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A Paradigm for Biology's Next Revolution

Fredric S. Young*

*Vicus Therapeutics LLC., 55 Madison Ave, Suite 400, Morristown, New Jersey 07960

A recent essay on biology's next revolution described attributes of a

future theory of biology that would replace post hoc modeling with an interplay
between quantitative prediction and experimental test, more characteristic of the
physical sciences

. The article suggested that flux from the environment whether it

be energy, chemicals metabolites, or genes is a defining characteristic of life. The
essay also suggests that an interdisciplinary approach to collective phenomena
centered on statistical mechanics and dynamical systems theory will be required to
make use of this perspective. Over the last 30 years we have developed an approach
to drug discovery and translational research that is based on a paradigm for
complex systems modeling that fits the description in the essay. The approach is a
new paradigm because it focuses on the control of non-equilibrium flux, rather than
genes. It has now been used to identify potential therapies for unmet medical needs
that are currently being tested in phase II clinical trials.

The technology development was driven by a principle of biological

organization based on non-equilibrium flux control, originally discovered through the
reverse engineering of

E. coli growth rate control systems

, and used in the design of a

nonlinear simulator for complex systems

. Because our approach is focused on non-

equilibrium flux rather than genes, it requires language that is unfamiliar to practitioners
of the current paradigm. The change of language that accompanies a new paradigm is a
theme in the cited essay

The conceptual organization of this paper is summarized in Figure 1. Starting

with (Panel a), we represent any non-equilibrium system as a combination of flux from
the environment interacting with an internal cycle in a 4 part in-up-out-down process.
This model for non-equilibrium steady-states involves discrete stochastic processes, such
as directed percolation that has an absorbing state phase transitions as in (Panel b). The
occupancy ratio of the internal carrier of flux is an order parameter for the absorbing
state phase transition, shown as a self-organized chemical reaction in Panel c. Biological
models are described within control theory (Panel d), with a universal flux control
module using integral control (Panel e) on multiple time scales. This single compartment
single flux model is further generalized to a multiple flux single compartment model of a
bacterium (Panel f), and a multiple flux multiple compartment model for multicellular
eukaryotes (Panel g). Allometric scaling laws (Panel h) and 1/

f fluctuations in

physiology (Panel i) are predictions of this model. This model of stochastic non-
equilibrium systems is shown to be an example of inertial scaling in multi-scale systems
as originally described by Kolmogorov for turbulence (Panel j) and later for discrete
complex systems including pattern formation in metallurgy (Panel k).

Nature Precedings : hdl:10101/npre.2008.1770.1 : Posted 6 Apr 2008

Because our approach emphasizes aspects of the non-equilibrium steady-state

that are independent of specific details, we can start with a simple example to illustrate
the concepts. The basic concept of the non-equilibrium steady-state is shown in Figure 2.
We start with a single compartment lattice model of heterogeneous surface catalysis of
the reaction between CO and O

to generate CO

, and a single internal process. Under

certain conditions the system can maintain a steady-state of throughput of the CO and O

reaction to allow a continuous efflux of CO

. There is a balance between input and

output flux and the as yet undefined internal process that must occur cyclically in a
steady-state. We refer to this process as the carrier/processor.

The internal carrier processor cycle is driven by flux from the environment, and

functions by binding the components that comprise the flux. This provides the energy
for an activation deactivation cycle This is shown in the Figure as a balance in the four
part in-up-out-down-process. The fluxes and the carrier/processors are stoichiometrically
distributed and the steady-state is defined by the ratio of occupied to unoccupied sites on
the carrier, defined by an equation for a biological module developed in collaboration
with James Lindesay and Pierre Noyes

For the reaction to occur one CO and two O atoms must occupy adjacent lattice

sites. As shown in Figure 3a, there is a range of CO to O

ratios that allows a steady-

state. There is a critical point that marks a transition between a frozen lattice and one that
is able to absorb more reactants. This phase transition is an example of an absorbing
state phase transition, and the ratio of input reactants is the order parameter for an
emergent non-equilibrium steady-state

