branches change to the closest branch point or the somaif no other branch point is available along its path and their parents are revised accordingly.

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To compare a pair of branches between two images, the attributes, branch length, parentbranch and position, are compared in a pre- screening step (the detailed pre-screening step isdepicted in the following section). The similarity of the branches is taken into considerationonly if the pair of branches pass the pre-screening. The similarity between two shapes iscalculated by Eq. (1)

(1)

where R is a rotation matrix and v is a translation vector. The number of points on b1 is n.The value of f(b1, b2) goes up when similarity goes down. The first term of Eq. (1) can besolved by the iterative closest pair method (Besl and MaKay 1992).

2.4 Pairwise Matching AnalysisFor two reconstructions of the same neuron traced from image stacks acquired at differenttime-points, the first one is designated N1 and the second one is designated N2, inchronological order. During the matching process, branches in N1 are categorized into 3types, remaining, retracted, and undefined. A branch in N1 is remaining if there is a matchedbranch in N2. A branch is retracted if there is no matched branch in N2. An undefinedbranch is a branch that has not been processed yet. Similarly, the branches in N2 are alsocharacterized into 3 types. The remaining and the undefined are the same as defined in N1.There is no retracted branch category in N2, instead, there are newly added branches, whichrefer to branches in N2 that do not have a match in N1.

Each iteration of the matching process consists of the following steps:

1. The longest undefined branch, B in N1 is chosen.

2. For each undefined branch, b̃ = < bj, tj > in N2, we check its attributes. b̃ is in thecandidate short list if it satisfied all criteria listed below:

a. Both B and b̃ are undefined or parent(B) and parent(b̃) are matched pair;

b.

c. position(B) - position(b̃) < β.

α sets the upper limit of variation allowed in the branch length for the two branchesbeing compared. β accounts for the largest variation allowed in the branch positionon the parent branch. Both parameters help take into account the difference instructure caused by neuronal growth over the imaging time interval. The values aredecided empirically and could be adjusted to optimize the program for specificapplications. In all of our experiments we used the default setting set α = 2.5 and β= 0.4.

The similarity (Eq. 1) between B and all branches in the candidate short list arecalculated. The default setting of the length of the suggested list is limited to five soat most, the most similar five branches will be included in the list. An example ofthe candidate branches listed in the suggest list is shown in figure 1B, B’, C and C’.

3. The analyst then uses the suggestion list to assign a matching branch for B. If theanalyst decides that B has a matching branch b̃ in the candidate short list, B and b̃are moved into the remaining category. If the analyst decides that there is nomatching branch for B, then B is assigned to the ‘retracted’ category. Based on theassignment of branches to categories, the attributes of some branches in both N1

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and N2 are updated. The following is the update procedure for the branches in N1

and N2:

a. If L(B) < γ, then the procedure stops. Here, γ stands for the minimumlength (measuring from the closest branch point to the tip) a branch musthave to be used for morphology comparison. This is because very shortbranches usually do not have many unique morphological features andcould be easily confused with other non-matching short branches. Thevalue of γ was determined empirically. During the course of ourexperiments, we set γ = 15 µm

b. If b̃ is categorized as remaining or retracted, no further process is needed.

c. Assuming an undefined branch, b̃ = < bk, tk > in N1 has a common pathwith B and the conjunction point of B and b̃ is c̃, then b̃'s parent andstarting point become B and c̃ respectively.

4. If there are no more undefined branches in N1, then all of the remaining undefinedbranches in N2 are changed to newly added and the process terminates. Otherwise,iteration restarts from step 1.

A graphic-user interface (GUI) software system was implemented to help the analyst tocomplete the matching process. Through the GUI, the analyst can decide the type of branchand set up parameters for the matching process.

