Document Sample
THE CELL THE CELL Powered By Docstoc
					                                                                                               By Kristin Sainani, PhD

           IN                                                           2010:
                                                           A M ODELING O DYSSEY

                                                                           T           he cell is like our financial
                                                                           system: Even if you have a diagram of all
                                                                           the complex interactions going on, you
                                                                           still cannot intuit how the whole system
                                                                           will react when perturbed. Indeed,
                                                                           the cell’s unpredictable responses to
                                                                           manipulation sometimes resemble
                                                                           the unanticipated magnitude of system
                                                                           failure seen in the 2008 financial crisis,
                                                                           says Gary An, MD, associate professor
                                                                           of surgery at Northwestern University
                                                                           Feinberg School of Medicine. >

Published by Simbios, the NIH National Center for Physics-Based Simulation of Biological Structures                     17
           With hundreds of trillions of atoms,                            York in the United Kingdom.
       thousands of proteins, and a host of                                   What follows are examples of how
       tiny organs, motors, and highways that                              cell-centered models are adding funda-
       often interact in non-linear ways, the                              mental insights into our understanding
       cell is a rich target for computational                             of cell behaviors—including how cells
       modeling. But modelers and cell biolo-                              divide, eat, sense, move, cooperate,
       gists haven’t traditionally worked                                  travel, and battle injury—as well as
       together. “In the past I think a lot of                             helping modelers bridge from the
       really interesting mathematical model-                              molecular to the tissue and organism
       ing was going on, but I’m not sure how                              levels. These models range in scale
       closely tied it was to the biologists’ con-                         from single-cell to multi-cell, but all
       sciousness,” says Steven Altschuler,                                have implications for the basic life sci-
       PhD, associate professor of pharmacol-            “When we’re       ences as well as for diseases, such as
       ogy at Southwestern Medical School.                                 cancer, heart disease, and sepsis.
           This is slowly changing. “Now is a
       time when both sides are realizing it’s
                                                        thinking about
       a good thing to get together. And I
       think a lot of progress is happening,”
                                                     multi-scale systems           MODELING
       Altschuler says.
           Greater integration stands to benefit      in biology, many             THE CELL:
       both cell biology and biomedical mod-
       eling alike.                                  people either start       BEYOND BIOCHEMISTRY
           Cell biologists need modeling to                                   Modelers have traditionally treated
       understand how genes, proteins, and                 at the very     the cell as a bag of chemicals, focusing
       pathways work together to make the                                  on signaling networks, such as positive
       cell go. “To me, it’s no longer possible           smallish level   and negative feedback loops. These
       to even imagine thinking about these                                models have led to important insights.
       problems properly without using mod-
       els as a crutch,” says Ed Munro, PhD,
                                                        or they start at   But the biochemistry isn’t happening
                                                                           in a vacuum; reactions unfold within,
       assistant professor of molecular genetics
       and cell biology at the University of
                                                       the tissue level;   and are influenced by, the cell’s hetero-
                                                                           geneous physical environment. To truly
       Washington. “There are simply too                                   understand cell behavior, you have to
       many moving parts and too many inter-           I think very few    account for the physics and geometry.
       actions for your brain to synthesize.”                                 “People normally think about bio-
           Even with relatively simple models,            people have      chemical networks and pathways. That’s
       Munro says his intuition about what                                 what systems biology is about. But, in
       will come out of a simulation is wrong              thought of      addition to that, there’s polymer physics,
       much of the time. “I’m often complete-                              membrane transport, electrophysiology,
       ly surprised,” he says. “That tells me            the cell as the   electrical events, cell mechanics, and
       that if we’re limited to assembling ver-                            the forces in adhesion,” says Leslie M.
       bal explanations for the things we
       study, then we’re in trouble.”
                                                           main point.     Loew, PhD, professor of cell biology and
                                                                           of computer science and engineering at
           At the same time, modelers need cell                            the University of Connecticut Health
       biologists. Traditionally, modelers have
                                                           But the cell    Center, and one of the creators of
       focused on either the molecular level                               Virtual Cell, a well-known cell model-
       (genes and proteins) or the macro level             is the basic    ing program (
       (tissues and organisms). But some are                                  “When people say that they want to
       arguing that when it comes to multi-          unit of life,” says   model the cell, they’re mostly talking
       scale modeling, it makes the most sense                             about what’s happening in time; very few
       to start in the middle—at the cell level.     Jenny Southgate.      modelers try to think about what’s hap-
       After all, molecular interactions coa-                              pening in space. And not only space, but
       lesce at the level of the cell, and tissues                         also mechanical processes, like forces
       are just a bunch of cells acting together.                          and movements,” says Alex Mogilner,
           “When we’re thinking about multi-                               PhD, professor of neurobiology, physiol-
       scale systems in biology, many people                               ogy and behavior and of mathematics at
       either start at the very smallish level or                          the University of California, Davis.
       they start at the tissue level; I think                                But incorporating space and
       very few people have thought of the                                 mechanics is challenging, Mogilner says.
       cell as the main point. But the cell is                             Several software programs can model
       the basic unit of life,” says Jenny                                 simple diffusion in a relatively nice
       Southgate, PhD, professor of molecular                              geometry, but that doesn’t capture the
       carcinogenesis at the University of                                 reality of the cell. “The inside of the cell

