Physics  of  Development  

Chaitanya  Athale  

Outline  

•  Collec7ve  morphogenesis-­‐  phenomenology  and  some  theory  

 

Pa<erns  of  Bacteria  

Budrene  &  Berg  (1995)  Dynamic  forma7on  of  symmetrical  pa<erns  by  chemotac7c  bacteria    

1mM  succinate  with  E  coli  Tsr-­‐  

2mM  succinate  with  E  coli  Tsr-­‐  

3mM  succinate  with  E  coli  Tsr-­‐  

3mM  succinate  with  E  coli  serine  blind  mutant    

•  Matsuyama  &  Matsushita  (2001)  Popula7on  morphogenesis  in  bacteria.  Forma  16:307-­‐326  

•  Morikawa  (2003)  Simula7on  study  of  bacterial  colony  with  mul7plying  rods.  Forma  18:59-­‐65  

Bacteria:  Free  Swimming  

Chemotaxis  in  liquid  media  Tumble:  change  direc7on,  Run:  straight  swimming  

Bacillus  sub7lis  with  flagella  

Matsuyama  &  Matsushita  (2001)  Forma  

Swarming  Behaviour  

•  Pa<erns  in  liquid  (Budrene  &  Berg  1991,  1995)  •  Surface  transloca7on  referred  to  as  swarming  

Bacteria  ac7vely  translocate  by  flagellar  rota7on  (C,  D,  E)  1-­‐3  days  

Spread  by  volume  increase  of  colony  (A,  B)  2-­‐4  weeks  

Dense  Branching  Morphology  (DBM)  

Taken  from  area  E  (mo7le)  Reminiscent  of  a  class  of  theore7cal  models  

DBM  Structure  

Two  cell  types:  (a)  Non-­‐mo7le  wall  and  7p  cells,  (b)  Mo7le  swirling  cells    inside  

Direc7on  of  branch  extension  

swirling  

Population Morphogenesis by Cooperative Bacteria 311

the tip wall. The outermost tip wall cells do not move by themselves, instead, the innerswirling cells are pushing out little by little these tip wall cells. Thus, in contrast to themoving behavior of individual cells in swirling cluster, the extension of the branch is quiteslow and unidirectional as shown in Fig. 5. Since bacteria have been thought to behaveindependently of each other, special arrangement of differently working cells in the branchpopulation of B. subtilis (division of labor in the bacterial world) was unexpected finding(MATSUYAMA et al., 1993; MATSUYAMA and MATSUSHITA, 1995). It is interesting thatsimilar differential cell arrangement is present in the tissue at the growing ends of themulticellular organism “plant”.

2.3. Physical factors inducing collective behavior of bacteriaIt is curious that bacteria moving on the surface are always getting together. A single

bacterium separated from others on the surface seemed to be immobile. Even in area Dwhere bacterial population seemed to be spreading homogeneously, translocating bacteriain the spreading front were making raft-like clusters (WAKITA et al., 1994). In the worldof bacteria which are so small, effective working forces are quite different from thoseeffective on organisms of the human size. Instead of gravitation, inter-molecular forcesworking on the surfaces of microorganisms are critical. With the size reduction oforganisms, ratio of surface area to volume of the organism will be greater and surface forcesworking on the organism will be more effective. In addition, water which is indispensablefor life has outstandingly strong surface tension. Thus, water around microbes will restrainthe movement of small unicellular organisms on the surface environments (MATSUYAMAet al., 1992; MATSUYAMA and NAKAGAWA, 1996). To overcome such restricting situationin the small scale surface environment, bacteria seem to evolve the translocation mechanismsby arranging collective cell groups. So, in the area E where nutrients are not enough forenergy supply to every bacterial cell, active cells are gathering at the special structural partin the population. Developing this functional and differentiated population, bacteria as awhole (including immobile cells) seem to be spreading efficiently on the nutrient-poormedium surface. In spite of ubiquitous presence of DBM-like pattern in nature, itsgeneration mechanisms have not been investigated by experimental micro-scale analyses.Morphogenic units of DBM-like pattern shown here are living bacteria which are clearlyvisible under an optical microscope. As shown herein, the microscopic video tracing of thedevelopment processes revealed the precise figures leading to the characteristic pattern,

