Dynamic biochemical signal control is important in in vitro cell studies. This work analyzes the transportation of dynamic biochemical signals in steady and mixing flow in a shallow, Y-shaped microfluidic channel. The characteristics of transportation of different signals are investigated, and the combined effect of transverse diffusion and longitudinal dispersion is studied. A method is presented to control the widths of two steady flows in the mixing channel from two inlets. The transfer function and the cutoff frequency of the mixing channel as a transmission system are presented by analytically solving the governing equations for the time-dependent Taylor–Aris dispersion and molecular diffusion. The amplitude and phase spectra show that the mixing Y-shaped microfluidic channel acts as a low-pass filter due to the longitudinal dispersion. With transverse molecular diffusion, the magnitudes of the output dynamic signal are reduced compared to those without transverse molecular diffusion. The inverse problem of signal transportation for signal control is also solved and analyzed.

References

References
1.
Hancock
,
J. T.
,
1997
,
Cell Signaling
,
Prentice-Hall
,
New York
.
2.
Palsson
,
B. O.
, and
Bhatia
,
S. N.
,
2004
,
Tissue Engineering
,
Prentice-Hall
,
New York
.
3.
Wolpert
,
L.
,
Beddington
,
R.
,
Jessell
,
T. M.
,
Lawrence
,
P.
,
Meyerowitz
,
E. M.
, and
Smith
,
J.
,
2002
,
Principles of Development
,
Oxford
,
New York
.
4.
Hartwell
,
L. H.
,
Hopfield
,
J. J.
,
Leibler
,
S.
, and
Murray
,
A. W.
,
1999
, “
From Molecular to Modular Cell Biology
,”
Nature
,
402
(
6761s
), pp.
c47
c52
.10.1038/35011540
5.
Hoffman
,
B. D.
,
Grashoff
,
C.
, and
Schwartz
,
M. A.
,
2011
, “
Dynamic Molecular Processes Mediate Cellular Mechanotransduction
,”
Nature
,
475
(
7356
), pp.
316
323
.10.1038/nature10316
6.
Cook
,
B.
,
Hardy
,
R. W.
,
McConnaughey
,
W. B.
, and
Zuker
,
C. S.
,
2008
, “
Preserving Cell Shape Under Environmental Stress
,”
Nature
,
452
(
7185
), pp.
361
365
.10.1038/nature06603
7.
Yu
,
H. M.
,
Meyvantsson
,
I.
,
Shkel
,
I. A.
, and
Beebe
,
D. J.
,
2005
, “
Diffusion Dependent Cell Behavior in Microenvironments
,”
Lab Chip
,
5
(
10
), pp.
1089
1095
.10.1039/b504403k
8.
Bennett
,
M. R.
,
Pang
,
W. L.
,
Ostroff
,
N. A.
,
Baumgartner
,
B. L.
,
Nayak
,
S.
,
Tsimring
,
L. S.
, and
Hasty
,
J.
,
2008
, “
Metabolic Gene Regulation in a Dynamically Changing Environment
,”
Nature
,
454
(
7208
), pp.
1119
1122
.10.1038/nature07211
9.
Davies
,
P. F.
,
1995
, “
Flow-Mediated Endothelial Mechanotransduction
,”
Physiol. Rev.
,
75
(
3
), pp.
519
560
. Available at http://go.galegroup.com/ps/i.do?id=GALE%7CA18253882&v=2.1&u=lom_umichanna&it=r&p=AONE&sw=w&asid=8ebe1968d750e45f168f0134f69514a5
10.
Zhang
,
X. L.
,
Yin
,
H. B.
,
Cooper
,
J. M.
, and
Haswell
,
S. J.
,
2008
, “
Characterization of Cellular Chemical Dynamics Using Combined Microfluidic and Raman Techniques
,”
Anal. Bioanal. Chem.
,
390
(
3
), pp.
833
840
.10.1007/s00216-007-1564-9
11.
Kuczenski
,
B.
,
Ruder
,
W. C.
,
Messner
,
W. C.
, and
LeDuc
,
P. R.
,
2009
, “
Probing Cellular Dynamics With a Chemical Signal Generator
,”
PLoS ONE
,
4
(
3
), p.
e4847
.10.1371/journal.pone.0004847
12.
Qin
,
K. R.
,
Xiang
,
C.
, and
Cao
,
L. L.
,
2011
, “
Dynamic Modeling for Flow-Activated Chloride-Selective Membrane Current in Vascular Endothelial Cells
,”
Biomech. Model. Mechanobiol.
,
10
(
5
), pp.
743
754
.10.1007/s10237-010-0270-2
13.
Kim
,
Y. T.
,
Joshi
,
S. D.
,
Messner
,
W. C.
,
LeDuc
,
P. R.
, and
Davidson
,
L. A.
,
2011
, “
Detection of Dynamic Spatiotemporal Response to Periodic Chemical Stimulation in a Xenopus Embryonic Tissue
,”
PLoS ONE
,
6
(
1
), p.
e14624
.10.1371/journal.pone.0014624
14.
Shin
,
H.
,
Mahto
,
S. K.
,
Kim
,
J. H.
, and
Rhee
,
S. W.
,
2011
, “
Exposure of BALB/3T3 Fibroblast Cells to Temporal Concentration Profile of Toxicant Inside Microfluidic Device
,”
Biochip J.
,
5
(
3
), pp.