2.5 Dynamics Branch AnalysisPairwise analysis of sequential images in a longer time-lapse data set requires that brancheshave unique identifiers that are maintained through the image series. Initially, the branchesare assigned an identifier or an “index” according to their length in descending order. Afterthe analyst confirms all the matching branch pairs in N1 and N2, the 4D SPA programadjusts the indices so that matching branches are assigned with the same identifier. Tocombine the multiple pairwise alignment results in data sets with more than 2 images, anextra step is added at the end of each comparison to synchronize the branch indices. Thisway, we can easily identify each individual branch in every time-point and analyze thedynamic changes on that particular branch over time.

3. RESULTSTen data sets of reconstructed full dendritic arbor were used in our experiments. The analystwas allowed to use two data sets to get familiar with the 4D SPA program and then recordedthe time to analyze the remaining eight data sets.

3.1 Pairwise AnalysisIn this analysis, N1 and N2 are two reconstructed neuronal arbors imaged at consecutivetime-points. Typically, for manual evaluation of structural dynamics in two images, theanalyst identifies a branch in N1, reviews all un-matched branches in N2, and selects the bestmatched one. This process is extremely time-consuming and subjective. Our programgenerates a reliable short-list of suggested matching branch candidates in N2 for everybranch in N1 based on the algorithm described above, which should greatly reduce theprocessing time. In addition, use of the same algorithm to generate the short list of suggestedmatching branch candidates helps to maintain consistent criteria to identify candidatematches and reduces human errors.

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We quantified the reliability of the algorithm by calculating the hit ratio. For a branch in N1,the 4D SPA method generates a list of suggested matching branches in N2. We get a hit ifone of the following two criteria is met.

1. The user decided there is no match, and the branch is identified as retracted, or

2. The user selected a matched branch from the suggested short list.

The hit ratio is calculated as the percentage of hits relative to the total number of branches inN1, which measures the accuracy of the suggested match list. The analysis result for eachdata set is listed in Table 1. The mean number of branches on the suggested match list was2.78 (Table 1). The average hit ratio was 85.8 ± 8.4 % (Table 1). Note that dataset No5,which showed the highest hit ratio, is also the most complicated dataset with the largest totaldendritic branch tip number. This indicates that the reliability of this matching program isnot compromised by increased complexity of the neuronal structure. A pair-wise alignmentresult of representative dataset number 6 is shown in online resource Video 2. In this video,each frame displays both N1 and N2, and only one matching pair, which had been confirmedby the analyst, is rendered in red. Among all the data sets, data set number 9 had the lowesthit ratio (70.3%) and the longest average list of the suggested matches. This is due to thehigh similarity between subtrees emanating from the same parent branch in N1 and N2 (Fig.3). This combination (similarity in both subtree structure and the parent branch) tends tomislead the algorithm, thus might require more human intervention to locate the correctmatching branch. The average time to align a pair of complete dendritic arbors was about 43minutes (Table 1). In the worst case (dataset No5), it took 111 minutes to process a set ofdata. Given that this time includes both the time it takes by the program to do the calculationas well as the time it takes the analyst to validate the matches, it is understandable that thetime increases with increased complexity of the dendritic arbor. Without the help of 4DSPA, it usually takes hours for an expert analyst to process a paired data set, depending onthe complexity of the arbor and the magnitude of change between the two neuronalstructures (He and Cline 2011).

3.2 Dynamic Branch AnalysisThis method can be easily applied to analyze data sets consisting of multiple time-points inwhich N1 is aligned with N2, then N2 is aligned with N3, …, and so on. Analysis of data setswith more than 2 time-points provides detailed analysis of branch dynamics, and oftenreveals important information about the underlying mechanisms of structural plasticity thatare lost when long-interval data points are compared (Haas, Li et al. 2006; Bestman andCline 2008; Chiu, Chen et al. 2008). In the analysis of branch dynamics, branches arecategorized as stable, newly added, retracted or transient. A stable branch is a branch that ispresent at all time-points. A retracted branch is a branch that is present at the first time-pointbut is lost at a later time-point.

