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PERSPECTIVE article

Front. Phys., 28 February 2020 | https://doi.org/10.3389/fphy.2020.00031

How Computation Is Helping Unravel the Dynamics of Morphogenesis

  • 1LifeD Lab, Madrid, Spain
  • 2Mechanical and Aerospace Engineering Department, University of California San Diego, San Diego, CA, United States
  • 3Institute for Engineering in Medicine, University of California San Diego, San Diego, CA, United States
  • 4Mechanical Engineering Department, University of Washington, Seattle, WA, United States
  • 5Center for Cardiovascular Biology, University of Washington School of Medicine, Seattle, WA, United States
  • 6Institute for Stem Cell and Regenerative Medicine, University of Washington School of Medicine, Seattle, WA, United States

The growing availability of imaging data, calculation power, and algorithm sophistication are transforming the study of morphogenesis into a computation-driven discipline. In parallel, it is accepted that mechanics plays a role in many of the processes determining the cell fate map, providing further opportunities for modeling and simulation. We provide a perspective of this integrative field, discussing recent advances and outstanding challenges to understand the determination of the fate map. At the basis, high-resolution microscopy and image processing provide digital representations of embryos that facilitate quantifying their mechanics with computational methods. Moreover, innovations in in-vivo sensing and tissue manipulation can now characterize cell-scale processes to feed larger-scale representations. A variety of mechanical formalisms have been proposed to model cellular biophysics and its links with biochemical and genetic factors. However, there are still limitations derived from the dynamic nature of embryonic tissue and its spatio-temporal heterogeneity. Also, the increasing complexity and variety of implementations make it difficult to harmonize and cross-validate models. The solution to these challenges will likely require integrating novel in vivo measurements of embryonic biomechanics into the models. Machine Learning has great potential to classify spatio-temporally connected groups of cells with similar dynamics. Emerging Deep Learning architectures facilitate the discovery of causal links and are becoming transparent and interpretable. We anticipate these new tools will lead to multi-scale models with the necessary accuracy and flexibility to formulate hypotheses for in-vivo and in-silico testing. These methods have promising applications for tissue engineering, identification of therapeutic targets, and synthetic life.

Introduction

Embryogenesis is a complicated ensemble of processes by which a single cell turns into a multi-cellular living organism. Through various developmental stages, the cell population proliferates while tissues develop, change their properties, differentiate, and gain their specific functionality [1]. During embryogenesis, biochemical, genetic, and epigenetic factors interact, forming a tangled network of processes with diverse physical length scales and time scales [2, 3]. Remarkably, the robustness and variability of these processes are balanced to make possible the reproducibility and diversity of living specimens [4].

Mechanics plays a central role in shaping the embryo [5, 6]. Gene expression gradients regulate tissue patterning and cellular properties, such as rheology, adhesion, and contractility [7]. At the same time, the embryonic cells sense mechanical cues from their microenvironment and convert them to biochemical signals, including gene expression [8, 9]. These cues are essential to guide morphogenesis but also tissue repair, given that immature cells can retain significant plasticity and reprogram in response to external forces [10, 11]. The cross-talk between biophysical and biochemical processes involves multiple mechanisms and molecules and occurs in multiple scales [12]. Besides, cells can follow complex trajectories within the developing embryo, thereby creating and being exposed to continuous changes in the microenvironment [1316].

Researchers have been long interested in discovering mechanistic links between physical processes and gene expression that lead to cell fate determination [1721]. Recent advances in microscopy, modeling, and computation have enabled quantifying 2D and 3D mechanical forces and rheological properties in multi-cellular colonies, including live developing embryos [2228]. These methods provide local data in space and time, and analyzing them to unravel cell fate maps is challenging. High-resolution, long-term observation in two or three dimensions is desirable to consider the whole range of scales at which mechanics can impact cell fate. Still, it complicates the analysis further because it involves massive amounts of data. Furthermore, the statistical treatment of the data needs to accommodate the highly heterogeneous and time-evolving properties of developing tissues [2931].