18 BIOMEDICAL COMPUTATION REVIEW       Spring 2010                   
is cluttered with all sorts of debris—           conceptual models that describe the               direct correspondence with experiment
cytoskeleton, organelles, and other stuff.       cell in caricature, Mogilner says.                and tend to be more accessible to biol-
In addition to diffusion, there’s also           Though it may seem that more detail               ogists and physicians, but they may add
directed transport by molecular motors.          would always be better, in fact there is          little to overall understanding.
Plus, diffusion may happen in the bulk           a tradeoff between complexity and                     “You can take biology, which is a big
of the cytoplasm or in the plane of the          insight. All-inclusive models have a              black box, and turn it into an accurate
membrane. It’s very difficult,” Mogilner
says. Virtual Cell has developed the abil-
ity to model diffusion along a membrane
and in complex geometries. These capa-
bilities are state of the art.
                                                        “When people say that they want to
    Spatial modelers make other simpli-
fications as well, such as modeling in
                                                        model the cell, they’re mostly talking
two dimensions or treating cells as per-
fect circles. But some are trying to                    about what’s happening in time; very
bridge to 3-D or account for versatile
and changing cell shapes. Virtual Cell                    few modelers try to think about
allows continuum models in 3-D; and
another cell modeling program, MCell                        what’s happening in space.
(, can do discrete
stochastic simulations in 3-D.
    As modelers account for more and
                                                            And not only space, but also
more of the cell’s physical realities, it
seems that, by necessity, models will get
                                                        mechanical processes, like forces and
more complex and detailed. This isn’t
always the case, however. Models can                      movements,” says Alex Mogilner.
range from all-inclusive models that
attempt to perfectly mimic the cell to

Modeling in Space. Programs like Virtual Cell allow researchers to        drite”). Courtesy of Sherry-Ann Brown, University of Connecticut
model the spatial realities of the cell, such as diffusion on a mem-      Health Center; published in: Brown, S., F. Morgan, J. Watras, and L. M.
brane. This Virtual Cell simulation shows lipid signaling and diffusion   Loew. 2008. Analysis of phosphatidylinositol-4,5-bisphosphate sig-
on a protrusion of membrane on a neural cell (called a “spiny den-        naling in cerebellar Purkinje spines. Biophysical Journal 95:1795-1812.

Published by Simbios, the NIH National Center for Physics-Based Simulation of Biological Structures                                                 19
       simulation, which in itself has become        random. They built a comprehensive            use some kind of error-correction
       a big black box,” Altschuler says. In         model of spindle assembly, including          mechanism.
       contrast, he says, conceptual models          hundreds of microtubules (represented            They simulated a number of plausi-
       “give you a glimpse into something            as rods that grow and shrink in differ-       ble mechanisms but “so far, what we are
       really fundamental.”                          ent directions) and tens of chromo-           finding is almost nothing can explain

                 Conceptual models “give you a glimpse into something
                      really fundamental,” Steven Altschuler says.