A ‘newly added’ branch is a branch that does not exist at the first time-point but appearslater and remains in place until the last time-point. The ‘added’ branch category includesthose that appear at the last time point. A transient branch is a branch that appears at a time-point after the first time-point and is then retracted by the last time-point. To better visualizethe alignment results and branch dynamics, we implemented a color-coding system for thefinal display of the matching results. The stable branches are coded black, the retractedbranches are blue, the transient branches are magenta, and the newly added branches aregreen (Fig 4). This implementation facilitates the identification of qualitative changes inbranch dynamics as well as possible spatial patterns of dynamic changes in the dendriticarbor over time. The results of the dynamic analysis can be exported as a spreadsheet forfurther analysis (Table 2). In addition, the matched neuronal filament data can be saved astxt files with the categorization information for each branch and used for further analysis.

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4. DISCUSSIONWe present a method to provide computer assisted 4D structural plasticity analysis (4DSPA) of neuronal dendritic arbors. Here, we describe a simple but efficient algorithm thattakes advantage of the presence of relatively stable branch points within the neuronal arborstructure combined with their geometry to facilitate the analysis of dynamic changes in theneuronal structure. To precisely identify similar structures within the tree structure bycomputer algorithms is a very difficult problem, given the subtle difference the arbors couldhave at different time points, and artifactual differences caused by shifts in the position ofthe animal during imaging and other factors. To achieve the most reliable result in anexpeditious manner, we combined the advantages of the computer algorithm and theexpertise of human analyst. Instead of having the computer generate the final analysis, weuse the computer algorithm to effectively narrow down the candidate list of the matchedbranches and let the human expert select the optimal match.

Many methods based on weighted-matching (Donte, Foggia et al. 2004) and theirapplications to biomedical data have been reported (Dumay, Geest et al. 1992; Haris,Efstratiadis et al. 1999). We compared the performance of two automatic weighted-matchingmethods, the Hungarian algorithm and the greedy method, to our method, using the samedata sets (data sets 3–10 in Table 1). The traced neuronal arbors were decomposed into setsof branches and equation (1) was used as the weighted function.

The processing time and the accuracy are two of the most important parameters to considerwhen comparing the matching methods. The average time cost per data set using theHungarian algorithm was 90.4 min, which is more than twice as the average processing timewith our method. In addition, the accuracy of the Hungarian algorithm was way from beingperfect, which means that human verification and correction will inevitably be required.Online resource video 3 (Hugarian-ICP.avi) shows the matching result of data set No 6reported by the Hungarian algorithm. The other automatic algorithm, the greedy method,was much faster. The average processing time was less than a minute. However, theaccuracy of the matching results was even worse. A representative video clip of the greedymethod is shown in online resource video 4 (Greedy_ICP.avi). These results suggest that ourstrategy of combining the computer program with human supervision is indeed a highlyefficient method.

4D SPA significantly increases the rate at which structural dynamics can be quantified andmapped onto the neuronal structure, and effectively reduces errors in the analysis anddiscrepancies between experimenters. As described in the methods section, there are threeparameters (α,β,γ) used in the program that can be adjusted by the analyst to optimize thealgorithm to particular applications and cell types. For instance, higher values of α and β canbe used if the images are taken over a longer time interval and the neuron is expected tohave grown or changed a lot by the second time point. On the other hand, for relativelystable neuronal structures, smaller values would be preferred to reduce false positives on thelist of suggested matching candidates. The value of γ can also be adjusted to better fitspecific types of neurons with unique morphological features. The accuracy of thesuggestion list decreases when the morphology of the subtrees attaching to the same parentbranch are highly similar, for instance in in highly symmetric neuronal structures. In thiscase, extra care needs to be taken using the suggestion list. In the cases where the realmatched branch is not included in the suggestion list, we have implemented a manualassignment function in the program, which allows the analyst to pick any branch in N2 andassign it as the matched branch for the branch in question.