This perspective discusses current advances in computational methods for the characterization of mechanical processes during embryogenesis and how these processes influence cell fate. Sections Digital Reconstruction of Embryogenesis, In vivo Quantification of Forces and Mechanical Properties, and Computational Models in this perspective are organized according to key steps in the analysis of experimental data and relevant methodological approaches. Each section presents our view into key advances and outstanding challenges. Section Morphomechanical Domains in Developing Tissues: Follow the Cell, Not the Voxel proposes a paradigm to deal with the massive data produced by experimental techniques and construct a multi-scale representation of embryo dynamics. Finally, section Understanding Multi-Scale Embryonic Dynamics by Machine Learning presents problems at the intersection between morphogenesis and Machine Learning that has not been so far tackled by the community.

Digital Reconstruction of Embryogenesis

Progress in live microscopy and fluorescence reporters now allow high-resolution, time-lapse imaging of developing embryos in two and three dimensions [3235]. Image analysis and computer vision methods can now create digital atlases of developing embryos (Figures 1A–F). These atlases contain spatio-temporal information about cell and tissue morphology, cell lineages, and functional patterns, such as gene expression or protein activity [3642]. Moreover, novel visualization tools allow for systematically browsing these digital embryos (Figure 1), and integrating them into numerical simulations and machine learning algorithms [36, 42, 43].

FIGURE 1
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Figure 1. Digital reconstruction of cell trajectories in a zebrafish embryo. (A) Three-dimensional (3D) rendering of cell nuclei (blue) in raw data and selection of cells (yellow) in the dorsal line, performed at 10.7 h-post-fertilization and backtracked to 7 hpf. From left to right, each panel shows a different spatial orientation (animal pole, lateral and ventral). (B) Detected cell nuclei (red) and cell selection as in (A) (yellow), shown in a spatial slice over the orthoslice of the raw data channel (gray). Same time step and view angles as in (A). (C) 3D rendering of cell nuclei (blue) and selection of cells of the dorsal line at 10.7 hpf (yellow). (D) Cell detection (red) and cell selection (yellow) in the same slice as (B). (E) Left: Two cell selections (green and yellow) over nuclei detection domains at 7 hpf. Middle: forward tracking (yellow to red colormap indicates time advancement) of the two selected cell domains. Right: forward tracking of the two cell selections from a lateral point of view. (F) Cell selections (green and yellow) at 10.7 hpf. Cell backward tracking (yellow to purple colormap) in same view angles than (E). This dataset and the visualization tool Mov-IT are freely available from the BioEmergences open workflow http://bioemergences.iscpif.fr/bioemergences/openworkflow-index.php [36].

The three-dimensional in-vivo imaging of whole embryos has challenges associated with image resolution, quality, and artifacts (e.g., anisotropic point spread function). Besides, photobleaching and phototoxicity make it challenging to extend imaging over intervals long enough to capture relevant morphogenetic processes. Multi-view light-sheet microscopy (LSM) [35, 44, 45] and view fusion algorithms [46, 47] allow for 3D imaging large embryos with cellular isotropic resolution. Recently, advances proposing adaptive optics and lattice LSM with ultrathin light-sheet excitation featured, promising sub-cellular resolution during long-term observation [48].

Reconstructing the multi-scale dynamics of embryogenesis requires not only long-term imaging with sub-cellular spatial resolution but also sub-minute temporal resolution. An established approach to achieve these joint demands is to record images of several embryos within the same cohort with different temporal resolutions and to register the resulting images spatially onto a common template [49, 50]. The projected growth in computing power of microscopy systems (e.g., by embedded GPU computing) makes it possible to envision enhanced microscopes with real-time adaptive multi-scale observation [51, 52].

Image processing workflows must be able to handle the massive amounts of complex data resulting from microscopy modalities to provide a quantification of structures, motion, and hierarchy [3, 53]. Intensity-based methods, such as optical flow or image registration produce continuous velocity fields [5355] that can leverage the powerful modeling and descriptive tools of continuum and statistical mechanics [56, 57]. On the other hand, tracking the motion and divisions of single cells yields discrete cell lineages, which presents apparent advantages [4, 36, 40].

Motion estimation is critical because determining cell fate involves reconstructing 3D cell trajectories across the various developmental stages, imposing quasi-error-free requirements (Figures 1E,F). Deep Learning tools, such as Convolutional Neural Networks can help to improve the performance under challenging conditions, such as deep-tissue segmentation provided tagged training data [58, 59]. Interactive annotation tools for correction and validation are still a suitable approach to generate reliable expert-driven data [36, 42, 43, 60] and potentially allow crowdsourced results [61]. Beyond image data repositories, sharing detailed experiment metadata through systematic frameworks (e.g., based on ontologies) can provide a “Big Data” substrate for machine learning to optimize pipelines.

