---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22209'
abstract:
- lang: eng
  text: The curvature of elongated microscopic building blocks plays a crucial role
    on their self-assembly into orientationally ordered phases. While rod-like molecules
    form a handful of liquid crystal (LC) phases, curved or banana-shaped molecules
    show more than fifty phases, with fascinating physical properties, such as chirality
    or polarity. Despite the fundamental and technological importance of these so-called
    ‘banana-shaped liquid crystals’, little is known about their microscopic details
    at the single-molecule level. Curved colloidal liquid crystals—liquid crystals
    formed by curved colloidal rods—are excellent model systems to optically resolve
    the structure and dynamics of curved building blocks within these condensed phases.
    Recent advances in the synthesis of curved rod-like particles have unlocked the
    potential for studying—at the single-particle level—the intimate relationship
    between shape and phase symmetry, and even confirmed the stability of elusive
    LC phases. Further developments in this nascent field promise exciting findings,
    such as the first observation of the colloidal twist-bend nematic phase or the
    fabrication of functional materials with curvature-dependent properties. In this
    Report on Progress, we will highlight recent advances in the synthesis and assembly
    of curved colloidal liquid crystals and discuss the upcoming challenges and opportunities
    of this field.
article_number: '094601'
article_processing_charge: No
article_type: review
author:
- first_name: Carla
  full_name: Fernández-Rico, Carla
  id: 492def71-6250-11f0-b278-d41dbd241b62
  last_name: Fernández-Rico
- first_name: Roel P A
  full_name: Dullens, Roel P A
  last_name: Dullens
citation:
  ama: 'Fernández-Rico C, Dullens RPA. Liquid crystals from curved colloidal rods:
    Waves, twists and more. <i>Reports on Progress in Physics</i>. 2024;87(9). doi:<a
    href="https://doi.org/10.1088/1361-6633/ad627b">10.1088/1361-6633/ad627b</a>'
  apa: 'Fernández-Rico, C., &#38; Dullens, R. P. A. (2024). Liquid crystals from curved
    colloidal rods: Waves, twists and more. <i>Reports on Progress in Physics</i>.
    IOP Publishing. <a href="https://doi.org/10.1088/1361-6633/ad627b">https://doi.org/10.1088/1361-6633/ad627b</a>'
  chicago: 'Fernández-Rico, Carla, and Roel P A Dullens. “Liquid Crystals from Curved
    Colloidal Rods: Waves, Twists and More.” <i>Reports on Progress in Physics</i>.
    IOP Publishing, 2024. <a href="https://doi.org/10.1088/1361-6633/ad627b">https://doi.org/10.1088/1361-6633/ad627b</a>.'
  ieee: 'C. Fernández-Rico and R. P. A. Dullens, “Liquid crystals from curved colloidal
    rods: Waves, twists and more,” <i>Reports on Progress in Physics</i>, vol. 87,
    no. 9. IOP Publishing, 2024.'
  ista: 'Fernández-Rico C, Dullens RPA. 2024. Liquid crystals from curved colloidal
    rods: Waves, twists and more. Reports on Progress in Physics. 87(9), 094601.'
  mla: 'Fernández-Rico, Carla, and Roel P. A. Dullens. “Liquid Crystals from Curved
    Colloidal Rods: Waves, Twists and More.” <i>Reports on Progress in Physics</i>,
    vol. 87, no. 9, 094601, IOP Publishing, 2024, doi:<a href="https://doi.org/10.1088/1361-6633/ad627b">10.1088/1361-6633/ad627b</a>.'
  short: C. Fernández-Rico, R.P.A. Dullens, Reports on Progress in Physics 87 (2024).
date_created: 2026-06-30T06:31:09Z
date_published: 2024-08-12T00:00:00Z
date_updated: 2026-07-15T06:27:28Z
day: '12'
ddc:
- '540'
doi: 10.1088/1361-6633/ad627b
extern: '1'
external_id:
  pmid:
  - '38996410'
fulldoi: https://doi.org/10.1088/1361-6633/ad627b
has_accepted_license: '1'
intvolume: '        87'
issue: '9'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1088/1361-6633/ad627b
month: '08'
oa: 1
oa_version: Published Version
pmid: 1
publication: Reports on Progress in Physics
publication_identifier:
  eissn:
  - 1361-6633
  issn:
  - 0034-4885
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Liquid crystals from curved colloidal rods: Waves, twists and more'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 87
year: '2024'
...
---
_id: '15315'
abstract:
- lang: eng
  text: Single and collective cell migration are fundamental processes critical for
    physiological phenomena ranging from embryonic development and immune response
    to wound healing and cancer metastasis. To understand cell migration from a physical
    perspective, a broad variety of models for the underlying physical mechanisms
    that govern cell motility have been developed. A key challenge in the development
    of such models is how to connect them to experimental observations, which often
    exhibit complex stochastic behaviours. In this review, we discuss recent advances
    in data-driven theoretical approaches that directly connect with experimental
    data to infer dynamical models of stochastic cell migration. Leveraging advances
    in nanofabrication, image analysis, and tracking technology, experimental studies
    now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical
    efforts have been directed towards integrating such datasets into physical models
    from the single cell to the tissue scale with the aim of conceptualising the emergent
    behaviour of cells. We first review how this inference problem has been addressed
    in both freely migrating and confined cells. Next, we discuss why these dynamics
    typically take the form of underdamped stochastic equations of motion, and how
    such equations can be inferred from data. We then review applications of data-driven
    inference and machine learning approaches to heterogeneity in cell behaviour,
    subcellular degrees of freedom, and to the collective dynamics of multicellular
    systems. Across these applications, we emphasise how data-driven methods can be
    integrated with physical active matter models of migrating cells, and help reveal
    how underlying molecular mechanisms control cell behaviour. Together, these data-driven
    approaches are a promising avenue for building physical models of cell migration
    directly from experimental data, and for providing conceptual links between different
    length-scales of description.