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4D SPA could easily be applied to neuronal axon arbors, which exhibit structural changesunder a variety of conditions (Reh and Constantine-Paton 1985; Antonini and Stryker 1993;Cantallops, Haas et al. 2000; Cohen-Cory 2002; Ruthazer, Akerman et al. 2003; De Paola,Holtmaat et al. 2006). Other neuronal structures, such as the neuromuscular junction(Turney and Lichtman 2008), of which the morphological changes under differentexperimental conditions have been studied intensively, could also benefit from this tool. Inaddition, 4D SPA could be applied to study the structural dynamics of other cell types, thevasculature (Zhang, Boyd et al. 2005) and extracellular space (Hochman 2012). In vivotime-lapse images of Xenopus radial glial cells collected at relatively short intervals hasdemonstrated rapid structural rearrangements of filopodia that were modulated by visualactivity, NMDA receptor activity and nitric oxide signaling (Tremblay, Fugere et al. 2009).Furthermore, images of Xenopus radial glial cells undergo significant structural changesduring proliferation and neuronal differentiation (Bestman, Lee-Osbourne et al. 2012). Inaddition, immune cells are highly dynamic and their structural dynamics are essential totheir function. In vivo imaging studies of microglia in rodent visual cortex demonstrate thatthey exhibit dynamic morphological rearrangements in response to visual deprivation andlight exposure, suggesting an active role of microglia cells in experience-dependent synapticmodifications (Tremblay, Lowery et al. 2010). Acute neuroinflamation in response to viralprotein induces mobility of both leukocytes and microglia in the CNS, resulting inengulfment of synaptic structures and immune cells (Lu, Tremblay et al. 2011). As a finalexample, the CNS vasculature shows significant structural changes under healthy anddiseased conditions (Carmeliet 2003; Zhang, Boyd et al. 2005; Thal, Grinberg et al. 2012).Similar to efforts to automate reconstruction of neuronal structures, recent work hassucceeded in automating reconstruction of vasculature from single time points (Zudaire,Gambardella et al. 2011), suggesting that comparisons of vasculature between could benefitfrom the algorithm presented here. Quantitative analysis of structural dynamics has been keyto gaining insight into the mechanisms and function of dynamics in neurons. We anticipatethat application of this algorithm to a variety of biological systems will be valuable.

Supplementary MaterialRefer to Web version on PubMed Central for supplementary material.

AcknowledgmentsThis work was funded by support from the National Institutes of Health (EY011261), the Hahn Family Foundationand the Nancy Lurie Marks Family Foundation to HTC, and the National Science Council, Taiwan, Grants98-2221-E-009-118-MY3 and 101-2221-E-009-143-MY3 to Y-TC. We thank Dr. Shu-ling Chiu for fostering thisproductive collaboration. P-CL would like to thank Dr. M. Giugliano for his help implementing the file converter.The authors declare no competing financial interests.

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Figure 1.Flow chart of the 4D SPA program.

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Figure 2.Application of computer assisted 4D structural plasticity analysis to evaluate changes indendritic arbor structure in neurons in daily time-lapse images. A. Schematic drawing of thestructure of a neuronal dendritic tree to illustrate the terminology used in this report. Thesoma is marked by the dark gray circle. Branch points are points where more than onebranch is rooted, such as points A and B. All of the points along the branch path that areneither the branch point nor the branch tip are called regular points. There are altogether 13branch points (including the soma) in the whole tree structure. The average tree size of theschematic neuron is 5.25, calculated as (3+4+2+3+4+8+2+2+3+5+13+14)/12; the tree sizesare listed in depth first traversal order. Branch point A is a ‘significant point’ because it hasa subtree that is larger than the average tree size of the entire arbor and the size of both of itssubtrees are larger than 3. Branch point B is not a ‘significant point’ since none of itssubtrees (shaded in light gray) is larger than 5.25. B, C. Reconstructions from a pair ofimages collected 24 hour apart (data set No 5). The soma position is marked with the greyoval. Significant points are marked with filled red circles. To illustrate the branch matchingprocess between arbors of 2 consecutive time-points, we colored one branch in the arborfrom the first time-point in B in red (an amplified image of the dendritic part in the box isshown in B’). The five candidate matching branches provided by the algorithm in the arborfrom the second time-point in C are shown in different colors to distinguish them from eachother. Amplification of the boxed part is shown in C’ with each individual candidatematching branch. Scale bar: 10 µm