In vivo Quantification of Forces and Mechanical Properties

Digital reconstruction of morphogenesis already provides structured data, but embedding biophysical formalisms is invaluable to decipher multi-scale dynamics. The study of biophysics in single cells is not new: the measurement of the rheological properties of cells, their internal stresses and the forces they exert has received significant attention in the past two decades [12, 23, 62]. The requirement of non-invasiveness, three-dimensionality, and the need for calibrated sensors that sensitive enough to resolve minute forces and deformations make this task particularly challenging in live embryos.

Laser ablation was one of the pioneering methods to quantify embryonic mechanics in vivo. This technique produces a localized cut in a tissue, which allows for estimating tissue tensions by letting the ablated region relax to a stress-free configuration [6365]. This technique is still widely used but it is disruptive. A non-invasive alternative is to use fluorescence reporters to measure acto-myosin activity as a surrogate metric of force generation. Still, both methods rely on independent measurements of tissue rheology [66, 67]. Molecular sensors based on fluorescence resonance energy transfer (FRET) also provide a minimally invasive means of measuring forces in vivo [68]. This modality is very attractive since it probes the tension born by specific molecules. However, it requires careful calibration, does not provide vector or tensor data, and needs a different sensor to measure the tension born by each molecule. It is undoubtable that these approaches will continue to shed light on numerous embryogenic processes. Even so, their critical examination has kindled the search for easy-to-calibrate quantifications of the strains, stresses and material properties inside live tissues.

Because in vitro assays allow for careful control of experimental parameters, they have experienced significant progress in the past 20 years, thus offering valuable lessons for the development of in vivo techniques. In particular, there is a diversity of force microscopy methods that exploit the linear properties and high deformability of hydrogelsto provide sensitive, calibrated strain-stress sensors. Cells are cultured on these hydrogels, the deformation caused by the cells on the hydrogel is measured, typically by tracking the motion of fiduciary markers (e.g., fluorescent microspheres), and the traction forces exerted by the cells are recovered from the measured deformations [6971]. Monolayer Stress Microscopy is an extension of traction microscopy that quantifies the collective distribution of intracellular stress in thin confluent cell cultures [72]. A similar approach was proposed to estimate ventral furrow invagination in Drosophila although in that case the stress-free configuration was not known [73]. Of note, traction forces can be highly three-dimensional even when the cells are plated on flat hydrogels [74], leading to significant bending and additional intracellular stress in cell monolayers [75]. Quantifying the forces involved in epithelial bending and invagination could offer new biomechanical insights about the morphogenesis of tissues and organs.

In live developing embryos, it is now feasible to measure strains (and strain rates, Figure 2) at the cellular level by tracking the morphological changes of segmented cells [55, 76]. Tissue-level strain fields can be derived from cell tracking and optical flow methods (Figures 2A–C) [57, 77]. By combining the cell-level and tissue-level strain quantifications it is possible to infer tissue rearrangements, such as cell deformation and cell intercalation [55, 60, 77, 78]. These metrics can be overlaid with functional data, such as gene expression and acto-myosin activity, to provide a correlation-based understanding of tissue dynamics [53, 77, 79]. Moreover, continuum strain fields enable the quantification of internal stresses based on a prescribed mechanical model for the embryo. These formulations are very advantageous—they allow for writing sets of equations that can be solved analytically or numerically to fully characterize the mechanical state of the tissue [80]. A mechanical formalism that has been applied to developing embryos with notable success relies on enforcing static equilibrium of forces between intracellular pressure and cortical tension. This formulation leads to a geometrical problem for cell shapes that can be closed by analyzing experimental images [8186]. However, it must be recalled that embryonic tissue properties are heterogeneous, highly non-linear and time-evolving, which makes it challenging to develop mechanical formalisms that are uniformly valid across different regions of space, instants of time, and genetic and pharmacological manipulations. Furthermore, a significant challenge is to establish the stress-free reference state to properly quantify visco-elastic forces.