214
219
.10.1007/s13206-011-5304-z
15.
Wang
,
Y.
,
Chen
,
Z. Z.
, and
Li
,
Q. L.
,
2010
, “
Microfluidic Techniques for Dynamic Single-Cell Analysis
,”
Microchim. Acta
,
168
(
3–4
), pp.
177
195
.10.1007/s00604-010-0296-2
16.
Martin
,
R. S.
,
Root
,
P. D.
, and
Spence
,
D. M.
,
2006
, “
Microfluidic Technologies as Platforms for Performing Quantitative Cellular Analyses in an In Vitro Environment
,”
Analyst
,
131
(
11
), pp.
1197
1206
.10.1039/b611041j
17.
Ziolkowska
,
K.
,
Kwapiszewski
,
R.
, and
Brzozka
,
Z.
,
2011
, “
Microfluidic Devices as Tools for Mimicking the In Vivo Environment
,”
New J. Chem.
,
35
(
5
), pp.
979
990
.10.1039/c0nj00709a
18.
Breslauer
,
D. N.
,
Lee
,
P. J.
, and
Lee
,
L. P.
,
2006
, “
Microfluidics-Based Systems Biology
,”
Mol. Biosyst.
,
2
(
2
), pp.
97
112
.10.1039/b515632g
19.
Chen
,
L.
,
Azizi
,
F.
, and
Mastrangelo
,
C. H.
,
2007
, “
Generation of Dynamic Chemical Signals With Microfluidic C-DACs
,”
Lab Chip
,
7
(
7
), pp.
850
855
.10.1039/b706304k
20.
Azizi
,
F.
, and
Mastrangelo
,
C. H.
,
2008
, “
Generation of Dynamic Chemical Signals With Pulse Code Modulators
,”
Lab Chip
,
8
(
6
), pp.
907
912
.10.1039/b716634f
21.
Xie
,
Y.
,
Wang
,
Y.
, and
Mastrangelo
,
C. H.
,
2008
, “
Fourier Microfluidics
,”
Lab Chip
,
8
(
5
), pp.
779
785
.10.1039/b718376c
22.
Kuczenski
,
B.
,
LeDuc
,
P. R.
, and
Messner
,
W. C.
,
2007
, “
Pressure-Driven Spatiotemporal Control of the Laminar Flow Interface in a Microfluidic Network
,”
Lab Chip
,
7
(
5
), pp.
647
649
.10.1039/b617065j
23.
Yamada
,
A.
,
Katanosaka
,
Y.
,
Mohri
,
S.
, and
Naruse
,
K.
,
2009
, “
A Rapid Microfluidic Switching System for Analysis at the Single Cellular Level
,”
IEEE Trans. Nanobiosci.
,
8
(
4
), pp.
306
311
.10.1109/TNB.2009.2035253
24.
Taylor
,
G. I.
,
1953
, “
Dispersion of Soluble Matter in Solvent Flowing Slowly Through a Tube
,”
Proc. R. Soc. London A
,
219
(
1137
), pp.
186
203
.10.1098/rspa.1953.0139
25.
Aris
,
R.
,
1956
, “
On the Dispersion of a Solute in a Fluid Flowing Through a Tube
,”
Proc. R. Soc. London A
,
235
(
1200
), pp.
67
77
.10.1098/rspa.1956.0065
26.
Gill
,
W. N.
, and
Sankarasubramanian
,
R.
,
1970
, “
Exact Analysis of Unsteady Convective Diffusion
,”
Proc. R. Soc. London A
,
316
(
1526
), pp.
341
350
.10.1098/rspa.1970.0083
27.
Chatwin
,
P. C.
,
1973
, “
On the Longitudinal Dispersion of Dye Whose Concentration Varies Harmonically With Time
,”
J. Fluid Mech.
,
58
(
4
), pp.
657
667
.10.1017/S0022112073002399
28.
Beard
,
D. A.
,
2001
, “
Taylor Dispersion of Solute in a Microfluidic Channel
,”
J. Appl. Phys.
,
89
(
8
), pp.
4667
4669
.10.1063/1.1357462
29.
Beard
,
D. A.
,
2001
, “
Response to ‘Comment on ‘Taylor Dispersion of Solute in a Microfluidic Channel’
,”
J. Appl. Phys.
,
90
(
12
), pp.
6555
6556
.10.1063/1.1417985
30.
Dorfman
,
K. D.
, and
Brenner
,
H.
,
2001
, “
Comment on ‘Taylor Dispersion of Solute in a Microfluidic Channel’
,”
J. Appl. Phys.
,
90
(
12
), pp.
6553
6554
.10.1063/1.1417984
31.
Lam
,
Y. C.
,
Chen
,
X.
, and
Yang
,
C.
,
2005
, “
Depthwise Averaging Approach to Cross-Stream Mixing in a Pressure-Driven Microchannel Flow
,”
Microfluid. Nanofluid.
,
1
(
2
), pp.
218
226
.10.1007/s10404-004-0013-8
32.
Desmet
,
G.
, and
Barton
,
G. V.
,
2002
, “
Chromatographic Explanation for the Side-Wall Induced Band Broadening in Pressure-Driven and Shear-Driven Flows Through Channels With a High Aspect-Ratio Rectangular Cross-Section
,”
J. Chromatogr. A
,
946
(
1–2
), pp.
51
58
.10.1016/S0021-9673(01)01546-1
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