                                                     somes (represented as randomly orient-        totally fast and accurate assembly,”
           HOW      A CELL DIVIDES:                  ed cylinders dispersed throughout a           Mogilner says. Their model provides
        HARNESSING THE WILDNESS                      spherical nucleus). Their simulations         constraints for researchers exploring
               OF MICROTUBULES                       showed that a purely random search-           alternative error-correction mecha-
          When a cell divides, it assembles an       and-capture would not be fast enough          nisms, he says.
       intricate piece of machinery called a         to assemble the spindle in the 15 to 20          Once microtubules have accurately
       “mitotic spindle” that physically sepa-       minutes it takes the cell. Instead, a         captured the chromosomes, they line
       rates the chromosomes. Chromosomes            “biased” search-and-capture was               them up evenly at the equator of the
       are pulled apart by filamentous rods,         required—molecular motors direct              nucleus. What’s unclear is how the
       called microtubules, anchored on              microtubules to grow in areas where           microtubules, which start at highly var-
       either side of the nucleus, at the cen-       they are more likely to bump into chro-       ied lengths, manage to even themselves
       trosomes. One of the fundamental              mosomes.                                      out. “The question is: how do you har-
       questions of mitosis is how this spindle         In a follow-up paper in PNAS in            ness the wildness of the microtubules,
       assembles. Mathematical modeling has          2009, Mogilner’s team ran simulations         which would otherwise be inclined to
       been instrumental in answering this           that probed not only the speed of             grow and shorten very randomly and
       question because it is difficult to exper-    biased search-and-capture, but also its       willy-nilly?” says David Odde, PhD,
       imentally follow and perturb individual       accuracy. The result: there were errors       professor of biomedical engineering at
       microtubules, Mogilner says.                  in a whopping 70 percent of micro-            the University of Minnesota.
          Microtubules are dynamic polymers          tubule-chromosome attachments (for               In a 2008 paper in Cell, Odde and
       that can rapidly shed or add proteins to      example, when a chromosome is cap-            his colleagues used a Monte Carlo sim-
       their unanchored end. It’s known that         tured by only one microtubule or by           ulation to predict that an unidentified
       microtubules find the chromosomes             two microtubules from the same pole).         molecular motor must regulate micro-
       through      a    “search-and-capture”        In real life, cell division is highly accu-   tubule length. Simulations showed
       process: they randomly grow and shrink        rate. So this revealed that the cell must     that deleting this protein would cause
       from the centrosomes until, by                                                                       microtubules to grow too long
       chance, they encounter a chro-                                                                       and uneven, and overexpress-
       mosome and hook it.                                                                                  ing it would cause micro-
          In an influential paper four                                                                      tubules to grow too short and
       years ago, Mogilner and his                                                                          to cluster near the poles of the
       colleagues showed that the                                                                           nucleus. His graduate student,
       process cannot be completely                                                                         Melissa Gardner, then identi-
                                                                                                            fied the protein experimental-
       Search and Capture. Visualization                                                                    ly: kinesin-5, a motor protein
       of a computer simulation of                                                                          not previously recognized as a
       microtubules (growing in blue,                                                                       player in microtubule assembly.
       shortening in red, captured in                                                                           The model shows that
       green) searching for chromo-                                                                         kinesin’s mode of action is
       somes during mitotic spindle                                                                         really simple, Odde says. The
       assembly. Courtesy of: Raja Paul                                                                     longer a microtubule becomes,
       and Alex Mogilner, University of                                                                     the more places kinesin—
       California, Davis. Reprinted from                                                                    which promotes disassem-
       Paul, R., et al., Computer simula-                                                                   bly—can attach to. “It evens
       tions predict that chromosome                                                                        the game out. It just keeps
       movements and rotations acceler-                                                                     penalizing the ones that keep
       ate mitotic spindle assembly with-                                                                   getting out ahead of the oth-
       out compromising accuracy, PNAS                                                                      ers,” Odde says.
       106(37) 15708-15713 (2009).                                                                              The finding has implica-

20 BIOMEDICAL COMPUTATION REVIEW       Spring 2010                                          
tions in cancer, as it means that anti-
kinesin drugs—which are already in
clinical trials—could help control
tumor growth by disrupting a critical
step in mitosis.

    Single-cell organisms obtain nutri-
ents via a process called cell eating, or
phagocytosis. Using its cytoskeleton—
                                               Virtual Cell Eating. A. Experimental
dynamic filaments including actin and
                                               images and corresponding computer
microtubules—the cell wraps itself
                                               simulation of a neutrophil engulfing a
around a particle until it’s fully
                                               bead. B. A close-up of the simulation:
engulfed. Cells of the immune system
                                               the arrows show the flow of the
use the same process to destroy bacte-
                                               “sludgy” cytoskeleton from the point of
ria and yeast and to clean up debris.
                                               view of the bead (top) and of the cell
“Without the phagocytosis of yeast,
                                               (bottom). Adapted with permission from:
you would be fermented within a day
                                               Marc Herant, Volkmar Heinrich and Micah
or so,” says Micah Dembo, PhD, pro-
                                               Dembo. Mechanics of neutrophil phagocy-
fessor of biomedical engineering at
                                               tosis: experiments and quantitative mod-
Boston University.
                                               els. Journal of Cell Science 119: 1903-1913
    “Though the components of cell
                                               (Figures 3 and 5,
eating have been well worked out,
mechanistic explanations are lacking,”
Dembo says. “We want to know: what
are the forces that the cell is producing?
How is the cell pushing? How hard is it
pushing? Where is it pushing? Is it
pulling? How does it orchestrate its lit-
tle hands and fingers to do something                           “We want to know:
like phagocytosis?”
    Dembo has built a model of phago-
cytosis for neutrophils (a type of white
                                                            What are the forces that
blood cell) in collaboration with
Volkmar Heinrich, PhD, an associate
                                                               the cell is producing?
professor of biomedical engineering at
the University of California, Davis,                         How is the cell pushing?
and Marc Herant, PhD, a research
assistant professor of biomedical engi-                      How hard is it pushing?
neering at Boston University. Rather
than model the cytoskeleton compo-                     Where is it pushing? Is it pulling?
nents as individual proteins or rods,
“we believe at its basis, the cytoskele-                     How does it orchestrate
ton is just kind of a gooey glop,”
Dembo says. “It’s got intermediate fila-
ments in there; it’s got actin in there;
                                                       its little hands and fingers to do
it’s got microtubules in there; it’s got
water; it’s got endoplasmic reticulum;
                                                        something like phagocytosis?”
it’s got big chunks like granules and
lysosomes; and the nucleus is a big rock                        Micah Dembo says.
in there. We think of it as a sludge,
which, to a good approximation, can
be regarded as a creeping fluid.” They
use a system of partial differential         forces to eat a bead: a protrusive force         out around the bead. At the same time
equations to keep track of the forces        and an intrusive force. The cytoskele-           the cytoskeleton and cell membrane
exerted by and on this viscous fluid as      ton and the cell membrane repulse                attract each other (the intrusive force),
it moves within the cell.                    each other (the protrusive force), caus-         causing cytoskeleton to build up near
    In a paper in the Journal of Cell        ing a gap to open between them; as               the membrane; as this excess cytoskele-
Science in 2006, Dembo’s team reported       cytoskeleton polymerizes in the gap,             ton depolymerizes, this sucks the bead
that neutrophils use two key interfacial     this causes fingers of cytoplasm to jet          into the cell.

