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1
A Systems Biology View of Modeling the
Visual Cortex
Hafiz Z. Noordin

Abstract— System-level understanding of biological systems
has become a topic of great importance in modern science. The
systems biology paradigm provides a fundamental framework for
methodically modeling and simulating biological systems. Recent
models can be shown to follow this structural approach, however
issues regarding assumptions and functional accuracy must be
considered during the process. This paper will present the
systems biology perspective of modeling the visual cortex, as well
as introduce and demonstrate a recently developed visual system
model, Topographica.
This model will be evaluated by
considering the significant issues inherent to the modeling
process.
Index Terms — computational modeling, cortical maps,
systems biology, visual cortex
I. INTRODUCTION
T
HE emergence of systems biology as a unified approach
to understanding biological systems has compelled
scientists and engineers to reevaluate modern methodologies.
In particular, the techniques used to characterize biological
systems as mathematical models must follow a particular
“Framework for Systems Biology” [1] in order to correctly
adhere to the four phases of system-level understanding [2].
This definition of systems biology research implies that the
modeling process should be accordingly structured in order to
demonstrate the validity of the resultant model.
Due to the recent availability of complete genome
sequences, as well as the emergence of high-throughput
measurement systems at the genetic level [2], much of the
recent systems biology research has been targeted towards
modeling at this low-level stage of the biological hierarchy.
This paper, however, will demonstrate how the systems
biology approach can be applied at a higher level, by applying
the aforementioned “Framework of Systems Biology” to
modeling the visual cortex. In particular, it will be shown that
the concepts emphasized by the systems biology paradigm are
certainly significant when considering the issues and
difficulties encountered when attempting to model complex
networks such as the visual cortex.
The paper will begin with a brief summary of the systems
biology approach, as well as an overview of the visual system
Hafiz Z. Noordin is with the Institute of Biomaterials and Biomedical
Engineering, University of Toronto, ON, Canada (e-mail: hafiz.noordin@
utoronto.ca).
in order to provide the necessary background. A recent
approach to modeling the visual cortex will then be
demonstrated, and finally design issues and model evaluation
from the perspective of systems biology will be discussed.
II. THE SYSTEMS BIOLOGY VIEW
Systems biology is made possible by recent parallel
advances in high throughput experimental technologies along
with advances in fields such as computer science and
engineering. Because of the mass of information produced by
the tools employed, systems biology is also an informational
science.
It aims to gather information from different
hierarchical levels of the biological system and to integrate
them to build predictive mathematical models of the system.
This will primarily be used to offer a comprehensive and
consistent body of knowledge in biology [2].
A systems level understanding is used to combine
component level and dynamic information in order to
determine the state of a system and how it changes. Four
fundamental experimental approaches are used to do this:
1.
2.
3.
4.
Structure and function determination
Dynamics of the system and interplay of different
components
Methods to control and perturb the system
Methods to design and modify the system, and forward
engineering
Progress has taken place in this order; however insufficient
progress has been made in simulating dynamics of the systems
[2]. In modeling the visual cortex, this is certainly an issue, as
the difficulties lie more in the interactions of network
components.
The basic “Framework of Systems Biology” [1] consists of:
1.
2.
3.
4.
Formulating an initial model by defining the
components of the system
Systematically perturbing and observing the
components, either through internal or environmental
means
Refining the model in an iterative manner by
continuously comparing predicted results and
experimental observations
Redesigning model structure and dynamics, as well as
experimentation and validation techniques based on the
2
success of the model.
These steps provide a generic approach to modeling, and
hence it will be shown how this approach is applied to a recent
model of the visual cortex.
III. PHYSIOLOGY OF THE VISUAL SYSTEM
In order to understand models of the visual cortex, it is
important that the reader has some background on the
physiology of the visual system, since the terminology utilized
in this field tends to reflect the complex nature of the visual
cortex itself. It is assumed, however, that the reader has basic
knowledge of the neuron, at least at a functional level.
The structure of the eye is shown in Figure 1. The eye
accepts photons of light via the retina, which contains a layer
of photoreceptors (rods and cones) interfacing indirectly to a
layer of ganglion cells. The purpose of this interface is to
transduce the light into a neural response [3]. The generated
neural signal is then transmitted to the brain via the optic
nerve. A key term that is used in describing this process is the
concept of a receptive field. A single ganglion cell’s receptive
field consists of a region of retina upon which incident light
alters the firing rate of the cell. Furthermore, the receptive
field contains either or both of an on-response (firing
immediately after the onset of a stimulus) and off-response
(firing immediately after termination of stimulus) [3].
those of the retinal ganglion cells [3]. Finally, the outputs of
the LGN synapse with the primary visual cortex by means of
optic radiation. An important feature of this stage of the visual
pathway is that an estimated 80-90% of the inputs to the LGN
are from higher cortical areas [3]. Thus we observe a
significant top-down feedback system, which becomes an
important issue to consider when modeling the visual system.