FIGURE 2
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Figure 2. Lagrangian representation of kinematics and genetic expression. (A) Three schematic snapshots of different time intervals of migrating cell nuclei within an area. The trajectories of two cells (gray and blue) are highlighted. In the second time step a gene expression pattern in yellow is shown affecting several cells. In the last time step another different gene expression pattern is represented in cyan affecting another set of cells. Green blobs represent mechanical sensors that sense local deformation. (B) Two snapshots showing the relative displacements of neighbor cells with respect of a reference cell (gray). These relative displacements are translated into a kinematic descriptor of relative area change rate that representation expansion (blue) and compression (red). The relative displacements in this schematic panel imply a local expansion (blue value) around the reference cell between timesteps t and t + 1 as shown by the average increasing distance between the cell nuclei. (C) same schematic than in (B) for a compressive case with cells getting closer to the reference cell (red value). (D) Lagrangian vectorization of compression/expansion descriptor [same colormap than (B,C)] and gene expression along time for the two reference cells. The data sensed with the mechanical probe is also vectorized in a Lagrangian representation with colormap dark blue to white. Gene expression is vectorized along the reference cell trajectories. (E) Schematic of a transformer (encoder-decoder) architecture trained to infer local forces from deformation measurements (input). The input is segmented into different temporal frames as subvectors. (F) Schema of a transformer architecture trained to infer mechanical factors (input) involved in the appearance of expression patterns at different temporal scales.

A recent approach for the in-vivo characterization of embryonic mechanics, without prior assumptions, consists of injecting microdroplets or hydrogel microspheres of size comparable to one cell, and that can act as calibrated sensors and/or actuators (Figure 2) [87]. After appropriate functionalization by surface coating, these sensors can be made biocompatible and are internalized by the embryo, thereby minimizing the invasiveness of the method. Incompressible fluorescent oil-droplets allow for quantifying anisotropic stresses [88], whereas hydrogel droplets with characterized compressibility allow for quantifying isotropic ones [89]. Moreover, ferrofluid droplets can be act as active sensors to measure the local tissue rheology [90]. An additional feature of these sensors is that they move with their neighboring cells during development, thus providing valuable information about the temporal evolution of mechanical stresses and tissue rheology. Their limitations stem from reduced sampling ability, given by the limited number of sensors that can be used per embryo, and the current lack of scalable computational frameworks to relate the measurements with cell fate determination. Even so, it is reasonable to expect that emerging innovations will simplify the implementation of these techniques, enabling their widespread application.

Computational Models

Computational models with explanatory and predictive power can infer causal links and contribute to the mechanistic understanding of embryogenesis. These models allow researchers to observe processes, reverse engineer mechanisms, and test hypotheses with much looser constraints than pharmacological or genetic manipulations. Many biological problems involving collective cell-cell and cell-matrix interactions have been simulated using discrete, continuum, and hybrid physical models [91, 92]. Discrete agent-based models initially considered cellular movements within a lattice to investigate multicellular interactions [93]. Lattice-free agent-based models consider continuous movements of each agent. A common approach is to conceptualize cells as objects with fixed geometry and biophysical properties, whose trajectories are dictated by the balance of forces exerted by their neighbors and the environment [94]. Subcellular resolution can be achieved through agent-based models in which each agent is deformable and occupies several nodes [95]. The cellular Potts model (CPM) is an energy-based stochastic model, typically defined on a lattice that can have subcellular resolution, that is particularly well-suited to deal with large deformations and multi-scale phenomena [96]. These features make the CPM well-suited to simulate collective cell dynamics in a diversity of scenarios, including morphogenesis [97]. While they are mostly phenomenological, these models are a promising, computationally efficient approach to study how meso-scale multicellular phenomena emerge from the self-organization of sub-cellular and cellular processes.

The cellular Potts model was initially applied to quantify epithelial dynamics including the rearrangements of different cells [98]. Subsequently, the CPM has provided insight about how cortical tension and cell adhesions drive cell sorting and tissue organization [99, 100]. More recently, agent-based models have proven useful to integrate mechanical cues with gene expression. Epithelial and mesenchymal tectonics were simulated together with gene regulatory network dynamics to recapitulate the dynamics of early zebrafish development [26]. Deformable agent-based models are a promising approach to quantify mechanotransduction, the heterogeneity of embryonic tissues, and their impact in larger-scale developmental processes [92, 101].