Published by Simbios, the NIH National Center for Physics-Based Simulation of Biological Structures                                       21
             Surprisingly, when the same neu-          the cell is trying to grab it.” The        says. “Without the modeling, you
         trophil eats a yeast particle, it loses its   researchers don’t really know why this     would just be looking at pictures of
         ability to generate the intrusive force.      happens, but perhaps the yeast particle    cells eating things.”
         “It has to slowly wrap its fingers around     has a defense mechanism that blocks
         the yeast without any sucking in              the intrusive force.                          HOW A CELL SENSES:
                                                                                                  FEELING THE ENVIRONMENT
                                                                                                      The cell’s environment plays a criti-
                                                                                                  cal role in directing cell behavior. In a
                                                                                                  landmark 2006 paper in Cell,
                                                                                                  researchers showed that the mechani-
            “Until you model it and think about it,                                               cal properties of the environment
                                                                                                  alone—just its elasticity, nothing bio-
            you never realize how clever the cell is                                              chemical—can influence cell fate: for
                                                                                                  example, a stem cell grown on a very
           and all the problems that the poor cell is                                             stiff substrate becomes a bone cell
                                                                                                  whereas the same stem cell grown on a
           facing to do these things,” Dembo says.                                                soft tissue becomes a brain cell. Follow-
                                                                                                  up experiments showed that substrate
                                                                                                  stiffness also directly affects cell shape,
                                                                                                  motility, growth, and malignancy. “The
                                                                                                  fundamental question is: how do they
         motion,” Dembo says. “So the cell is             “I love this kind of thing because      sense the stiffness?” Odde says.
         trying to make a big enough hand, and         until you model it and think about it,         Cells bind to and interact with their
         it will eventually manage to do that.         you never realize how clever the cell is   environments (typically, the extracellu-
         But in the meantime the yeast is getting      and all the problems that the poor cell    lar matrix) through proteins called
         pushed away [by the protrusive force] as      is facing to do these things,” Dembo       integrin receptors. These receptors clus-
                                                                                                  ter in the cell membrane to form “adhe-
                                                                                                  sion complexes” that link the cell’s
                                                                                                  actin cytoskeleton to the matrix and
                                                                                                  play a key role in cell movement and
                                                                                                  cell-to-matrix communication.
                                                                                                      In a December 2009 paper in PLoS
                                                                                                  Computational Biology, Daniel A.
                                                                                                  Hammer, PhD, professor of bioengi-
                                                                                                  neering and of chemical engineering,
                                                                                                  and his colleagues, revealed a “simple
                                                                                                  calculation that shows why substrate
                                                                                                  elasticity affects the biology so strong-
                                                                                                  ly.” They modeled the cell membrane
                                                                                                  and the substrate as lattices of springs
                                                                                                  and the integrins as individual springs
                                                                                                  that can diffuse along the cell mem-
                                                                                                  brane, cluster with each other, bind to
                                                                                                  the substrate, and pull on the mem-
                                                                                                  brane and substrate.
                                                                                                      In simulations, they found that as
                                                                                                  you make the substrate stiffer and
                                                                                                  stiffer, it drives receptor clustering. “If
                                                                                                  the receptors remain distributed, then
                                                                                                  they have to pull up the substrate at
                                                                                                  many locations, and that’s energetically
                                                                                                  very unfavorable on stiff surfaces,”
                                                                                                  Hammer says. “What they’d rather do is
                                                                                                  get together in a cluster and then pull
                                                                                                  up the surface just in small regions.”
                                                                                                      The extent of clustering is directly
                                                                                                  correlated with cell activation. “I think
                                                                                                  the effect of substrate mechanics on cell
Surrounded! This shows a 3D simulation of a neutrophil engulfing a bead and the corresponding     biology is nothing more than this phys-
experimental images. Courtesy of: Marc Herant, Boston University; Volkmar Heinrich, University    ical chemistry of driving clustering in
of California, Davis; and Micah Dembo, Boston University.                                         these receptor patches,” Hammer says.
                                                                                                      The work has important implica-

