Biofilm s as self -shaping growing nematics Japinder Nijjer1 Mrityunjay Kothari23 Changhao Li4 Thomas Henzel2 Qiuting Zhang1 Jung- Shen B. Tai1 Shuang Zhou5 Sulin Zhang46 Tal Cohen27 Jing Yan18

2025-04-27 0 0 4.9MB 50 页 10玖币

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Biofilms as self-shaping growing nematics

Japinder Nijjer1, Mrityunjay Kothari2,3, Changhao Li4, Thomas Henzel2, Qiuting Zhang1, Jung-

Shen B. Tai1, Shuang Zhou5, Sulin Zhang4,6, Tal Cohen*2,7, Jing Yan1,8*

1Department of Molecular, Cellular and Developmental Biology, Yale University, New Haven, CT, USA.

2Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.

3Department of Mechanical Engineering, University of New Hampshire, Durham, NH, USA

4Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA, USA.

5Department of Physics, University of Massachusetts Amherst, Amherst, MA, USA.

6Department of Biomedical Engineering, Pennsylvania State University, University Park, PA, USA.

7Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.

8Quantitative Biology Institute, Yale University, New Haven, CT, USA.

Abstract:

Active nematics are the nonequilibrium analog of passive liquid crystals in which anisotropic units

consume free energy to drive emergent behavior. Similar to liquid crystal (LC) molecules in

displays, ordering and dynamics in active nematics are sensitive to boundary conditions; however,

unlike passive liquid crystals, active nematics, such as those composed of living matter, have the

potential to regulate their boundaries through self-generated stresses. Here, using bacterial

biofilms confined by a hydrogel as a model system, we show how a three-dimensional, living

nematic can actively shape itself and its boundary in order to regulate its internal architecture

through growth-induced stresses. We show that biofilms exhibit a sharp transition in shape from

domes to lenses upon changing environmental stiffness or cell-substrate friction, which is

explained by a theoretical model considering the competition between confinement and interfacial

forces. The growth mode defines the progression of the boundary, which in turn determines the

trajectories and spatial distribution of cell lineages. We further demonstrate that the evolving

boundary defines the orientational ordering of cells and the emergence of topological defects in

the interior of the biofilm. Our findings reveal novel self-organization phenomena in confined

active matter and provide strategies for guiding the development of programmed microbial

consortia with emergent material properties.

Main Text:

Active nematics are collections of anisotropic particles which metabolize free energy to generate

mechanical work. Unlike conventional liquid crystals (LCs), they exist far from equilibrium and

activity plays an important role in shaping their collective structure and dynamics1–6. One

prototypical example of active nematics, with non-conserving particle number, are growing

colonies of bacterial cells with elongated shapes7–12. When bacteria collectively secrete

extracellular matrix to adhere to each other and to a substrate, they form multicellular communities

known as biofilms13. Biofilms grow in diverse set of environments including in the ocean, in soil,

and in humans, and as they develop, they take on a rich variety of three-dimensional (3D)

morphologies and internal architechtures14–18. Moreover, the anisotropic shape of bacterial cells

can lead to parallel alignment and nontrivial global organization19–22, which allows one to use

biofilms as model living nematic systems to probe the feedback between evolving boundaries and

internal ordering. Understanding this feedback could allow for controlled growth of beneficial

biofilms, elimination of harmful ones, and the potential development of a new class of growing

active materials that not only respond to but also actively alter their geometry to maximize

functionalities.

Competition between confinement and interfacial forces controls biofilm morphogenesis

Here, we use confined Vibrio cholerae biofilms as the model system to demonstrate the self-

shaping and self-organizing capability of a 3D growing nematic system. To focus on the cell

organization and mechanical aspect of biofilm growth, we used a locked biofilm-forming strain,

labeled as WT*14,23. To tune the effect of the boundary, we employed a geometry where the

biofilm-forming bacteria were confined between a soft hydrogel and a stiff glass substrate14. We

varied the stiffness of the overlaying gel by varying the agarose concentration from 0.2% to 2.5%,

resulting in shear moduli that ranged from 150 Pa – 150 kPa (Extended Data Fig. 1). The gel mesh

size was smaller than the cells and therefore confined them, but large enough to allow free

diffusion of nutrient and waste molecules. In each case, the biofilms grew clonally from a single

cell into a mature biofilm consisting of thousands of cells. Using time-lapse 3D imaging and cell-

segmentation algorithms14,20, we extracted and tracked the evolution of biofilm architectures at

single-cell resolution. Figure 1a shows a series of segmented biofilms grown under gels of different

concentrations consisting of approximately 8600 cells. We found that as the biofilms matured they

developed into one of two bulk shapes indicating two distinct growth modes: under soft

confinement (≤1%), the biofilms grew as hemispherical structures, which we label “domes,”

whereas under stiff confinement (≥2%), the biofilms grew as flatter structures, which we label

“lenses” (Fig. 1b). At intermediate gel concentrations (1% <<2%), we observed the

coexistence of both lenses and domes. To quantify this shape transition, we measured the contact

angle () that the biofilms made on the glass substrate for hundreds of mature biofilms for each

condition (Fig. 1c; Extended Data Fig. 2 and 3). Interestingly,  exhibited a bifurcation-like

transition with increasing stiffness. Biofilms possessed larger  when grown under soft gels

(median  range 101°-121° for = 0.2%-1%) and smaller  when grown under stiff gels

(median  range 23°-39° for =2%-2.5%); at intermediate concentrations (= 1.3%-1.75%),

a bimodal distribution of  emerged, with each peak coinciding with either the large  (small

stiffness, median  range 127°-131° for the subset ≥75°) or small  (large stiffness, median

 range 33°-40° for the subset <75°) behavior (Fig. 1d).