Vertex models bridge the discrete and continuum descriptions [102]. In these models, each cell is approximated by a polygon in 2D or a polyhedron in 3D, and the tissue measurements are sampled at the junction of three or more cells [102, 103]. Vertex models provide more information on cell interfaces than agent-based models permitting the analysis of topological changes in the cell environment [104, 105]. Curved cell geometries can be resolved with finite-elements [106, 107], and the biophysical interaction between the membrane and the cytoplasmic fluid can also be incorporated using immersed boundary methods [108]. Vertex models have been widely applied to study the mechanics of epithelia, which are represented as manifolds that can fold or invaginate [109114]. These models have made contributions to our understanding various tissue behaviors: growth [115117], cell division and packing [118], planar polarity [119] and the formation of compartments [120]. Dynamic cellular finite-element models have been also proposed for individual and collective cell movements and mechanics [121].

As stated above, continuum models can adapt mechanical theories, such as hydrodynamics and statistical mechanics to live matter [122], taking advantage of a massive body of knowledge and powerful tools from applied mathematics and computation, such as stability theory, perturbation methods, and computational fluid dynamics. In addition to providing a means to relate measurements of strain fields to internal stresses [78, 123], these models are well-suited to perform predictive simulations large-scale embryo dynamics. The widely studied formation of the ventral furrow in Drosophila [124] is a good example of a process governed by hydrodynamics [56]. Most continuum models are limited by their inherent coarse-grained, but fusion between these models and agent-based models could help resolve the contribution individual cells to tissue behavior [125].

Morphomechanical Domains in Developing Tissues: Follow the Cell, Not the Voxel

Although microscopy experiments provide increasingly rich data about embryonic development, the data is obtained in a form that makes it difficult to extract the relationships between cellular and subcellular dynamics, large-scale biomechanical phenomena, and cell fate maps. The root for this difficulty can be illustrated using the analogy between the cell trajectories and a flow; observation through the microscopy imposes a perspective in a fixed reference frame as an external observer of embryogenesis (i.e., Eulerian frame). However, a perspective as an internal observer that records data along the trajectory of each cell would be more suitable (i.e., Lagrangian frame). The Lagrangian framework allows for computing deformation rates and finite deformations over arbitrarily long time intervals [57]. It also helps discover Lagrangian coherent structures [126, 127] formed by cells that experience similar histories of mechanical cues, and which potentially organize the embryogenic flow (Figure 2D).

The Lagrangian trajectories of embryonic cells can be obtained by single-cell tracking or by approximating their motion as a continuous flow [14, 15, 53]. Moreover, in the Lagrangian framework, descriptors related to morphology, mechanics, genetics, etc. can be expressed in terms of the cell trajectories at specific time intervals. The usefulness of this approach depends on whether it can identify true morphomechanical fields. That is, if it finds connected domains of cells with a similar history of cues, if these domains are reproducible across several specimens, and if they can be related to the fate maps. We previously showed that machine learning does identify morphomechanical fields by classifying cell populations with similar Lagrangian cues either via clustering or with training data [57]. Comparison of cohorts can be either performed using a canonical embryo as reference or computing a statistical average of morphomechanical fields. This is a different approach from statistical spatial atlases frequently used to align information within a cohort [49, 50]. However, several fundamental questions and methodological obstacles remain unanswered. In particular, the sensitivity of the automatic classification of morphomechanical fields to intra-phenotypic variability, and its usefulness in establishing inter-phenotype differences need to be addressed in more detail. In particular, automating these analyses for cohorts of embryos requires systematic scanning across entire embryos to compensate for the different development rates of each embryo and its phenotype variability. Then, through the spatio-temporal registration of fields [54], it could be possible to infer robust phenotyping structures and assess the impact of dynamics variability into morphological configuration of tissues and organs.

Understanding Multi-Scale Embryonic Dynamics by Machine Learning

Biological systems are often defined as networks of discrete elements or biochemical processes, which serve as a conceptual framework to glean mechanistic insight about their organization [128, 129]. Framing embryogenesis using this paradigm involves identifying morphogenetic events and fields [130], which can be diverse in nature, duration, and length-scale. Based on image data, one can define morphogenetic events as spatio-temporal spots of statistically abnormal behavior given a reference window. They may comprise subcellular or mesoscopic regions and a variable number of time frames and can be encapsulated by applying spatio-temporal connectivity [131]. When these fields are backtracked, they become unwound in time and space, allowing the discovery of intersections with past events and/or environmental cues. Likewise, forward tracking of events can reveal cascade effects that propagate into one or more morphogenetic fields. The structured representation of digital embryos as spatio-temporally connected fields is a form of dimensionality reduction that fits machine learning-driven approaches.