22 BIOMEDICAL COMPUTATION REVIEW         Spring 2010                                        
                                                                                                  model to explain movement in fish kera-
                                                                                                  tocytes, fan-like cells that are among the
                                                                                                  fastest moving animal cells. “It turned out
                                                                                                  that a very simple mechanistic model,
                                                                                                  with very few equations, describes every-
                                                                                                  thing,” Mogilner says. As actin polymer-
                                                                                                  izes at the leading edge, it pushes on the
                                                                                                  cell membrane, causing tension all along
                                                                                                  the membrane (which does not stretch).
                                                                                                  This force, in turn, pushes back on the
                                                                                                  growing actin filaments. Actin density is
                                                                                                  highest in the middle of the leading edge,
                                                                                                  so the force per filament is lowest here,
                                                                                                  and actin grows rapidly. Actin density is
                                                                                                  lowest at the sides, so the force per fila-
                                                                                                  ment is high here, which restricts poly-
Sensing Stiffness. LEFT: This computer simulation provides one possible explanation for how       merization. The work was published in
cells sense the mechanical stiffness of their environment. As myosin motors pull on actin         Nature in 2008.
bundles, molecular clutches (modeled as springs) engage and disengage with the substrate              The model predicted that the high-
(also modeled as a spring). Stiff substrates have little give, and thus the clutches frequently   er the ratio of actin in the center to
slip and disengage; soft substrates can stretch and move with actin, so the clutches remain       actin in the sides, the more canoe-
engaged longer. RIGHT: The motor-clutch model was tested against a series of experiments;         shaped the cell would be and the faster
for example, cell traction can be measured by labeling neurons (green) and soft substrates        the cell would move. These predictions
with fluorescent beads (red). Chan CE and Odde DJ, Traction Dynamics of Filopodia on              were borne out by experiment.
Compliant Substrates, Science; 322: 1687-1691 (2008). Reprinted with permission from AAAS.            “The equations are very enlighten-
                                                                                                  ing because they connect the biochem-
tions for cancer, because tumors are              HOW A CELL MOVES:                               istry (the kinetics of actin cytoskele-
stiffer than normal tissues; and this         CRAWLING ON SUBSTRATES                              ton) with the geometry (the shape) and
stiffness promotes malignancy and               Cells move by crawling along sub-                 with the physics (the forces and move-
growth. For example, breast tumors get strates, propelled by actin filaments—                     ments),” Mogilner says. “So I think this
stiffer and stiffer as they progress. “It which add proteins to one end and shed                  is a very cool thing.”
used to be thought that this was an them from the other (called “tread-                               Like Mogilner’s model, most models
effect of breast cancer, but now people milling”). Actin polymerizes at the lead-                 of cell movement are two dimensional.
are starting to think that it might be ing edge of the cell, pushing forward a                    This is a problem, because 3-D is not
one of the causative determinants of protrusion of cytoplasm, which grabs                         simply an extension of 2-D, says
breast cancer,” Hammer says.                 hold of the substrate via clusters of inte-          Muhammad Zaman, PhD, assistant pro-
    In a 2008 paper in Science, Odde and grins. Then the back of the cell detaches                fessor of biomedical engineering at
his colleagues similarly used modeling from the substrate and is pulled forward                   Boston University. In 2-D models, the
to explore how the cell senses stiffness by the contraction of the actin cytoskele-               cell interacts with the substrate only on
as it moves across a substrate. They ton. Though the general principles are                       one side. But when a cell moves in the
modeled actin filaments as individual well understood, specific details are lack-                 body, it interacts with the extracellular
rods, and integrins and substrate mole- ing; for example, it’s unclear what deter-                matrix on all sides. “In reality a cell does
cules as individual springs. They found mines a moving cell’s shape and speed.                    not have a top or a bottom or a ventral
that more springy substrates can stretch        Mogilner’s team devised a simple                  or a dorsal surface; reactions happen all
and move with actin as the cell
moves, so the clusters of inte-
grin—which act like motor
clutches—remain         engaged
longer. But less springy sub-
strates have little give, and
thus the clutches slip and dis-
engage more frequently.
    “So, cells, through that
motor clutch system, actually
have the innate ability to sense
stiffness. How they actually
read it out for these decisions
that they make is now the next        Cells on the Go. Computer simulations of motile fish keratocyte cells. The color represents actin density
problem. And we’re moving on          (red/hot=high; blue/cold=low) and the arrows represent the flow field. The cell on the left is more canoe-
to that and trying to apply it to     shaped and moves faster due to the pattern of actin flow, whereas the cell on the right is rounder and
brain cancer cells and how            moves slower. Courtesy of Raja Paul and Alex Mogilner, University of California, Davis.
they migrate,” Odde says.

Published by Simbios, the NIH National Center for Physics-Based Simulation of Biological Structures                                                23
       over the surface,” Zaman says. Thus the       power to run such large simulations.          prediction appeared in PNAS in 2006.
       relevance of 2-D models for biological           In a 2005 paper in Biophysical                Their work may have practical
       processes in vivo “is very limited if not     Journal, Zaman’s team explored how            implications for cancer. For example,
       completely inaccurate,” he says. “More        altering the 3-D environment affects          there is a relationship between the col-
       often than not, we find that the 2-D par-     cell velocity. Others had predicted that      lagen density in a woman’s breasts and
       adigms break down completely.”                if you increase ligand density in the         her chance of developing invasive
          Unfortunately, most experiments are        matrix—that is, give integrins more           breast cancer. It may be that, at opti-
       conducted in 2-D—on glass                     points where they can attach—this will        mal collagen densities, rapid cell
       or plastic plates—which                       give the cell a better grip and allow         movement increases the potential for
       creates a severe bot-                               swifter motion. But, surprisingly,      invasion and metastasis.
       tleneck for would-                                       they showed that there is an
       be 3-D modelers.                                              optimal ligand density,