In addition, the kinetics of shape evolution also significantly differed between the two regimes, as

quantified by the evolution of the maximum height ℎ and maximum radius  of the biofilms

(Fig. 1e). For soft confinement, the biofilms grew nearly isotropically with the maximum height

and radius scaling as ℎ ∼1/3 and  ∼1/3, respectively (where  is the number of cells).

For stiff confinement, the biofilms grew faster horizontally than vertically, leading to an

increasingly anisotropic shape over time. This was reflected in the different scaling laws for

biofilm radius and height where ℎ ∼1/5 and  ∼2/5, reminiscent of those observed

during hydraulic fracturing24,25. Correspondingly, we observed two diverging trajectories of 

(Fig. 1f) where  either increased or decreased above ~100 cells.

Previous work suggests cell-substrate friction as a key determinant in biofilm morphogenesis16,26,

which in V. cholerae is mainly achieved by two redundant adhesion proteins RbmC and Bap127,28.

Upon deleting these adhesins, we found that the critical stiffness at which the shape transition

occurred decreased (Extended Data Fig. 4). To further demonstrate the effect of cell-substrate

friction on biofilm shape, we generated a strain with an arabinose-inducible expression vector with

titratable expression of bap1. Indeed, as bap1 expression increased, the critical stiffness at which

the biofilms transitioned from domes to lenses also increased (Fig. 2a). A bimodal distribution of

shapes was again observed near the phase boundary in the two-dimensional phase diagram.

To confirm the important role that cell-substrate interactions play in shaping the final biofilm

shape, we employed experimentally benchmarked agent-based simulations (ABSs)14,29. In the

simulations, we introduced a frictional force that resisted the growth-induced sliding of cells

parallel to the substrate to mimic the effect of the two adhesins in the experiment. By varying the

surface friction coefficient and gel stiffness in the ABSs, we reproduced a similar transition from

large to small  upon decreasing friction or increasing gel stiffness (Fig. 2b), which suggests that

the adhesion proteins indeed control biofilm morphology by increasing the friction between the

biofilms and the substrate.

An energetic model of biofilm morphogenesis explains the shape transition

To elucidate the origins of the two different growth regimes, we consider the energetics of biofilm

growth confined at the bonded interface between a semi-infinite elastic material and a rigid

substrate, while accounting for the frictional losses that are experienced by the biofilm as it slides

along the substrate. Here we model the biofilm as a volumetrically expanding liquid because it can

continuously reorganize itself during growth20,30,31. As the biofilm expands, it can either deform

the surrounding gel or delaminate the gel from the glass substrate, or both. We consider the total

potential energy of the system =+ as the sum of31: (1) adhesion energy () =

Γ(

2−2) invested in delaminating the gel-glass interface with energy density Γ, starting from

an initial basal radius of the biofilm  to its final basal radius , and (2) the elastic energy stored

in the gel (,) = 

3(/

3), where  is the shear modulus and =(/

3) is the

dimensionless elastic potential energy as a function of dimensionless volume, obtained from finite

element simulations. Frictional forces come into play only after the gel begins to delaminate and

the biofilm expands on the substrate, which we model using the Rayleigh dissipation function,

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摘要：

Biofilmsasself-shapinggrowingnematicsJapinderNijjer1,MrityunjayKothari2,3,ChanghaoLi4,ThomasHenzel2,QiutingZhang1,Jung-ShenB.Tai1,ShuangZhou5,SulinZhang4,6,TalCohen*2,7,JingYan1,8*1DepartmentofMolecular,CellularandDevelopmentalBiology,YaleUniversity,NewHaven,CT,USA.2DepartmentofCivilandEnvironmental...

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Biofilm s as self -shaping growing nematics Japinder Nijjer1 Mrityunjay Kothari23 Changhao Li4 Thomas Henzel2 Qiuting Zhang1 Jung- Shen B. Tai1 Shuang Zhou5 Sulin Zhang46 Tal Cohen27 Jing Yan18.pdf

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Biofilm s as self -shaping growing nematics Japinder Nijjer1 Mrityunjay Kothari23 Changhao Li4 Thomas Henzel2 Qiuting Zhang1 Jung- Shen B. Tai1 Shuang Zhou5 Sulin Zhang46 Tal Cohen27 Jing Yan18

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