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Figure 3.Examples of subtree structure that is potentially confusing to the algorithm. A-C.Reconstructions of dataset number 8 and 9. Images were collected every 24 hours over 3days. The subtree structures that caused confusion to the program were marked with redboxes. As shown in the figure, these subtrees share highly similar morphology and areattaching to the same parent branch with their positions right next to each other. This resultsin very similar attribute values for the branches and could increase the possibility ofmismatching in the candidate list provided by the algorithm. This is turn might require morehuman intervention. Significant points are marked with filled red circles, and the soma ismarked by dark grey circles. Scale bar: 10 µm

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Figure 4.Application of computer assisted 4D structural plasticity analysis to identify branchdynamics over relatively short time periods. A-C. Reconstructions of time-lapse imagingdata of a representative optic tectal neuron imaged at 4 hour intervals. A’-C’. Computergenerated reconstructions of the neuron at the timepoints corresponding to A–C to show theaccuracy of the 14 reconstruction generated by the 4D SPA program. Dendritic branches arecolor-coded according to their dynamic properties. The stable branches are black, theretracted branches are blue, the transient branches are magenta, and the newly addedbranches are green. Position of the neuronal soma is marked with black oval. Scale bar: 10µm.

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Tabl

e 1

Para

met

ers f

or 4

D S

PA d

ata

anal

ysis

resu

lts. E

ach

data

set c

onta

ins a

pai

r of n

euro

nal d

endr

itic

arbo

rs (r

econ

stru

cted

from

the

sam

e ne

uron

imag

ed a

tdi

ffer

ent t

ime

poin

t, N

1 an

d N

2). H

it ra

tio m

easu

res t

he p

erce

ntag

e of

cor

rect

mat

ches

in th

e su

gges

ted

list r

elat

ive

to th

e to

tal b

ranc

h nu

mbe

r. Ti

me

reco

rds t

he to

tal t

ime

take

n fo

r the

ana

lysi

s of t

hat d

ata

set.

Size

of N

1 (o

r N2)

show

s the

tota

l bra

nch

num

ber o

f the

den

driti

c ar

bor.

Avg

list

size

show

sth

e av

erag

e nu

mbe

r of b

ranc

hes i

n th

e ‘s

ugge

stio

n lis

t’ fo

r eac

h br

anch

in N

1 du

ring

the

anal

ysis

of t

hat d

ata

set.

The

first

two

data

sets

(sha

ded)

wer

eus

ed fo

r the

ana

lyst

to b

ecom

e fa

mili

ar w

ith th

e pr

ogra

m, a

nd th

us w

ere

not i

nclu

ded

in th

e fin

al c

alcu

latio

ns o

f the

mea

n hi

t rat

io, m

ean

time,

and

mea

nA

vg. l

ist s

ize,

whi

ch a

re li

sted

at t

he b

otto

m o

f the

tabl

e.

Dat

aH

it ra

tioT

ime

(min

.)si

ze o

f N1

size

of N

2A

vg. l

ist s

ize

10.

969

-31

241.

407

20.

856

-69

802.

814

30.

921

4276

632.

422

40.

859

4363

792.

422

50.

967

111

8984

2.42

2

60.

795

1338

583.

051

70.

917

4658

593.

483

80.

758

4460

803.

515

90.

704

3580

943.

741

100.

833

513

182.

5

mea

n H

it ra

tio: 0

.858

±0.0

84

mea

n T

ime:

42.

