A Neural Nanonetwork Model Based on Cell Signaling Molecules ´ Aron Szab´ o *† , G´ abor Vattay *§ and D´ aniel Kondor *§ * Department of Physics of Complex Systems E¨ otv¨ os University, H-1117 Budapest, P´ azm´ any P. s. 1/A, Hungary † Email: szaboahun@gmail.com ‡ Email: vattay@elte.hu § Email: kondor.dani@gmail.com Abstract—All cells have to adapt to changing chemical en- vironments. The signaling system reacts to external molecular ‘inputs’ arriving at the receptors by activating cellular responses via transcription factors generating proper proteins as ‘outputs’. The signal transduction network connecting inputs and outputs acts as a molecular computer mimicking a neural network, a ‘chemical brain’ of the cell. The dynamics of concentrations of various signal proteins in the cell are described by continuous kinetic models proposed recently. In this paper we introduce a special neural network model based on the ordinary differential equations of the kinetic processes. We show that supervised learning can be implemented using the delta rule for updating the weights of the molecular neurons. We demonstrate the concept by realizing some of the basic logical gates in the model. I. I NTRODUCTION All living entities have to adapt to their environment. This is particularly true for unicellular organisms. In this case, en- vironmental signals are quite simple, eg. temperature changes or changes in the chemical composition of the environment. Their so-called signaling network which consists of thousands of proteins reacts to such external stimuli. Its role is similar to the neural network of higher organisms. The high degree of interconnectedness and complexity of the protein network makes it very similar to a neural network. The nodes of this network are the proteins that travel in the cell’s inner volume by diffusion. Proteins in the signaling network can be regarded as in- formation processing units: they produce molecules according to their molecular input. These proteins have two states: an activated and a deactivated. A protein in its activated state is also called phosphorylated. Hence this two-state system can be regarded as a binary bit based information storage system and passage of the activated state from protein to protein can be regarded as information propagation in the network. Such properties of the cellular signaling network enable us to use this system for computations and also as a nanoscale communication network. Recently, it has been shown [1] that cell based molecular nano-communication networks can be modeled in terms of information theory. The receptor of the cell membrane (ligand) can be regarded as a sender and the cellular nucleus can be regarded as a receiver of the intra-cell communication. The response of the nucleus for the incoming cellular signals can be the initiation of the transcription of a specific gene. The tran- scription factors are the output nodes of the cell signaling net- work. Linear network coding [2] is one of the ways to formu- late the signaling pathway network. The phosphorylation/de- phosphorylation process can be represented by a network coding model [1]. Control of engineered molecular motors via signaling pathways [3], [4] is also possible [1] making possible to develop cellular systems which respond to external stimuli with various mechanical or electrical actions. The realization of a deterministic process based program- ming of cellular communication systems requires further ad- vances in molecular technology. Yet, logical gates operate in vivo cellular systems: the design logic of cannabionoid receptor signaling network has recently been uncovered [5]. In living cells the information flow is carried by a swarm of activated protein molecules and information passage between proteins is described by reaction-diffusion equations govern- ing the concentrations of macroscopic number of molecules. Such computational systems – based on the concentrations of signaling protein molecules – has been envisioned by Bray [6] in 1995. In this paper we show that the mass action kinetics of cell signaling networks can be designed and trained to carry out logical calculations. Elements of training algorithms developed in machine learning such as ‘delta rule’ and ‘feed forward networks’ can be realized. The article is organized the following way. In section II we introduce a mass action kinetic model of the signaling network. In section III we deduce a learning algorithm for tuning the parameters of the network. Finally, in section IV we present some of the basic logic gates to illustrate the concept. II. THE MODEL Hereby we introduce a simple model of the network de- scribed in the Introduction. We assume that the distribution of protein concentrations in the system is spatially homogeneous and hence we can treat the problem with ordinary differential equations in the framework of mass action kinetics like in [7]. Let us assume the overall concentration of a protein including activated and deactivated parts is constant, c i for the ith protein. The concentration of the ith protein’s activated part is denoted by x i , the deactivated part’s concentration is c i − x i accordingly. We assume, following Kartal and Ebenh¨ oh [7], that the change of protein concentrations is described by the following equations: 1st IEEE International Workshop on Molecular and Nano Scale Communication (MoNaCom) 978-1-4577-0248-8/11/$26.00 ©2011 IEEE 485