                                                                                                        MANY CELLS:
                                                                                                         BRIDGING TO TISSUES
                                                                                                           AND ORGANISMS
                                                                                                           The aforementioned models
                                                                                                         focus on the behaviors of single
                                                                                                          cells. But cells rarely act alone.
                                                                                                           To truly understand cell biology
                                                                                                            and to bridge to tissue and
                                                                                                             organism biology, multi-cell
                                                                                                              models are needed.
                                                                                                                   Though several approach-
                                                                                                                es for multi-cell modeling are
                                                                                                                 available, agent-based mod-
                                                                                                                 eling is gaining momentum.
                                                                                                               Unlike traditional continuum
                                                                                                         models, which treat groups of cells
                                                                                                   as homogenous masses, agent-based
       3D Obstacle Course.                                                                         models treat cells as individual
       Computer rendition of a 3D extracellular matrix.                                            autonomous entities. Besides capturing
       The red fibers are collagen fibers that surround the cell; the cell must navigate through   the heterogeneity of cells and their inter-
       these during migration and invasion. Courtesy of Muhammad Zaman, Boston University.         actions, agent-based models facilitate
                                                                                                   collaboration between biologists and
       “Modeling and experiments go hand in          after which speed decreases. At this          modelers.
       hand. It’s very hard to publish or think      point, the back of the cell experiences          “The cell really is an autonomous
       about 3-D if you don’t have any real          difficulty detaching, creating drag.          unit. It lends itself very well to agent-
       data to compare it to,” Zaman says. To        “That was counterintuitive, but we            based modeling, where you have the
       counter this problem, Zaman’s team            showed that experimentally indeed it          one-to-one relationships between the
       measures cells moving through 3-D gels        was the case. And the match was not           computational model and the actual
       derived from in vivo sources.                 only qualitatively accurate, but also         cell,” says Southgate, a biologist who
          Using these data, they built the first     quantitatively accurate,” Zaman says.         works closely with modelers. “For cell
       3-D model of cell migration, a compre-        The validation of their computational         biologists, that’s important, because you
       hensive, multi-scale model. At the low-
       est level, they zoom in on individual
       snippets of proteins in the cell and              “The cell really is an autonomous unit.
       matrix, solving Newton’s force equa-
       tions for these snippets. “So you’re look-        It lends itself very well to agent-based
       ing for the right conformations that will
       bind, that will attach, that will stretch,             modeling, where you have the
       things like that,” Zaman says. Then
       they zoom out, feeding relevant infor-
       mation from the lower level into higher
                                                            one-to-one relationships between
       level models that solve similar force
       equations for proteins, protein com-
                                                              the computational model and
       plexes, or whole cells (with continuum
       rather than stochastic equations). Grid               the actual cell,” says Southgate.
       computing provides the computational

24 BIOMEDICAL COMPUTATION REVIEW       Spring 2010                                           
can immediately see the relationship         have been linked to cancer.
between the modeling and the cell.”              Southgate’s team studies cell-
     Rod Smallwood, PhD, professor of        to-cell interactions in human
computational systems biology at the         bladder epithelial tissue aided by
University of Sheffield in the United        agent-based modeling. In their
Kingdom, agrees. “Because you can talk       model, rules govern whether
about a computational object as if it was    each cell bonds to other cells,
a physical object, this seems to make        grows, divides, migrates in two
the discussions with cell biologists a lot   dimensions, or dies. For exam-
easier. It seems much more intuitive to      ple, each cell’s probability of
be able to talk about cells as if you have   binding to its neighbor is pro-
physical objects interacting with each       portional to the local calcium
other rather than to talk about sets of      concentration. The local signal-
differential equations,” he says.            ing milieu is determined by a
    Agent-based cell models also fill an     series of mathematical models
important and largely untapped niche         linked to the agent-based model.
in multi-scale modeling: the middle-         “We often adopt other people’s
out model. The models can easily             pathway models, deriving rules
embed molecular-level modules, such          that we then incorporate into
as signaling networks—allowing them          the agent-based models,”
to scale down; at the same time, the         Southgate explains.
collective behavior of cells falls right         In a 2010 paper in the
out of the simulations—allowing the          Journal of Theoretical Biology,
models to scale up.                          Southgate’s team introduced
                                             anti-social cells—cells lacking
  HOW CELLS COOPERATE:                       functional cadherin—into their
  GROWING INTO TISSUES                       models to see how they would
   Cell cooperation plays a key role in      influence normal cells and
promoting tissue growth during devel-        affect population behavior. In
opment and inhibiting it later in life.      some situations, just a few anti-
Cells bind to and interact with each         social cells could influence the
other through surface receptors called       growth of the entire popula-
cadherins. Mutations in the cadherins        tion. The model illustrates one Incomplete Repair. An agent-based simulation that
                                             way that cancerous cells can shows why wounds greater than 2 centimeters
                                             disrupt the growth behavior of across cannot heal spontaneously. Different colors
                                             normal tissue.                     represent different cell types: blue cells are ker-
                                                 Cell cooperation is also atinocyte stem cells; they change to light green as
                                             important in wound healing. they migrate and proliferate and then to dark green
                                             To heal a wound, cells migrate as they differentiate. When the wound (red) is too
                                             into the rift and multiply to fill big, the cells differentiate and stop moving before
                                             the gap. The process is gov- they can fill the gap. From: Tao Sun, Salem Adra, Rod
                                             erned by both cell-to-cell and Smallwood, Mike Holcombe, Sheila MacNeil.
                                             environment-to-cell signaling. Exploring hypotheses of the actions of TGF-β1 in
                                                 Smallwood and his col- epidermal wound healing using a 3D computational
                                             leagues are working out the multiscale model of the human epidermis. PLoS ONE
                                             details using 3-D, multi-scale, 4(12): e8515. doi:10.1371/journal.pone.0008515.
                                             agent-based models. The
                                             agents are cells that can bond, migrate, Smallwood says. “Things move in time
                                             divide, or differentiate. External mod- steps and at the end of each time step,
                                             ules determine cell signaling and the forces are resolved and the position
                                             resolve the forces between cells. “So and size of the cell is updated.” To make
                                             there are models of particular cell sig- the calculation computationally
                                             naling pathways that others have creat- tractable, they model the behavior of
                                             ed that you can download. The func- 10,000 cells—just a fraction of the mil-
                                             tions that control cell transitions can lion cells involved in wound healing,
                                             be culled from these external models,” but enough to capture the fundamental