Figure 2: The geniculostriate pathway from the retina to the primary visual
cortex in humans. Adapted from [5].
Neurons in each of the topographic maps interact in two
ways: excitatory and inhibitory. In addition to interactions
between maps, there is also a certain amount of lateral
interaction between neurons of the same map. This further
adds to the complexity of modeling neurons in the cortical
map, as there is a multitude of input/output relationships.
The primary visual cortex, or V1, is the most important
cortical region in the occipital lobe of the brain, since almost
all signals from the optic nerve will pass through this region.
Although there are many other cortical regions (i.e. V2-V6)
utilized in visual processing, usually only V1 is considered
when modeling due to the complexity of interconnections
between the various cortical regions. Beyond the cortical
regions are other areas of the brain where visual processing is
performed, such as at the temporal and parietal lobes. Overall,
however, V1 is central to the processing of visual information.
IV. MODELING THE VISUAL CORTEX:
TOPOGRAPHICA/LISSOM
Figure 1: Structure of the human eye. Adapted from [4].
The most dominant pathway for the optical signal in humans
is the geniculostriate pathway, which is illustrated in Figure 2.
The major termination for the optic tract nerve in this pathway
is at the lateral geniculate nucleus (LGN). This structure
contains topographic maps of the visual field, which are
essentially projections of the visual field onto a network of
neurons. The term map is utilized since the organization of
this biological neural network is similar to a roadmap, in that
the spatial relations between points of light on the retinal
surface are preserved. Due to this organization, each lateral
geniculate neuron is associated with a receptive field similar to
One of the most recent models of the visual system is the
Topographica software package [6], [7]. This is also one of
the few models that are intended to complement current
models for the neuron (e.g. NEURON, GENESIS). By default,
however, the software utilizes a simple neuron model. In fact,
the fundamental unit or component of the model is a sheet of
neurons, which consists of a two-dimensional continuous area
of a finite number of neurons, rather than just individual
neurons.
The significance of the Topographica model is that current
simulators lack specific support for biologically realistic,
densely interconnected topographic maps, as well as for
generating input patterns at the topographic map level [7].
Using today’s more powerful computers, Topographica is
capable of simulating networks of tens of thousands of
3
neurons, resulting in interconnections on the order of millions
to tens of millions [7], which was not previously possible.
rule, normalized such that the sum of weights from each type
of RF ρ is constant for each neuron (i,j) [8]. The iterative
nature of this calculation is due to the weights adapting as a
function of previous weight values, as well as the current
synapse properties:
wij ,  ab( f  1) 
wij ,  ab( f )   ijX  ab
 ab[ wij ,  ab( f )   ijX  ab]
(3)
where ηij now represents the final activity for neuron (i,j),
wij,ρab(f) is the connection weight from the previous fixation, α
is the learning rate associated with each type of connection,
and Xρab is the presynaptic activity.
Overall, these equations demonstrate that neuronal weight
change is determined by many factors, primarily the product of
the pre- and post-synaptic activity, distances between laterally
correlated neurons, as well as a learning rate [8].
V. EVALUATION OF THE MODEL
Figure 3: Topographica model [6], [7]
The underlying model in the Topographica software is the
LISSOM model. The HLISSOM model is a version of
LISSOM that also includes simulation of the LGN structure.
The following demonstrates the process that occurs in this
model via the respective equations at each stage of Figure 3.
For more details on the equations, refer to [8].
Firstly, the input to the model consists of the activity
patterns on the sheet of photoreceptors, such as grayscale
images. The response of each LGN unit (i,j) is then calculated
as a scalar product of a fixed weight vector and its receptive
field (RF) on the photoreceptor sheet [8]:
 ij   (  ab X  abwij ,  ab)
(1)
where σ is a piecewise linear sigmoid activation function,
Xρab is the activation of input unit (a,b) in RF ρ, wij,ρab is the
corresponding weight value, and γρ is a constant scaling factor.
[8]
The V1 neurons are calculated in a similar fashion.
Iterations of the formula are required, however, since the V1
activity settles after the effects of short-range excitatory and
long-range inhibitory lateral interaction. The variable s
illustrates the iterative nature of this calculation, since Xρab(s-1)
is the activation of input (a,b) during the previous settling step.
