Full governing equations for linear deformations, and the
reduced forms for bending or tension dominance
Bending stiffness
Membrane tension
4
2
⎛
⎞
⎛
∂
u
∂
u3 ⎞
'
3
Kb ⎜
−N⎜
−p=0
4 ⎟
2 ⎟
⎝ ∂ x1 ⎠
⎝ ∂ x1 ⎠
Bending K b' u / λ 4
Kb
∝
∝
>> 1
2
2
Nλ
Tension
Nu / λ
4
⎛
∂
u3 ⎞
'
Kb ⎜ 4 ⎟ = p
⎝ ∂ x1 ⎠
u = displacement
p = pressure difference
R = radius of curvature x = spatial coordinate
K b'
<< 1
2
Nλ
⎛ ∂ 2 u3 ⎞
⎛ 1⎞
p = −N ⎜
≅
N
⎜⎝ ⎠⎟
R
⎝ ∂ x12 ⎠⎟
N = membrane tension λ = characteristic length 1
Cell Motility: Actin
Ruffles, lamellipodia
and Blebs in Motile
Cells
Charras, et al., Nature, 2005.
Figures removed due to copyright restrictions.
2
Cell migration in 3D (Polacheck, 2012)
4/30/15
Confidential
4
© source unknown. All rights reserved. This contentis excluded from our Creative
Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
3
Vascular network formation
)LJXUHRIYDVFXODUQHWZRUNIRUPDWLRQUHPRYHGGXHWRFRS\ULJKWUHVWULFWLRQV
4
Real-time imaging of 3D migration
Bill Polacheck
Figures removed due to copyright restrictions.
5
Tumor cells dispersing from a spheroid
Figures removed due to copyright restrictions.
6
T-cell targeting of liver cancer cells
~23mins / frame Figures removed due to copyright restrictions.
7
Cell Migration on 2D Substrates
Cell migration patterns. In the absence of
an external signal (e.g., chemoattractant
gradient), the migration pattern resembles
a random walk.
a)
Random, nondirected
migration.
b)
Migration in
the presence of
a chemotactic
gradient
Migration speed (S) tends
to vary inversely with
persistence time (P).
Mean-free-path ~ SP ~
const.
d 2 ~ S 2 Pt
© source unknown. All rights reserved. This contentis excluded from our Creative
Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
8
Macrophages enhance cancer cell migration
Figures removed due to copyright restrictions.
9
Different types of cell migration
Figures removed due to copyright restrictions.
10
Stages of metastatic cancer
Courtesy of Macmillan Publishers Limited. Used with permission.
Source: Wirtz, Denis, et al. "The Physics of Cancer: The Role of Physical Interactions and
Mechanical Forces in Metastasis." 1DWXUH5HYLHZV&DQFHU 11, no. 7 (2011): 512-22.
Wirtz et al., Nature Cancer Reviews, 2011
11
Courtesy of Macmillan Publishers Limited. Used with permission.
Source: Cahoon, Lauren. "Let's Get Physical: Mechanical Forces Drive a New Field of Study." 1DWXUH0HGLFLQH 17, no. 3 (2011): 271.
#)4233
12
"+--%%%,,-'#
2228.56:7/27095639.4
.
#*
'
$$*
%
32+#
9+/0
9+.*
$$#
Courtesy of Elsevier, Inc., http://www.sciencedirect.com. Used with permission.
Source: Guck, Jochen, et al. "Optical Deformability as an Inherent Cell Marker for Testing Malignant
Transformation and Metastatic Competence." %LRSK\VLFDO-RXUQDO 88, no. 5 (2005): 3689-98.
13
#
&
#
.
#
#
Kraning-Rush, PLoS ONE, 2012
Courtesy of the authors. License: CC BY.
Source: Kraning-Rush, Casey M., et al. "Cellular Traction Stresses Increase
with Increasing Metastatic Potential." 3OR621( 7, no. 2 (2012): e32572.
14
Extravasation
Courtesy of Macmillan Publishers Limited. Used with permission.
Source: Wirtz, Denis, et al. "The Physics of Cancer: The Role of Physical Interactions and
Mechanical Forces in Metastasis." 1DWXUH5HYLHZV&DQFHU 11, no. 7 (2011): 512-22.
Wirtz et al., Nature Cancer Reviews, 2011
15
In vitro model of extravasation
Figures removed due to copyright restrictions.
16
Tumor cells extravasating
Figures removed due to copyright restrictions.
17
Tumor cell extravasation
Figure removed due to copyright restrictions.
Source: Chen, Michelle B., et al. "Mechanisms of Tumor Cell Extravasation in an In Vitro
Microvascular Network Platform." ,QWHJUDWLYH%LRORJ\ 5, no. 10 (2013): 1262-71.
18
Figure removed due to copyright restrictions.
Source: Chen, Michelle B., et al. "Mechanisms of Tumor Cell Extravasation in an In Vitro
Microvascular Network Platform." ,QWHJUDWLYH%LRORJ\ 5, no. 10 (2013): 1262-71.
19
MIT OpenCourseWare
http://ocw.mit.edu
20.310J / 3.053J / 6.024J / 2.797J Molecular, Cellular, and Tissue Biomechanics
Spring 2015
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