acknowledgement: This work was supported by the Deutsche Forschungsgemeinschaft (German
  Research Foundation)—Project-ID 201269156—SFB 1032 (Project B12). D B B was supported
  by an NOMIS Fellowship and an EMBO Fellowship (ALTF 343-2022). We thank Joachim
  Rädler, Alexandra Fink, Erwin Frey, Pierre Ronceray, Ricard Alert, Edouard Hannezo,
  Henrik Flyvbjerg, Ulrich Schwarz, Joshua Shaevitz, Greg Stephens, Andrea Cavagna,
  Grzegorz Gradziuk, Fridtjof Brauns, Nikolas Claussen, Tom Brandstätter, Johannes
  Flommersfeld, Christoph Schreiber, Nicolas Arlt, Matthew Schmitt, Joris Messelink,
  Federico Gnesotto, Federica Mura, Bram Hoogland, Manon Wigbers, Isabella Graf, Jessica
  Lober, and many others for inspiring discussions. We also thank Claudia Flandoli
  for the artwork in figures 1, 5, 8 and 9.
article_number: '056601'
article_processing_charge: Yes (in subscription journal)
article_type: review
arxiv: 1
author:
- first_name: David
  full_name: Brückner, David
  id: e1e86031-6537-11eb-953a-f7ab92be508d
  last_name: Brückner
  orcid: 0000-0001-7205-2975
- first_name: Chase P.
  full_name: Broedersz, Chase P.
  last_name: Broedersz
citation:
  ama: 'Brückner D, Broedersz CP. Learning dynamical models of single and collective
    cell migration: a review. <i>Reports on Progress in Physics</i>. 2024;87(5). doi:<a
    href="https://doi.org/10.1088/1361-6633/ad36d2">10.1088/1361-6633/ad36d2</a>'
  apa: 'Brückner, D., &#38; Broedersz, C. P. (2024). Learning dynamical models of
    single and collective cell migration: a review. <i>Reports on Progress in Physics</i>.
    IOP Publishing. <a href="https://doi.org/10.1088/1361-6633/ad36d2">https://doi.org/10.1088/1361-6633/ad36d2</a>'
  chicago: 'Brückner, David, and Chase P. Broedersz. “Learning Dynamical Models of
    Single and Collective Cell Migration: A Review.” <i>Reports on Progress in Physics</i>.
    IOP Publishing, 2024. <a href="https://doi.org/10.1088/1361-6633/ad36d2">https://doi.org/10.1088/1361-6633/ad36d2</a>.'
  ieee: 'D. Brückner and C. P. Broedersz, “Learning dynamical models of single and
    collective cell migration: a review,” <i>Reports on Progress in Physics</i>, vol.
    87, no. 5. IOP Publishing, 2024.'
  ista: 'Brückner D, Broedersz CP. 2024. Learning dynamical models of single and collective
    cell migration: a review. Reports on Progress in Physics. 87(5), 056601.'
  mla: 'Brückner, David, and Chase P. Broedersz. “Learning Dynamical Models of Single
    and Collective Cell Migration: A Review.” <i>Reports on Progress in Physics</i>,
    vol. 87, no. 5, 056601, IOP Publishing, 2024, doi:<a href="https://doi.org/10.1088/1361-6633/ad36d2">10.1088/1361-6633/ad36d2</a>.'
  short: D. Brückner, C.P. Broedersz, Reports on Progress in Physics 87 (2024).
corr_author: '1'
das_tickbox: '1'
dataavailabilitystatement: No new data were created or analysed in this study.
date_created: 2024-04-14T22:01:01Z
date_published: 2024-04-04T00:00:00Z
date_updated: 2026-10-01T10:09:41Z
day: '04'
ddc:
- '530'
department:
- _id: EdHa
doi: 10.1088/1361-6633/ad36d2
external_id:
  arxiv:
  - '2309.00545'
  isi:
  - '001196692400001'
  pmid:
  - '38518358'
file:
- access_level: open_access
  checksum: c5910078230ade20f4dd83592e862a72
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  creator: dernst
  date_created: 2024-08-20T11:00:03Z
  date_updated: 2024-08-20T11:00:03Z
  file_id: '17451'
  file_name: 2024_ReportPhysics_Brueckner.pdf
  file_size: 4376898
  relation: main_file
  success: 1
file_date_updated: 2024-08-20T11:00:03Z
fulldoi: https://doi.org/10.1088/1361-6633/ad36d2
has_accepted_license: '1'
intvolume: '        87'
isi: 1
issue: '5'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '04'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 34e2a5b5-11ca-11ed-8bc3-b2265616ef0b
  grant_number: ALTF 343-2022
  name: A mechano-chemical theory for stem cell fate decisions in organoid development
publication: Reports on Progress in Physics
publication_identifier:
  eissn:
  - 1361-6633
  issn:
  - 0034-4885
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: no
title: 'Learning dynamical models of single and collective cell migration: a review'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
  name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
  short: CC BY (3.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 87
year: '2024'
...