Fig. 5. Schematic illustration of an extending branch. Open box indicates an vigorously swirling bacterial cell.Closed box indicates an inactive cell. Branch extending direction is indicated by an arrow.

inac7ve  Growing  branch  

Chemicals  Inducing  Surface  Spreading    

•  Surface  ac7ve  agents  (surfactants)  

•  Serra7a  marcescens    

S.  marcescens  N38  

N38-­‐09  mutant  defec7ve  in  surfactant  “serrawe^n  W1”  produc7on    

Concentric  Pa<erns  Bacillus  sub7lis  (phase  C-­‐  high  nutrient,  medium  s7ffness)  

Proteus  mirabilis  on  hard  agar  medium  

Proteus  colony  dynamics  shows  intermi<ent  growth  

Collec7ve  Behaviour  

Low  agar  concentra7on  ‘Rads’              Hard  agar  form  disk  like  structure  

Differen7a7on  

Free  living  vs.  collec7ve  modes  of  migra7on  

Chemotaxis  Minimal  medium  agar  plate    Central  disk  of  filter  paper  with  L-­‐alanine  (2.5  uM)    Proteus  inocolated  at  4  points  

Simula7on  of  Bacterial  Rods  

rij=distance  between  central  segments  of  two  rods  I  and  j  lb=length  of  rod  a=radius  of  rod  

Simulation Study of Bacterial Colony 61

the bacteria divides into two new individuals at lb = 14a. Therefore the number of rodsincreases with the simulation step and will form a bacterial colony. In the colony, there isa direct repulsive interaction between rods. The potential energy between the rods i and jis represented as

u ra r r a

r aij

ij ij

ij( ) = ( ) >( )

∞ ≤( )#$%

&%( )

2 22

112

/

where rij is the distance between central segments of rods i and j. Since u(rij) includes asoftcore term (2a/rij)12, the rods can push and shove each other (WAKITA et al., 2001). Asa result, more active rods push other rods. This biological repulsion corresponds to a “short-range repulsive chemotaxis” (KOZLOVSKY et al., 1999).

The movement of the rod is classified as passive or active (BERG, 1992). A passivemovement is caused by a fluctuation of surrounding mediums and thus it depends on thetemperature T and the viscosity of the mediums. From the Stokes’ law, the mean displacementδP

2 = 2Δτk T fB xy/ and the mean rotational angle θP2 = 2Δτk T fB r/ of the rod

for a unit time Δτ are adopted (BERG, 1992). Here fxy = 3πηlb/ln(lb/a) is the viscous dragcoefficient of the rod moving at random and fr = πηlb

3/3(ln(lb/a) – 1/2) is the rotationalfrictional drag coefficient of the minor axis. kB is Boltzmann’s constant. η is the coefficientof viscosity of the surrounding mediums, which depends on not only the concentration ofagar but also the lubricant such a surfactant secreted by the bacteria. An increase in theamount of lubricant decreases the friction between the bacteria and the agar surface. Froma reaction-diffusion model for a bacterial colony including a time-evolution equation of alubricant, Kozlovsky et al. suggested that the coupling of the bacterial motion to thelubricant should be replaced by a density-dependent diffusion coefficient for the bacteria(KOZLOVSKY et al., 1999). We adopt the suggestion into our model and define thecoefficient of viscosity η = η0/s(n) for each rod i, where n is the number of surrounding rodswhich are less than 10a from the rod i. Since the function s(n) is regarded as an increasingfunction, we assume s(n) = 2n × 0.01 + 0.99.