. The phase transition is defined by the geometry

of percolation shown in Figure 3b for a random resister network

The phase transition occurs at a balance of in-up-out-down at a particular value

of the ratio of the activated and deactivated forms of the flux carrier. Another example of
an absorbing state phase transition is the Bak sandpile model of self-organized
criticality

, originally suggested as a general model for complexity. If the input rate is

low enough to allow the pile to rearrange between successive grain additions, the system
will be in a steady-state with a balance between in up out and down

, where the 4 relative

rates are evenly distributed over the lattice. In Figure 3c we represent the range of fluxes
as a control parameter for the system from order at low flux to chaos at high flux with the
absorbing state phase transition as the edge of chaos. In these examples, the phase
transition involves different mechanisms

In a one compartment system, an emergent non-equilibrium steady-state with

respect to the flux of an input from the environment is a single module. A single
compartment model can contain multiple modules each of which controls a single flux.
Converging and diverging connections to other modules define a bow tie organization

Within the single compartment these fluxes are distributed stoichiometrically

To summarize our model shown in Figure 2: a module is an emergent self-

organized state of a single flux at an absorbing state phase transition. A single

Nature Precedings : hdl:10101/npre.2008.1770.1 : Posted 6 Apr 2008

compartment model with multiple modules puts a constraint on the fluxes connecting the
modules. A single compartment containing a connected set of modules each at an
absorbing state phase transition for interaction with the carrier processor is an abstract
model for a bacterium. The ratio of filled to unfilled sites on the carrier characterizes any
controlled flux in the complexity pyramid of systems, organs, tissues, and cells.

To make the model more biologically relevant, we describe non-equilibrium

steady-state for energy metabolism in which energy input drives an activation
deactivation process that leads to capture and storage of the energy as shown in Figure
2b. In this case we replace the surface catalyst with a complex of two enzymes and a
carrier. One enzyme attaches three units of energy to a carrier that releases two units to
a storage enzyme. The carrier is left with one bound unit of energy and two free binding
sites. The energy units are input from the environment, and the system can maintain a
non-equilibrium steady-state.

We model this in Figure 2b as a carrier cycle between ATP and AMP, the tri and

monophosphate forms of the adenylate universal energy carrier. Energy is produced
through electron transport driven by metabolism of food and captured in the synthesis of
ATP and ADP. One covalent bond in ADP and two in ATP store energy. ATP donates
energy to cellular reactions releasing two phosphate groups

As shown in Figure 2, the energy carrier in this example and the catalyst in the

first example have an internal cycle which interacts with the energy flux. The energy
system also has an absorbing state phase transition that depends on the rates of the energy
activation and relaxation processes. This can now be used to model energy metabolism
in a bacterium. At the absorbing state phase transition the order parameter is the ratio of
absorbing to non-absorbing sites on the carrier that is determined by the relative rates of
the activating and deactivating reactions. In actual biological systems the ratio of
occupied to unoccupied sites on the carrier is called the cellular energy charge

. It has a

value of approximately 0.8 in most cells

which in our model represents the order

parameter for the absorbing state phase transition of energy flux at maximum efficiency.

A complete model for even a single order parameter self-organized module of a

bacterium, must include a controller that stabilizes the system at the order parameter that
defines the maximum efficiency or throughput rate. A complete module must include a
sensor of the ratios that define the self-organized state and an actuator that changes the
input flux when it is too high for the system to process, or too low to be efficient. The
minimal model for asymptotic tracking of a control signal is integral control where an
error signal triggers action whenever there is deviation form an internal model

13-15

Reciprocal control is needed to damp perturbations that can be above or below the set
point. This reciprocal control logic is the method used by all cells to stabilize the energy
charge ratio

13,15

, and is an example of auto-tuning that allows biological systems to go

beyond the non-tuned SOC model. This is an example of a system with an internal
model where the controller is not separate from the controlled process

Nature Precedings : hdl:10101/npre.2008.1770.1 : Posted 6 Apr 2008

Feedback processes selected by evolution keep biological systems in maximum

efficiency in a non-equilibrium steady-state at or near the critical points of an absorbing
state phase transition. Concentrations of metabolites in bacteria are critical or near
critical

17-18

and ultrasensitive reciprocal control systems sensing these metabolites

may

represent a general mechanism for keeping control systems at bifurcation points where
there is maximum sensitivity to changes in flux

. When a system is balanced with

respect to in-up-out-down in a non-equilibrium steady-state the errorless set points for the
integral controller represent the inertial state of a physical system that is in balance and
dependent on an energy flux from the environment.

