Topology in biology

Date:
July 23, 2021
Source:
Max Planck Institute for Dynamics and Self-Organization
Summary:
A phenomenon known from quantum systems could now make its way
into biology: Researchers show that the notion of topological
protection can also apply to biochemical networks. The model
which the scientists developed makes the topological toolbox,
typically used only to describe quantum systems, now also available
to biology.



FULL STORY ==========================================================================
When can we say that a certain property of a system is
robust? Intuitively, robustness implies that, even under the effect of
external perturbations on the system, no matter how strong or random,
said property remains unchanged. In mathematics, properties of an
object that are robust against deformations are called topological. For example, the letters s, S, and L can be transformed into each other by stretching or bending their shape. The same holds true for letters o,
O, and D. However, it is impossible to turn an S into an O without a discontinuous operation, such as cutting the O apart or sticking the
two ends of the S together. Therefore, we say that the letters s, S and
L have the same topology -- as do the letters o, O and D -- whereas the
two groups of letters have different topologies. But how does topology
relate to biology?

========================================================================== "During the last decades, physicists have discovered that certain
properties of quantum systems depend only on the topology of some
underlying feature of the system, such as the phase of its wave
function or its energy spectrum" explains Evelyn Tang, co-first author
of the study. "We wanted to know if this model can also be applied to biochemical systems to better describe and understand processes out of equilibrium." As topology is insensitive to continuous perturbations
-- like the stretching or bending of letters in the example above
-- properties linked to topology are extremely robust. They will
remain unchanged unless a qualitative change to the system occurs,
such as cutting apart or sticking together the letters above. The
scientists Evelyn Tang, Jaime Agudo-Canalejo and Ramin Golestanian now demonstrated that the same concept of topological protection may be found
in biochemical systems, which ensures the robustness of the corresponding biochemical processes.

Flowing along the edges One of the most famous observations regarding
topology in quantum systems is the quantum Hall effect: This phenomenon
occurs when a two-dimensional conducting material is subjected to
a perpendicular magnetic field. In such a setting, the electrons
in the material begin to move in tiny circles known as cyclotron
orbits, which overall do not lead to any net current in the bulk of
the material. However, at the material's edges, the electrons will
bounce off before completing an orbit, and effectively move in the
opposite direction, resulting in a net flow of electrons along these
edges. Importantly, this edge flow will occur independently of the shape
of the edges, and will persist even if the edges are strongly deformed, highlighting the topological and thus robust nature of the effect.

The researchers noticed a parallel between such cyclotron orbits in the
quantum Hall effect and an observation in biochemical systems termed
"futile cycles": directed reaction cycles that consume energy but
are useless, at least at first sight. For example, a chemical A may
get converted to B, which gets converted to C, which subsequently gets converted back to A. This raised the question: is it possible that, like
for cyclotron orbits in the quantum Hall effect, futile cycles can cause
edge currents resulting in a net flow in a two-dimensional biochemical
reaction network? The authors thus modelled biochemical processes that
occur in a two-dimensional space. One simple example are the assembly
dynamics of a biopolymer that is composed of two different subunits X and
Y: A clockwise futile cycle would then correspond to adding a Y subunit,
adding an X subunit, removing a Y subunit, and removing an X subunit,
which would bring the system back to the initial state. Now, such a two-dimensional space will also have "edges," representing constraints
in the availability of subunits. As anticipated, the researchers found
that counterclockwise currents along these edges would indeed arise spontaneously. Jaime Agudo-Canalejo, co-first author of the study,
explains: "In this biochemical context, edge currents correspond to
large-scale cyclic oscillations in the system. In the example of a
biopolymer, they would result in a cycle in which first all X subunits
in the system are added to the polymer, followed by all Y subunits,
then first all X and finally all Y subunits are again removed, so the
cycle is completed." The power of topology Like in the quantum Hall
system, these biochemical edge currents appear robust to changes in
the shape of the system's boundaries or to disorder in the bulk of the
system. Thus the researchers aimed to investigate whether topology indeed
sits at the heart of this robustness. However, the tools used in quantum systems are not directly applicable to biochemical systems, which underlie classical, stochastic laws. To this end, the researchers devised a mapping between their biochemical system and an exotic class of systems known
as non- Hermitian quantum systems. Evelyn Tang, who has a background in topological quantum matter, recalls: "Once this mapping was established,
the whole toolbox of topological quantum systems became available to
us. We could then show that, indeed, edge currents are robust thanks to topological protection. Moreover, we found that the emergence of edge
currents is inextricably linked to the out-of- equilibrium nature of the
futile cycles, which are driven by energy consumption." A new realm of possibilities The robustness arising from topological protection, coupled
to the versatility inherently present in biochemical networks, results in
a multitude of phenomena that can be observed in these systems. Examples include an emergent molecular clock that can reproduce some features
of circadian systems, dynamical growth and shrinkage of microtubules
(proteins of the cell skeleton) and spontaneous synchronization
between two or more systems that are coupled through a shared pool of resources. Ramin Golestanian, co-author of the study and Director of
the Department of Living Matter Physics at MPI-DS, is optimistic for
the future: "Our study proposes, for the first time, minimal biochemical systems in which topologically-protected edge currents can arise. Given
the wealth of biochemical networks that exists in biology, we believe it
is only a matter of time until examples are found in which topological protection sensitively control the operations in such systems." ========================================================================== Story Source: Materials provided by Max_Planck_Institute_for_Dynamics_and_Self-Organization.

Note: Content may be edited for style and length.


========================================================================== Journal Reference:
1. Evelyn Tang, Jaime Agudo-Canalejo, Ramin Golestanian. Topology
Protects
Chiral Edge Currents in Stochastic Systems. Physical Review X,
2021; 11 (3) DOI: 10.1103/PhysRevX.11.031015 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2021/07/210723105230.htm

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