On the other hand, the active movement of a bacteria is driven by rotation of severalflagellar filaments. When these flagella turn counterclockwise, they form a synchronousbundle that pushes the body steadily forward; this mode is said to “run.” When they turnclockwise, the bundle comes apart and the flagella turn independently. As a result, thebacteria moves in a highly erratic manner; this mode is said to “tumble.” In our model, amimic bacteria also moves due to either “run” or “tumble” mode. In the “run” mode, abacteria goes ahead with the mean displacement δ A

2 = 2ΔτA fb a/ , where the value Ab

represents an “activity” of the bacteria, which equals the amount of nutrients ingested bythe individual. fa is a viscous drag coefficient moving lengthwise written as fa = 2πηlb/(ln(lb/a) – 1/2). In the other mode, “tumble”, a bacteria randomly turns clockwise andcounterclockwise by the mean rotational angle θA

2 = 2ΔτA fb r/ .The alternative modes are determined by a parameter µ which relates to the recent

Poten7al  energy  Short  range  repulsive  chemotaxis    Run  Tubmle  Viscosity  η0      Φij  Nutrient  triangular  la^ce  Diffusion  and  inges7on  

Simulated  Pa<erns  

Swarming  in  Eukaryo7c  Cells  

•  Tumour  growth  as  a  paradigm  

Biological  Case  Studies  

1.  Tumour  growth  2.  Collec7ve  cell  behaviour  

Tumour  Growth  

Glioblastoma  mul7forme  (GBM)  

Washington University, School of Medicine

Why  Study  GBM  Most  aggressive  and  commonest  form  of  human  glioblastoma  

Death  <1  yr  of  disease  Mul.forme:  necrosis  &  haemmorhage,pleiomorphic  nuclei  &  cells,  gene7c  dele7ons,  amplifica7on  and  point  muta7ons,    microvascular  prolifera7on  

Subclones  within  tumour  Tumour  of  109  cells  might  harbour  106  cells  with  muta7on  in  any  one  gene  

THERAPY:  surgery,  chemo-­‐  and  radio-­‐therapy  SUCCESS:  Long  term  nil  

Holland (2000)

A.  Pre surgery B.  Post-surgery and radiation-therapy C.  Recurrence in 6 months at 2 sites D.  Post resection of 2 tumours E.  Recurrence of tumour at resection margin

Gene-­‐Protein  Network  in  

GBM  

Qiagen

Therapeu7c  Approaches  •  Surgical  resec7on  •  Radia7on  and  chemotherapy  

•  Mouse  and  in  vitro  models  •  Modified  viruses  •  An7bodies  against  EGFR,  PDGF,  Angiogenesis  (VEGF)  •  siRNA  •  Synthe7c  pep7des  

Understanding  the  basis  of  tumour  growth  and  expansion  

Stages  of  Tumour  Growth  

Modelling  Tumour  Growth  

•  MRI  resolu7on  ~1mm  •  In  vitro  and  mouse  models  do  not  behave  like  human  

•  Single  cell  events  lead  to  malignant  spread  

GOAL:  Understanding  of  tumourigenesis  at  clinically  undetectable  stage  

In  Vitro  Experiments  

Deisboeck et al. (2001)

In  Vitro  Kine7cs  

Emprical  Models  

Comparison  

Experimental volumes (µm3) measured in cell culture tumor spheroids

Discrete  Model  

Cell  as  automaton  Leaves  non-­‐diffusive  a<ractor  trail  Path  of  least  resistance  carved  in  medium  

Square  la^ce  (128x128)  a=  La^ce  constant  =  cell  diameter    Chemotaxis:  Nutrient  Homotype  a<ac7on:  Paracrine  

Sander & Deisboeck (2002)

Signalling  in  a  Mul7cellular  context  

Synthesis

Autocrine

Recycling

Degradation Signalling

Paracrine

Cell 2

Cell 1

Growth  Pa<erns  

Diffusive  growth:  Only  random  walk    Compact                                                  

χ = chemotaxis coefficient β= drift velocity η=homotype attraction Dc=cellular diffusion coefficient

Chemotac7c  and  Homotypic  growth  Disperesed  Chain  forma7on  

Sander  &  Deisboeck  (2002)  Growth  pa<erns  of  microscopic  brain  tumors.  Phys.  Rev.  E  66,  051901  (2002)  

Branching  Pa<erns  

Simula7on  results.  Very  strong  homotype  a<rac7on  and  very  strong  chemotaxis  result.    (Scale  approx.  1  mm).      