Furthermore, ρ takes two values, corresponding to the RF’s on
ON and OFF LGN sheets [8].
 ij ( s)   (  ab X  ab( s  1) wij ,  ab)
Models serve to simplify the complexities of reality by
making assumptions. These assumptions can be general
principles or specific simplifications in the experiment.
Although this allows modelers to reduce the dimensions of a
complex problem, difficulties can arise in neurobiology, since
an assumption may ease development of a physical model, but
have no application in biology. In other words, there is no
guarantee that biological mechanisms will adhere to a
modeler’s assumptions [9]. The goal in evaluating a model,
therefore, is to conclude whether or not the assumptions made
are supported by experimental observations. However, this
does not necessarily validate the model in its entirety, since the
collaboration of various assumptions can imply other
assumptions that are not necessarily well tested in biology.
Most models of the visual cortex, including the
Topographica model, have a common set of assumptions [9]:
(2)
Once the activity of the V1 neuron has settled (i.e. after (2)
has converged), the V1 weights adapt according to the Hebb




Hebb synapses
correlated or spatially patterned activity in the afferents
to cortical neurons
fixed connections between cortical neurons which are
locally excitatory and inhibitory at slightly greater
distances
normalization of synapse strength
Certain types of simplifications can lead to powerful and
elegant models, but can become difficult to relate to the actual
biological systems. At the same time, an extreme amount of
detail in the model can increase the possibility of disproving
the model, and thus components must be carefully chosen
according to the desired functionality [9].
For the Topographica model, evaluation consisted of
simulating a two-stage process of development, based on
prenatal and postnatal training. By doing this, it was shown
that the model network first develops an initial orientation map
4
through prenatal spontaneous activity, then gradually refines
based on experience with postnatal natural images, without
changing the overall shape of the map. This has been
supported by data collected in the ferret visual cortex [8]. The
significance of this testing methodology is that training and
test data (i.e. images) can be closely related to tests done in
biology. However, since this model only interfaces with an
external environment, image data must be carefully chosen in
order to conclusively correlate predicted results with
experimental results. This is the fundamental requirement in
Steps 2 and 3 of the “Framework of Systems Biology”.
The basic question that comes out of this analysis is the
validity of assumptions. In the case of a Hebb-based model
such as Topographica, it must be investigated whether or not it
is sufficient to consider this strict local learning rule, in which
only pre- and postsynaptic elements are involved [10]. It may
be possible that non-local effects should be incorporated into
the synapse.
Another more general issue is that of the actual
computational processes taking place within the cortical maps
[10]. In the case of the visual cortex, biological data
explaining the internal connections within each cortical area is
relatively low, with the exception of the primary visual cortex,
which has been more extensively studied and thus is the focus
of modern visual system models.
VI. COMPLEXITY IN MODELING
In addition to the issue of creating assumptions in models,
the problem of dealing with complexity is significant, as it
essentially affects all systems biology-based modeling.
A high amount of feedback has been physiologically
observed in the visual system. In systems biology this has
profound effects on the difficulty of modeling. Consider the
ability of a control systems engineer, who is capable of
performing open-loop experiments that isolate forward and
reverse pathways in a system by removing feedback. Compare
this to a biological system, such as the visual cortex, which
contains multiple-input multiple-output systems, and high
amounts of interconnected forward and reverse pathways that
simply cannot be isolated. This is a fundamental issue in
systems biology in general, and is exemplified by the visual
cortex example. Complexity in such biological networks is
largely due to the adaptive nature of biological systems.
Evolution has shown that survival is largely based on
robustness, and thus most biological systems are naturally
inclined to contain high amounts of redundancy.
This relates back to the issue of assumptions, since modelers
must be careful not to over-simplify model structure and
dynamics. Details that are difficult to measure within a
biological system may have a large effect on overall inputoutput relationships, and so the model plan must be capable of
accommodating such complexities.
VII. CONCLUSION
Despite the various issues involved in evaluating visual
cortex models, the Topographica model provides a good
example of the systems biology approach.
A key attribute of this model is that it fills and important gap
between existing detailed models of individual neurons and
higher-level models for cognitive processes [7]. Thus the
components of the model are well defined and adaptable to
new discoveries or requirements at a fundamental (i.e.
neuronal) level.
Furthermore, the functionality of the model is designed in a
hierarchical fashion, such that further refinements can be made
based on new experiments. This iterative design is vital in the
systems biology approach.
Issues exist, however, when considering the accuracy of the
model as well as the inherent assumptions. Although many
aspects of map formation have been measured and modeled in
great detail, many functional questions remain.
Future work in this field, therefore, should consist of
conclusively validating the functionality of visual cortex
models with actual biological data.
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