                                             Anti-Social Cells. These bladder epithelial cells are labeled with a fluorescent antibody to
                                             E-cadherin (green), with nuclei stained blue. The top panel shows the normal pattern of E-
                                             cadherin concentrated to junctions between cells, whereas cells in the bottom panel have
                                             been genetically modified to disrupt E-cadherin and create anti-social cells. Courtesy of
                                             Jenny Southgate, University of York.

Published by Simbios, the NIH National Center for Physics-Based Simulation of Biological Structures                                         25
       biology, Smallwood says.
          In a paper in press with PLoS
       Computational Biology, Smallwood’s
       team used simulations to explain, for
       the first time, why wounds wider than
       two centimeters cannot heal sponta-
       neously. The reason: cell-to-cell sig-
       naling drives the cells to first start
       migrating and then to differentiate;
       once they differentiate, they can no
       longer move. If the distance the cells
       have to migrate is too great, they dif-
       ferentiate before they have filled the
       gap. “If you can’t move on any more,
       you’re not going to heal. So that’s quite    Traffic in the Bloodstream. Agent-based models in conjunction with in vivo experimental
       interesting. You can actually see the        models are used to study the recruitment of circulating cells in the microvasculature of
       critical reason why the wound doesn’t        ischemic muscle. The left panel shows a confocal micrograph image of the macrovessels (yel-
       heal,” Smallwood says.                       low) and microvessels (blue and red) in mouse muscle; immune cells (monocytes) are stained
          This suggests that it might be possi-     in green. The right side is a screenshot from an agent-based model of this same system.
       ble to get large wounds to heal if you       Courtesy of Shayn Peirce-Cottler, University of Virginia.
       could override the cells’ differentiation
       rules, he says.                                  Peirce-Cottler’s team is exploring         putational models. You can actually
                                                    the build up of plaques in the arteries        follow an individual monocyte and say
            HOW CELLS TRAVEL:                       (arteriosclerosis). Because inflamma-          ‘hey, where did you come from?’”
              TRAFFICKING IN                        tion is a major contributor to arte-
             THE BLOODSTREAM                        riosclerosis, it turns out that the traf-              HOW CELLS
           When the body is injured or invad-       ficking of immune cells (particularly                BATTLE INJURY:
       ed, immune cells travel through the          monocytes) to plaques plays a critical           TESTING DRUGS IN SILICO
       bloodstream to the site of injury. They      role in their initiation, progression,            A major insult to the body, such as
       exit the bloodstream through a precise       and eventual rupture. Peirce-Cottler           an overwhelming infection or injury,
       set of steps: first, they roll along blood   and others believe that microvessels—          can cause a condition called sepsis:
       vessel cells, then they halt to a stop,      the small blood vessels that feed into         The immune system goes into over-
       and, finally, they slide through the         large vessels—may be an important              drive, leading to collateral damage of
       blood vessel wall. The process is            conduit of monocytes to plaques. They          otherwise normal tissue, subsequent
       orchestrated through adhesion mole-          are using simulations to tease out the         organ failure, and death. In the 1990s,
       cules on both the vessel cells and           relative contribution of monocytes             researchers reasoned that since certain
       immune cells (selectins and inte-            from the microcirculation versus the           cytokines incite immune cells, admin-
       grins), as well as signaling molecules       macrocirculation.                              istering anti-cytokine drugs would
       called cytokines. A fundamental ques-            “That’s hard to quantify experimen-        cure sepsis. But they were wrong. “It
       tion is how cells decide where to stop       tally, because you need to have a system       turns out that none of the drugs
       in circulation.                              where you’re tracking individual cells         worked, and some of them actually
           Shayn Peirce-Cottler, PhD, assistant     in vivo and watching to see, when a            hurt people,” says Gary An, who is a
       professor of biomedical engineering at       monocyte shows up in a plaque, where           trauma surgeon and ICU doctor at
       the University of Virginia, studies          does it come from. And technically             Northwestern University Feinberg
       immune cell trafficking with agent-based     speaking, we just don’t have the tools         School of Medicine.
       computational models. Cells drift,           to be able to do that,” Peirce-Cottler            Frustrated by these failures and the
       adhere, roll, stop, or enter tissues based   says. “That’s the great thing about com-       lack of effective treatments for his sep-
       on concentrations of simulated
       cytokines and adhesion receptors. The
       cells are embedded within a simulated
       microvascular network—complete with
       pressure, flow velocities, and wall shear
       stresses—that shuttles cells around the
       body. It’s a complex system. The
       researchers have to keep track of the
       cells in time and space, monitoring the
       state of hundreds of chemokines and cell
       surface receptors as well as the cells’
       behaviors, Pierce-Cottler says. The mod-
       els are two dimensional, since moving to
       3-D would make them computationally
       intractable at this point, she says.