Experimental  Branching  

&  7me  

Receptor  signalling  

Synthesis

Autocrine

Recycling

Degradation Signalling

Mul7cellular  context  

Synthesis

Autocrine

Recycling

Degradation Signalling

Paracrine

Cell 2

Cell 1

Mul7cellular  mechanics  

Free Surface

Tumor Spheroid

Cells

Division

Migration

NEXT  

•  Cell  adhesion,  compartmentaliza7on  and  forming  a  hole  (lumen)  

•  Epithelial  morphogenesis  •  Mesenchymal  morphogenesis  •  Pa<ern  forma7on:  segmenta7on,  axes  and  asymmetry  

NEXT  •  Developmental  processes  in  metazoans  •  Cleavage  and  blastula  •  Cell  states  •  Cell  adhesion,  compartmentaliza7on  and  forming  a  hole  (lumen)  

•  Epithelial  morphogenesis  •  Mesenchymal  morphogenesis  •  Pa<ern  forma7on:  segmenta7on,  axes  and  asymmetry  

•  Organogenesis  

Scale  of  Descrip7on  

Molecular  dynamics:  details  at  atomic  and  molecular  scales    

Par7al  differen7al  equa7ons:  pressure,  temperature,  velocity  

La^ce  Gases  (cellular  automata)  

Spa

tio-te

mpo

ral s

cale

Complex  Systems  

Macroscopic  systems  with  many  interac7ng  microscopic  objects  

Sophis7cated  stochas7c  methods  used  to  create  simula7ons  of  complex  systems  

Capable  of  exhibi7ng  collec7ve  behaviour  and  phase  transi7ons  

Physical  Examples  

Freezing  or  boiling  of  a  liquid    Magnet  with  ferromagne7c  or  paramagne7c  transi7ons  

 Glass    Liquid  crystals  

Biological  Examples  Protein  folding  Membrane  organiza7on  Spontaneous  pore  forma7on  Targe7ng  of  transcrip7on  factors  to  genes  Cell  division  Cell  migra7on  Collec7ve  cell  migra7on  (would  healing,  development)  

Tissue  repair  and  regenera7on  Tumours  Organ  development  

nm

µm

mm

ms

µs fs

s

min

hr

La^ce  Gas  Automata  

FHP  2D  triangular  

la^ce  (Frisch,  Hasslacher,  Pomeau)  1986  

x

y

Rules: 1.  Collisions Scatter if 2 particles

approach head on Momentum conservation by

random choice 2. Transport

HPP  2D  square  la^ce  

(Hardy,  Pomeau,  dePazzis)  

x

y

FHP  Collision  Rules  

Applicability  of  LGA  for  Hydrodynamic  Modelling  

La>ce  Gas  Automata   Tradi.onal  Hydrodynamics  

High  viscosity  inbuilt  in  rules   Flexible  viscosity  values  

Finite  spa7al  resolu7on   No  predetermined  resolu7on    

Imprac7cal  for  turbulence  studies   Turbulence  can  be  handled  

Complex  boundary  condi7ons     Simple  boundary  condi7ons  

Intui7ve  approach   Not  intui7ve  for  complex  phenomena  

Need  sta7s7cal  averaging   Gives  a  sta7s7cal  average  

Less  flexible  for  parameter  range  for  generality  

Completely  flexible  and  general  

Successful applications: flows in porous media, immiscible flows and instabilities, spreading of droplets, wetting phenomena, microemulsion and transport problems Pattern formation, reaction-diffusion, nucleation-aggregation and growth phenomena.

La^ce  Gases  and  Fluids  

•  Fluid:  La^ce  gas  •  Geometry  of  la^ce  •  Discrete  states  permi<ed  •  Update  rule  based  on  neighbours  •  Compact  state  descrip7on  and  lookup  table  •  Conserva7on  laws