Owing to recent advances in machine learning methods, computers can now perform human-like reasoning in tasks, such as conversation or gaming [132134]. Deep learning (DL) architectures, such as Feed-Forward Networks, Recurrent Neural Networks (RNN) and Convolutional Neural Networks (CNN) can be applied to analyze interactions in the networks of elements employed in systems biology [135]. Consequently, the applications of DL to biomedicine are quickly becoming ubiquitous [136139]. The analysis of high-throughput genomics data to study genetic variations in regulatory networks is no exception [140, 141]. A main barrier toward adopting DL in developmental biology has been its black-box nature, which does not easily permit inferring mechanisms or causal relationships, and makes it challenging to manipulate models to test hypotheses. Most ongoing efforts to mitigate these limitations can be encompassed under the epistemological paradigm of the Visible Neural Network [142]. One approach toward VNN is to represent the nodes in the network as “visible” data-driven models. This approach has been used to relate cell genotypes and phenotypes based on cell ontologies [143]. An alternate approach is to build the nodes in the network using explicit models based on theoretical or semi-empirical laws [144]. Both approaches allow for manipulating the inner machinery of the DL architecture, thereby facilitating hypothesis testing, the inference of causal relationships, and elucidating mechanisms. Furthermore, coupling DL model-driven architectures with multi-level structured training data can help reduce the amount of inputs, simplify the architecture and facilitate its interpretation [145]. Exhaustive simulations running on cloud technologies [146, 147] can leverage computational models and feed machine learning workflows to create multiple hypothesis to be tested in-vivo. In the case of embryo development, most theoretical and computational models are coarse grained and, thus, better suited to represent meso-scale and large-scale phenomena (see section Computational Models). Consequently, it could be beneficial to develop hybrid approaches in which cell-scale phenomena are modeled with DL. This type of bottom-up methodology has shown great potential to improve the prediction of chaotic deterministic systems, such as turbulent flow [148], but it should be noted that, epistemologically, it constitutes a transparent network of opaque nodes. Given that multiple relationships among genetic and biophysical processes evolve dynamically in space and time during morphogenesis, RNNs are a suitable approach to treat experimental data sequences. Several architectures of RNN have been proposed to improve training and solve the vanishing gradient problem through time [149]. LSTM comprise memory cells to infer long-term dependencies in sequences [150152]. Gated Recurrent Units are another RNN architecture that addresses the long-term memory problem and outperforms LSTM in some applications [153, 154]. Sets of LSTM can be combined to design an encoder-decoder that approaches the problem as a conversion of the input sequence into an intermediate fixed-length sequence (encoder) that can be further classified (decoder) [153, 155]. Recent advances in sequence analysis have been based on the idea of attention [156161]. Attention architectures deal with long inputs by focusing on relevant frames of the sequence, eliminating the restriction of a fixed-length intermediate sequence, and leveraging intermediate states of the encoder as additional input to the decoder. Attention also provides clarity of the input-output relationships [156] and has shown promising results in end-to-end entailment of complex data sequences [162]. The transformer, an architecture without recurrence that relies on feed-forward layers and attention, has been proposed to exploit the potential of attention while allowing for massive parallelization [161, 163].

A key issue is how to pre-train [163, 164] and train these architectures with the data streams of morphogenesis. For instance, contextual bidirectional pre-training might facilitate characterizing strain-stress relationships given past and future tissue states (Figures 2E,F), in order to generate stress maps. Also, entailment of morphogenetic cues and mechanical events with fate map determination could be possible using the input defined by the profiles of cell trajectories, labeled according to a given morphogenetic field or a mature organ. In this regard, the scalability of biological domain tagging could introduce bottlenecks in the generation of training sets, particularly when considering the inherent variability of biological data. These tasks may require using several input vectors at the same time requiring extending current speech-oriented DL architectures [165, 166].