A more flexible system is needed to adjust the internal cycles to match changes

in flux from the environment. For example, if the energy processors of our first example
could be packed at a higher density, there could be a higher throughput of energy
conversion. We expand the model to include a process that adds and removes the energy
processor at a steady state rate and that operates on a slower time scale, When the
environmental energy flux is doubled, the rate of carrier input and output is doubled.
This is an example of scale invariance, and this additional process is an abstract model
for gene expression.

The elementary model of a flexible biological system that has multiple steady-

states starts with the core model for an E. coli order parameter for a non-equilibrium
steady-state of energy flux. The order parameter or ratio of filled to unfilled carrier sites
is now read by a sensor coupled to an actuator that controls energy flux and a second
sensor coupled to an actuator operating on a slower time scale that controls the
manufacture of the carrier and the extractor. The elementary system uses a two level
integrator to select a steady-state flux of carrier that maximizes the efficiency of energy
conversion by that carrier. The internal model is the ratio of fluxes to the carrier cycle.
Additional modules control element fluxes. This two level integral control of flux
mediated by an emergent self-organized module is shown in Figure 4 as a universal
module for biological modeling. These modules must fit into the system as in a template
setting the maximum flux rate

The emergent state of any biological module has flux through a carrier processor

over a range of states. It is has been shown that interlocked cycles can act as switches

that can be binary or graded depending on interactions

. The interaction of an object flux

with a switch made up of an interlocked set of interacting cycles. This can be modeled as
an abstract carrier with binding sites for the object fluxes, each of which can be empty or
filled. The universal module is composed of an object flux and a carrier with empty and
filled sites.

Gene expression is directly coupled to the carrier cycle. A change in flux or

carrier ratios serves as an error signal for the integrators that either stabilize the steady-
state through reciprocal feedback or triggers a change in the slow process representing
gene expression that leads to a new steady-state with a different value of absolute flux.
Virtually all global control processes in bacteria utilize what is called a two component

Nature Precedings : hdl:10101/npre.2008.1770.1 : Posted 6 Apr 2008

regulator

23-24

which as shown in Figure 4 exactly follows the design logic of the universal

module. A module for the control of stoichiometrically consistent fluxes such as carbon
or nitrogen is hierarchically organized. An example is the lactose operon in the E. coli
carbon module. The lac operon is expressed when lactose is present in the growth
medium and the global regulator does not sense increased flux from a preferred carbon
source such a glucose

25-26

. When both glucose and lactose are present, the global

regulator overrides the specific control.

For a multiple compartment model in a non-equilibrium steady-state each

compartment is at or near the critical point of an absorbing state phase transition where
sensitivity is maximal. The fluxes between compartments are constrained to rates that
leave the inputs and outputs in each compartment at the value that allows a steady-state
of flux. For the multi-compartment model the allometric scaling laws

and the 1/

fluctuations in heart rate variation

are all consequences of in up out down balance. The

relation between allometric scaling laws and even distribution of substance flow through
a volume has been corroborated by others

29-30

. Maximum efficiency of carrier/processor

function with regard to flux at the absorbing state phase transition defines the allometric
scaling relations

. The 1/

f pattern in heart rate variation requires both a phase

transition

and reciprocal control by the autonomic nervous system

33-34

System's Biologists discuss an iterative process of fitting models to experimental

data

, it has not yet proceeded beyond post hoc empirical modeling, to models based on

underlying principles as in the physical sciences. The models in the physical sciences
involve equations derived using the method of dimensional analysis to eliminate any
dependency on arbitrary choices of units

. This results in mathematical expressions that

identify key dimensionless ratios that represent descriptions of a system that are free of
arbitrary units.

