Nature-based Information Networking: On Exploring
Robustness in TCP Inspired by Cellular Signaling
Jian-Qin Liu

Kenji Leibnitz

Masayuki Murata

NICT KARC, Bio ICT Group
588-2 Iwaoka, Iwaoka-cho, Nishi-ku
Kobe, Hyogo, 651-2492 Japan

Osaka University, IST
1-5 Yamadaoka, Suita
Osaka, 565-0871 Japan

Osaka University, IST
1-5 Yamadaoka, Suita
Osaka, 565-0871 Japanliu@nict.go.jp

leibnitz@ist.osaka-u.ac.jp

murata@ist.osaka-u.ac.jp

ABSTRACTIn this paper we will discuss the similarities found in thedynamics of cellular signal transduction networks in nature andthat of communication network protocols. Based on the simplified
observations from the signaling processes of the cyclin (cln)protein during the cell cycle in yeast, we formulate a genericmaster equation, which describes the general robustness of thesystem and can be applied to characterize different variants of theTransmission Control Protocol (TCP) such as FAST, Reno,
HSTCP, or STCP. By presenting the generalized controller
mechanism for describing the dynamics of cln signaling at systemlevel, we infer that any corresponding second order system issimilarly controllable. It is our intention that this formulation of amaster equation leads to a better quantitative description of thecellular signaling process, as well as to a more robust design ofprotocols to be applied in new generation network architectures.

Keywords
Cellular signaling, cell cycle, information networks, TCP/RED

1. INTRODUCTION
When we compare the abstract view of the basic dynamics ofcellular signaling in nature and that of engineered information
networks, we notice that they share a commonality from theviewpoint of informatics. For instance, the robustness found in
signal transduction networks in cells is a particular feature, whichis also highly desirable in information networks. In this work we
specifically consider the signal transduction network of the cell
cycle of yeast, which has been a well-studied topic in
bioinformatics [1,2]. In previous work the robustness of the cell
cycle has been extensively studied and the intention of this paper
is to discuss how we can explore hints from nature to improve thedesign of new protocols in future network architectures. We will
begin this paper with a brief outline of signal transduction
networks form the viewpoint of information networking anddiscuss the essential feedback-based dynamics of the cell cycle ofyeast, which we refer to as master equation. Based on thisequation, we will sketch a controller structure, which incorporates
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the robustness features and can be used as the basis for a morerobust and fair bandwidth sharing in the Transmission Control
Protocol (TCP).

2. SIGNAL TRANSDUCTION FROM AN
INFORMATION NETWORKING VIEW
The biological functions of signal transduction networks are
crucial for the operation of cells. These cellular signaltransduction networks take the form of biochemical reactions andwe abstractly view the molecules as nodes within an information
network and the corresponding biochemical reactions as the links.
Thus, signal transduction networks can be represented as graphswith activating or inhibiting unidirectional links [2].
The lifetime of a cell, referred to as the cell cycle, is controlled bytransitions through various stages of growth leading to mitosis, inwhich the cell splits into two equivalent cells. This feature is oneof the most important components of living organisms and it isdriven by the periodic dynamics of a family of proteins called
cyclin (e.g. Cln2). The concentration of cyclin is periodical overtime and it roughly resembles the dynamics of the TCP
congestion window size in computer networks [3]. Biologicalmodels as described in [1] often give a very detailed view of theinteractions of the various proteins, but we limit our abstraction to
the interaction of two specific quantities, the concentration of thecyclin Cln2 and the mass of the cell. When we transfer thismetaphor to information networks, we can find analogies between
cyclin as the TCP congestion window size and mass as thebottleneck queue length in an intermediate RED (Random EarlyDetection) router [3].
In general, the dynamics can be formulated by two dynamicequations, one corresponding to the chemical processdCln2 = f (Cln2, mass, coefficients)dt
and another to the physical processmass(t) = g(u(Cln2), v(mass(t - 1))
where u refers to a positive feedback function from Cln2 and v toa negative feedback function from mass(t-1).
The similarities that can be recognized from the dynamics ofcellular signaling and TCP leads to a generalization of thedynamics in terms of mathematical equations. In [4], ageneralized equation system is formulated that is suitable tocharacterize a wide range of TCP variants.

⎛ q (t) ⎞dw i (t) = κ i (t) ⎜1− i ⎟dt⎝ u i (t) ⎠(1)

In Eq. (1), w i (t) refers to the window size of a TCP source i andqi (t) is the end-to-end packet loss probability. The otherfunctions κ i (t) = κ i (w i (t),T i (t)) and u i (t) = u i (w i (t), T i (t))
are used to describe the different flavors of the protocol, i.e.,
FAST, Reno, HSTCP, STCP, in a single master equation.
Based on this description and the similarities of the cellularsignaling process and TCP, we extend (1) to include a feedback
component in a generalized master equation [5] as in Eq. (2)⎛ q (t) ⎞dwi (t) = κ i (t)⎜1− i ⎟ + ϕ i (t)dt⎝ u i (t) ⎠(2)

where we now consider κ i (t) = kG exp(μ t) inspired by theexponential growth of the cell mass and the additional functions
as follows.

u i (t) =k1∑ k w (t) + ∑ k q (t) + ∑ k T (t)01il1

ϕ i (t) =l1l2

02 il303 il2l3

k2 kG exp(μ t) ζ i (t)∑ k w (t) + ∑ k q (t) + ∑ k T (t)21im1m222 im1

m323 i

m2

m3−1

⎞⎛
⎟
⎜
k3
⎟
ζ i (t) = ⎜m1
m2
m3⎜⎜ k 31 w i (t) + k 32 qi (t) + k 33T i (t) ⎟⎟ .
z2z3
⎠⎝ z1

∑

∑

All indices l i , mi , z i ∈ (−∞,+∞), i = 1,2,3 are integer values.

3. PROPOSAL OF ROBUST SYSTEMCONTROLLER STRUCTURE
Based on the dynamics of the signal transduction network of thecell cycle [2,5,6], we propose a robust controller structure as
illustrated in Fig. 1, where Cln2 and Cln3 are cyclin andki , i = 1,2,3 are the coefficients for the feedback to the controller.
Let us consider a second order system to describe the statetransitions of the above controller

X (t + 1) = A X (t) + B U (t)where X (t) is the state vector and U (t) is the input signal.
Matrices A and B control the influence of the input signal andthe previous state and can be given as⎡1 0⎤A =⎢⎥⎣ 0 1⎦

4. CONCLUSION
In this paper we briefly discussed the analogies between thesignaling processes of the biological cell cycle and TCP andgeneralizing their dynamics by a master equation, inspired byanalytical models for TCP/RED and the dynamics of cyclin.
Based on its robustness features [6], we propose a genericcontroller structure for a biologically inspired scheme for robust
information network control.

5. REFERENCES

where∑Figure 1: The controller structure for the signal transduction
network that consists of Cln2 and Cln3 with feedbacks⎡ 0 1⎤B =⎢⎥⎣1 0⎦

where A1,1 = B1,2 = 1 provide the control and A2,2 = B2,1 = 1 areused for communication. The matrix B : AB has a rank of 2,
which states that the system is controllable where “:” refers tomerge operator for matrices as defined in automatic control theory.

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