26 BIOMEDICAL COMPUTATION REVIEW      Spring 2010                                            
sis patients, An turned to computation-        the cell responds. Those sorts of behav-       were 30 to 40 percent, no better than
al modeling “as a means of addressing          iors can be converted to rules and com-        standard treatment. He also tested dif-
the bottleneck in translational                puter code for agent-based modeling            ferent combinations of the drugs
research.” It was clear that sepsis exhib-     relatively straightforwardly.”                 (which some had hypothesized were
ited complex behaviors that could not             He built agent-based models of              needed to override redundancies in the
be predicted through reductionism and          sepsis and used them to run in silico          immune system), as well as various
linear thinking alone, he says.                drug trials based on actual clinical           doses and durations of treatment, but
However, his path to computational             studies. The agents are the immune             nothing worked.
                                                                                                 “By running the computational
                                                                                              models, you identify that the disease
                                                                                              state itself is very, very stable and resist-
    “System-level computational models                                                        ant to change,” he says. “When you
                                                                                              simulate the intervention, you get this
  are invaluable in identifying these types                                                   sort of pebble in the stream effect
                                                                                              where you might see a little bit of a
  of unexpected behaviors, and will play a                                                    result initially, but the flow of the sys-
                                                                                              tem is such that it basically swallows up
                                                                                              your intervention and it doesn’t have
  critical role in addressing the challenges                                                  any effect.”
                                                                                                 “System-level computational mod-
     of developing effective therapeutic                                                      els are invaluable in identifying these
                                                                                              types of unexpected behaviors, and will
         interventions,” Gary An says                                                         play a critical role in addressing the
                                                                                              challenges of developing effective ther-
                                                                                              apeutic interventions,” An says.

research had a significant hurdle.             and blood vessel cells at the blood-to-             BRINGING MODELING
   “I was not a computer science or a          vessel interface. The cells change                   AND CELL BIOLOGY
math guy at all; I hadn’t taken anything       states based on cell-to-cell interac-                   TOGETHER
in those areas since high school. So the       tions, the presence of mediators such              Despite these recent successes in
computational bar was kind of high,”           as cytokines, and the influence of             pairing cell biology and computation-
he says. Fortunately, he discovered an         drugs. When enough of the blood ves-           al modeling, the two fields remain
agent-based modeling toolkit called            sel cells are injured, then the simulat-       only loosely integrated. Breaking
StarLogo that was designed for teach-          ed person dies.                                down these barriers will take long-
ing kids, and thus was very intuitive.            In a paper in Critical Care Medicine        term collaborations, Zaman says. For
    “The results of a cell biology paper       in 2004, he simulated what would hap-          example, his lab comprises half exper-
are: I take this cell; I stimulate it with     pen if you treated populations of in sili-     imentalists and half modelers. Yet, he
this particular compound that performs         co patients with various anti-cytokine         says, “I still see it in many of my stu-
this particular function; I then see how       drugs. He showed that mortality rates          dents that it takes a long time before
                                                                                              they can speak a common language.”
Sepsis Explosion. (Lower opposite page and below) These serial screenshots from a 2-D             “We need a more integrated envi-
agent-based simulation of inflammation and sepsis follow the progression from infec-          ronment, not only for the computa-
tion, to initial immune response, to cell death and the start of healing. Upon infection      tions to be more powerful, but also for
with bacteria (gray areas), the healthy blood vessel cells (red) become damaged (dark         the experiments to be more probing
red) or die (black). Gradually, inflammatory cells (white neutrophils) gather near the bac-   and much more quantitative,” Zaman
teria and become activated (yellow or other colors). The inflammatory cells gradually         says. “I think the burden of responsibil-
clear the bacteria, allowing healing to occur. Courtesy of Gary An.                           ity is on both sides.” ■

Published by Simbios, the NIH National Center for Physics-Based Simulation of Biological Structures                                           27

ghkgkyyt ghkgkyyt