The problem of extending this method to complex systems as in biology has been

discussed by Rosen, who showed that biological systems have corresponding
dimensionless numbers that represent aggregates of variables

37-38

. Features of patterns

that classify them independent of units must represent invariant aspects of the geometry
and topology. These are the pattern features that can be used as classifiers in a pattern
recognition system. The dimensionless numbers of mathematical physics are a
quantitative description of pattern similarity. An effective pattern recognition system
identifies the same pattern independent of changes in size. Therefore there is a
relationship between the dimensionless numbers in mathematical equations of physical
systems and the features used in a pattern recognition classifier

Rosen grouped these variables that classify the similarity of systems into

environment, genotype and phenotype, with phenotype resulting from the interaction of
environment and genotype. A subset of the genes would represent the fundamental
variables on which the derived variables would depend. An additional analysis of
dimensions by Barenblatt

and Goldenfeld

showed that systems that could not be

analyzed with usual dimensional analysis, could be analyzed as self-similar systems with

Nature Precedings : hdl:10101/npre.2008.1770.1 : Posted 6 Apr 2008

an additional length scale or anomalous dimension. These systems exhibit scale invariant
flux between a maximum and minimum length.

An analogy beween heart rate variation in a multi-level system and turbulence is

based on Kolmogorov scaling with a balance between energy input and output and
upward and downward cascades that match the in-out-up-down balance of our model

A scaling argument for complex systems

, and an analogy between turbulence and

critical phenomenon

can be directly applied to our model. Methods similar to those

used to explain non-equilibrium pattern selection in physical systems

45-46

are used to

predict the future states of biological systems as shown in Figure 5. The principle
involved is the equipartition of energy as shown in Figure 1a for thermodynamic
equilibrium and in Figure 1b for a non-equilibrium system. Gradients driving non-
equilibrium flux interact with internal order parameters in self-organized pattern forming
systems as in Figure 5c to produce patterns such as shown in Figure 5d for metallurgy.

Specific processes are modeled by setting the carrier of one flux produced and

utilized by different aggregated reaction blocks as a central module with converging and
diverging connections. The module level describes the interaction of a directed flux with
an internal carrier cycle. The module is made up of a network of molecules at the bottom
level, and a multi-level network of modules represents the system level in a 3-level
model. When the system is in a steady-state of homeostasis, the carrier ratios are all at
their steady-state value.

To produce a disease model which we use as a schematic model for therapy

development, we start with the above described stoichiometric matrix of fluxes and
carrier/processors using aggregated reaction blocks in top down control analysis

47-48

We then identify modules that are not at homeostasis with respect to the mathematical
relation that defines the universal module. We identify these imbalances at the coarsest
grained level possible in the top down modeling process

. We then identify drug

products that modulate flux through the relevant reaction blocks.

Dynamic processes of disease progression are modeled using the energy driven

flux from the environment that gives irreversibility or directionality to the flux. The
distribution of flux perturbations relative to the set points of the central modules allows
prediction of the future evolution of the system

. The progressiveness or downward

spiral characteristic of diseases involves the natural evolution of a system trying to bring
the various modules to their set points under conditions of abnormal energy homeostasis
and physiology

Acknowledgments

The development of this paradigm has benefited from many years of discussions

with Pierre Noyes, Three-way discussions with Pierre Noyes and James Lindesay during
2004-2006 led to the derivation of an equation for the universal module. Pierre Noyes
and James Lindesay also provided helpful commentary on the preparation of this

Nature Precedings : hdl:10101/npre.2008.1770.1 : Posted 6 Apr 2008

manuscript. Support was provided by the Chroma Group Inc., and Vicus Therapeutics.
LLC.

Legends to Figures

Figure 1.