375

min

mea

n A

vg. l

ist s

ize:

2.7

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Tabl

e 2

An

exam

ple

of o

utpu

t dat

a sp

read

shee

t of 4

D-S

PA d

ynam

ic a

naly

sis r

esul

ts. E

ach

bran

ch is

iden

tifie

d by

an

inde

x nu

mbe

r and

cat

egor

ized

by

its p

rese

nce

at d

iffer

ent t

ime

poin

t of t

he ti

me-

laps

e se

ries (

type

). Th

e ba

se le

ngth

dep

icts

the

leng

th fr

om so

ma

to th

e br

anch

tip

of th

e br

anch

at T

0 (o

r fro

m so

ma

toth

e la

st b

ranc

hing

poi

nt in

cas

es o

f new

ly-a

dded

and

tran

sien

t bra

nche

s, w

hich

do

not e

xist

at T

0). C

hang

e in

the

bran

ch le

ngth

, as m

easu

red

from

the

last

bran

chin

g po

int t

o th

e tip

of e

ach

bran

ch a

t T1

and

T2, a

re a

lso

liste

d.

inde

xty

peba

seT

0T

1T

2

0R

etra

cted

108.

347

0−1

0.00

98−8

.626

1R

etra

cted

100.

107

0−2

.826

5#

2St

able

96.2

109

01.

6266

0.85

6

3R

etra

cted

93.4

048

00.

1274

−3.0

637

4St

able

88.8

920

−1.2

518

−10.

9032

5St

able

86.5

705

0−7

.694

413

.040

1

6St

able

82.7

616

0−0

.349

3−4

.236

7

7R

etra

cted

82.5

884

0−1

.250

2#

8R

etra

cted

82.3

081

0−0

.712

3−2

.936

5

9R

etra

cted

82.1

164

0−2

.522

9#

10St

able

78.0

166

0−1

9.88

6−0

.812

2

11R

etra

cted

76.6

955

0−7

.487

2−5

.186

12R

etra

cted

69.4

699

0−4

.455

5#

13St

able

69.3

531

00.

8682

0.10

89

14R

etra

cted

67.5

669

0−4

.482

7#

15R

etra

cted

66.0

081

0−2

.114

8#

16R

etra

cted

65.2

153

0−8

.544

1#

17St

able

64.1

979

0−8

.802

3−0

.491

3

18R

etra

cted

63.9

182

0−1

1.65

71#

19R

etra

cted

63.2

111

09.

3652

−2.7

323

20R

etra

cted

61.1

388

0−1

.480

3#

21St

able

59.4

221

0−2

.769

70.

768

22St

able

59.2

012

010

.917

7.58

43

23St

able

57.0

635

0−0

.077

2−2

.515

6


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inde

xty

peba

seT

0T

1T

2

24St

able

54.4

850

1.54

443.

1327

25R

etra

cted

54.3

478

0−7

.919

7#

26R

etra

cted

53.8

825

0−1

5.54

46#

27R

etra

cted

53.1

091

0−0

.848

#

28R

etra

cted

52.8

387

0−8

.701

2#

29St

able

51.9

241

01.

8833

−5.6

866

30R

etra

cted

49.4

744

0−1

.533

8#

31St

able

47.4

518

00.

2116

−1.0

798

32St

able

47.1

564

0−3

.664

31.

3552

33R

etra

cted

40.5

623

0−6

.859

2#

34R

etra

cted

36.5

024

0−9

.909

9#

35St

able

35.9

169

00.

1452

−1.7

61

36R

etra

cted

35.6

123

0−3

.594

1#

37R

etra

cted

35.2

614

0−6

.722

8#

38St

able

35.0

497

022

.596

3−3

.793

5

39R

etra

cted

34.7

067

0−3

.145

4#

40R

etra

cted

33.6

457

01.

4−5

.911

6

41R

etra

cted

31.2

966

0−4

.704

1#

42R

etra

cted

30.8

287

0−1

2.13

39#

43R

etra

cted

30.4

663

0−2

.026

#

44N

ewly

_Add

ed75

.707

3*

4.03

13−2

.018

2

45N

ewly

_Add

ed56

.572

7*

4.74

53−5

.480

7

46Tr

ansi

ent

55.4

71*

3.53

34−3

.533

4

47Tr

ansi

ent

55.4

71*

3.02

59−3

.025

9

48Tr

ansi

ent

52.1

022

*5.

5507

−5.5

507

* bran

ch n

ot e

xist

ing

at T

0.

# bran

ch a

lread

y re

tract

ed a

t T1,

thus

not

cou

nted

at T

2.


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