Biology Reference
In-Depth Information
mechanism through which activation of these protein
kinases is achieved is by phosphorylation in response to
upstream signals. The duration of such activation is the
result of the balance between input signaling and the activity
of specific phosphatases. Alternatively, sequential inhibi-
tory phosphorylation by protein kinases involved in other
concurrent pathways can also regulate signal consolidation
[67]
. Scaffold proteins (such as AKAPs) can recruit protein
kinases and phosphatases into dynamic complexes, thereby
assembling the network topology required for regulation of
signal consolidation necessary to evoke a physiological
response.
In summary, the mechanism of signal consolidation
depends on two fundamental capabilities of the network.
First is the network's ability to propagate signaling infor-
mation for various lengths of time across different cellular
locations, in order to achieve physiological responses that
depend on the integrated functioning of several cellular
machines and which operate over different timescales. The
second arises from differential connectivity of isoforms of
a protein, resulting in both differential subcellular locali-
zation that depends on interactions with scaffolding
proteins and the diverse ability to route signals through
various pathways within a network, in response to prox-
imal upstream and downstream components. Thus, only
a proper spatial localization of the molecular entities
involved in the network (i.e., the active form of MAP
kinase or a second messenger such as cAMP) can result
in a consolidated signal leading to cell physiological
response. Such regulatory mechanisms are used by the cell
to set local thresholds for the conversion of biochemical
reactions into physiological responses
[68]
.Thesepre-
dicted system properties need to be tested by explicit
experimentation.
behavior of a mammalian cell unit can be divided into two
main categories: deterministic and stochastic. Determin-
istic models are used when the number of molecules of
each reactant is considered to be high enough such that the
inherent biochemical noise can be averaged and each
interaction (i.e., reaction) can be described by mean reac-
tion rates. The change in the concentration of reactants with
respect to time is completely determined by the initial
concentrations of the reactants and the reaction rates
between the reactants.
Stochastic models, by contrast, involve reactions
between molecules that are present in small numbers and
hence react with each other in a probabilistic manner. In
a stochastic model, changes in the reactant concentrations
with respect to time cannot be fully predicted from the
initial conditions alone: in these systems, because the
concentration of components is quite small, reactions can
occur by chance. Such unregulated reactions generate what
is termed biochemical 'noise'. Sometimes, depending on
the trajectory and state of the system, such noise can be
significant enough to switch the system from one
biochemical state to another
[69
72]
.
Generally dynamical models of biochemical systems,
such as signaling networks, are based on solution kinetics,
where the spatial heterogeneity of the cell is ignored, allowing
for the pathway or network to be represented as a system of
ordinary differential equations (ODE). In order to better
represent certain dynamic cellular features such as trafficking
and transport, compartmental ODE models can be used with
reactants confined to one or more compartments and a rate
specified for movement between compartments. The move-
ment of molecules across different compartments is modeled
like a flux
[73]
. When explicit representation of the move-
ment of each reactant in the systemneeds to be specified, then
asystemofpartial differential equations (PDE) can be
used. PDEs allow for representation of two or more variables,
and usually changes in concentrations of reactants or products
with respect to space and time are calculated. Both the
compartmental and the reaction
e
DYNAMICAL MODELS
Although network models are very useful for understanding
the relationship between the organization of components
and their function, they are not fully predictive, as many of
the capabilities, such as switching between different func-
tional states, enabled by a particular organization such as
a positive feedback loop, occur only when the concentra-
tion of components and reaction rates are in the appropriate
range. It is reasonable to consider a mammalian cell as
a complex chemical reactor, where reactions between
different molecules, together with changes in their dynamic
localization, give rise to the different mechanical, chemical
and electrical properties of the cell. One of the major goals
in system biology is to computationally represent this
complex reactor using differential equations and mathe-
matical modeling, to accurately predict the dynamics of
such a cellular system. The mathematical models that are
currently available to quantitatively describe the biological
diffusionmodelsareamore
realistic way to represent biochemical reactions within the
cell, but they usually imply a high level of complexity in terms
of great numbers of parameters to be considered, and there-
fore can be expensive in terms of required computational
time. Regardless of this complexity, some stochastic models
have been used to study specific systems such as neuro-
transmitter release, immunological synapses, endocytic
vesicles or signaling in dendrites
[74
e
77]
.
e
POSITIVE FEEDBACK LOOPS CAN FORM
SWITCHES: THE CONCEPT OF BISTABILITY
One of the key findings from the use of dynamical models is
that positive feedback loops can form switches, i.e., function