Outlook

In this perspective, we have critically surveyed recent advances in computational methods for the characterization of embryogenesis, focusing on how to integrate data from biophysical measurements or models into cell fate maps. The ongoing surge in research efforts to quantify the biophysics of morphogenesis is leading to important methodological contributions and new insights about how genetics unfold into phenotypes. Despite these advances, the mechanistic description of morphogenesis remains challenging, given the dynamic and multi-scale nature of the underlying processes and the notable plasticity of immature cells. Thus, new methods are required to understand the interplay of physics, genetics, and epigenetics, leading to cell fate map determination. State-of-the-art imaging systems, image analyses, and computer vision methods are enabling the digital curation of multi-dimensional, high-resolution atlases of developing embryos. These data need to be structured in a systematic way to ensure experimental reproducibility and compatibility of different databases, which are necessary for statistically significant comparisons of large cohorts. In this sense, we posit that data analysis would benefit from a Lagrangian representation based on cell trajectories containing the cumulative histories of the spatio-temporal events and environmental cues cells experience along their paths. This representation integrates spatial information into temporal sequences allowing for multi-scale discovery of morphomechanical fields.

Computational models offer a powerful toolbox to assimilate and explain experimental data, as well as to test new hypotheses. As these models grow in sophistication, they are beginning to predict and decipher the dynamics of developing embryos, based on multi-scale biophysical formalisms that can tackle spatio-temporal heterogeneity and complex mechanobiological interplays. These formalisms are benefitting from novel, minimally-invasive experimental approaches to measure the evolving mechanical properties of live embryos. However, the increasing diversity of models makes it difficult to identify, harmonize, and cross-validate a set of laws that govern the dynamics of morphogenesis. The lack of long-term maintenance of many open-source modeling codes makes this task additionally challenging.

In parallel, machine learning is quickly gaining traction as an alternative to classic model-driven computation to leverage intensive experimentation machine learning and causality inference tools [167, 168] can help test the completeness of models. In particular, these tools can elucidate morphomechanical domains formed by cells with similar dynamics, and link the formation of these domains with upstream biomechanical events. Deep learning (DL) architectures are becoming transparent and interpretable by nesting data-driven or model-driven visible nodes, and have been proven useful to discover causal links in other biological processes. For a holistic approach, DL is suitable to analyze spatio-temporal profiles, seek for events, discover patterns and identify dynamic entities. Multi-scale comparison of cohorts with model-driven DL architectures can be the basis to discover “missing data,” factors and critical spatio-temporal processes regulating phenotype configuration. Overall, the methodologies and approaches here discussed will have valuable practical applications for tissue engineering, stem cell research, genetics and behavior of diseases, drug studies, and synthetic life.

Data Availability Statement

The dataset used for visualization in Figure 1 and the free version of the visualization tool Mov-IT are freely available from the BioEmergences open workflow http://bioemergences.iscpif.fr/bioemergences/openworkflow-index.php. Data and tool are described in Faure et al. [36].

Ethics Statement

A dataset of a developing wild-type zebrafish embryo was presented in Figure 1. This dataset was produced by the BioEmergences lab (bioemergences.eu) as described in Faure et al. [36].

Author Contributions

DP-E conceived the work, made the figures, and co-wrote the manuscript. JÁ advised for this work and co-wrote the manuscript.

Funding

This work was supported by NIH grants 1 R01 HD092216-01A1, NIH 1R01HL128630, 1R01HL130840, NIH 2R01 GM084227, and NSF grant NSF CBET – 1706436/1706571.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

We thank BioEmergences Lab-CNRS and Nadine Peyriéras for the joint work on computational developmental biology that inspired this work. We also thank Nicole Gorfinkiel for discussions on tissue mechanics. We thank the Biomedical Image Technologies Lab-UPM, Andres Santos, María Jesús Ledesma-Carbayo and Jose M. Goicolea for their collaboration on previous work.

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Keywords: morphogenesis, cell mechanics, multi-scale modeling, morphomechanical fields, deep learning, cell fate map, fluorescence microscopy, digital embryo

Citation: Pastor-Escuredo D and del Álamo JC (2020) How Computation Is Helping Unravel the Dynamics of Morphogenesis. Front. Phys. 8:31. doi: 10.3389/fphy.2020.00031

Received: 31 October 2019; Accepted: 04 February 2020;
Published: 28 February 2020.

Edited by:

Carlos Gershenson, National Autonomous University of Mexico, Mexico

Reviewed by:

Ignazio Licata, Institute for Scientific Methodology (ISEM), Italy
Reinaldo Roberto Rosa, National Institute of Space Research (INPE), Brazil

Copyright © 2020 Pastor-Escuredo and del Álamo. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: David Pastor-Escuredo, david@lifedlab.org; Juan C. del Álamo, jc@ucsd.edu; juancar@uw.edu