Concept flow for the new paradigm. (a) The conditions necessary for the

maintenance of a persistent steady-state rate in a non-equilibrium system involve a four
part balance we call in-up- out-down. A theorem by Morowitz states that a self-
organized system must have at least one cycle

. The back flow loop regenerates the

empty carrier allowing the steady-state to persist. (b) This leads to the definition of the
balanced condition for a persistent non-equilibrium steady-state as a phase transition in
the universality class of directed percolation

5,6

. (c) A system under these conditions of

discrete non-equilibrium balance represents an emergent self-organized state such as an
oscillating chemical reaction

. This steady-state of flux is stabilized using integral

control from process control engineering

13,14

. (d) Biological models are described within

control theory, with a universal flux control module using integral control (Panel e) on
multiple time scales. The control system maintains the invariants of rate equations and
defines a universal module for the control of non-equilibrium steady-state flux. (f)
Generalizing the model to multiple fluxes in a single compartment provides a model of
bacteria and (g) multiple fluxes in multiple compartments provides a model for
multicellular organisms. (h) Comparison of single and multiple compartment models
shows how fractal spectra in physiology

and (i) allometric scaling laws

27,30

follow as

consequences of balanced non-equilibrium flux control in multicellular organisms. The
theoretical basis of these relations is found in the energy cascades that maintain inertial
states in multiscale systems such as the Kolmogorov argument for scaling in turbulence

43-

. (j) The cascade in the Kolmogorov theory represents the up and down parts of our 4

part in-up-out-down formula. It balances the in out flux for the inertial turbulent system.
(k) These relations hold for discrete complex systems such as pattern formation in
metallurgy

46,47

Figure 2. Comparison of persistent steady-states of in-up-out-down-balance for catalysis
and cellular energy charge. (a). In-up-out- down balance in a persistent steady-state for
the surface catalysis of carbon monoxide and oxygen to generate carbon dioxide. (b) In-
up-out-down balance in a persistent steady-state of energy flux in a top down model of a
single compartment cellular growth state such as a bacterium. Energy is captured
through metabolism and stored in two high energy phosphate bonds in ATP and one in
ADP. Energy is transferred from ATP to cellular reactions with the release of
pyrophosphate and the regeneration of AMP.

Figure 3. Minimization of free energy in steady-state system as critical point. The
balance of in-up-out-down in a system with multiple flux control modules puts collective
constraints on the individual modules that are necessary to maintain a collective steady-
state. (a). Range of Carbon monoxide and oxygen ratios allowing a steady-state of flux
for the model of figure 2a. This state of distributed but not chaotic correlation represents
the edge of chaos as a second order critical point in complexity theory. (b) Random
resister model of percolation. Current will flow until a critical number of connections

Nature Precedings : hdl:10101/npre.2008.1770.1 : Posted 6 Apr 2008

have been cut. When the critical connection has been severed there is no long range
cluster of connected resisters that spans the system (c) Representation of the range of a
control parameter for non-equilibrium flux. The edge of chaos is the flux that just fills
the system without redundancy

Figure 4.

Universal process module. Non-equilibrium flux is represented as input and

output through a carrier cycle. Processes are represented as flows to show that rate
control processes in biology use integral control as does the process control industry.
These control processes can be described without including many specific details of
biology. The occupied to occupied forms of the carrier define a carrier ratio that is input
to sensor actuator pairs functioning on multiple time scales. The diagram shows
processes operating on two time scales for the rapid control of flux and the long term
control of remodeling that includes gene expression. The two level integral control
module uses two phase transitions The slow timescale process sets the number of
processors and is at or near an absorbing state phase transition. The fast time scale
process is control of enzyme rate by binding allosteric effector binding. The functional
modules must fit inside a template with a limited number of attachment sites, giving rise
to a maximum rate for any process.

Figure 5. Pattern selection in non-equilibrium systems (a). Representation of the in-up-
out-down formula in a non-equailibrium system shown with the constraints that allow
prediction of the patterns formed. (b) Illustration of energy spreading evenly following
the removal of a barrier between two thermodynamic compartments. (c) Examples of
non-equilibrium pattern forming systems with non-equilibrium energy gradients that
drive pattern formation. (d) Magnification of one of the examples in Panel c involving
Spinodal decomposition in Metallurgy.

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