Computational Biology and Chemistry 41 (2012) 10–17 Contents lists available at SciVerse ScienceDirect Computational Biology and Chemistry jou rnal h omepa g e: www.elsevier.com/locate/compbiolchem Stochastic synchronization of interacting pathways in testosterone model Md. Jahoor Alam a , Gurumayum Reenaroy Devi a , R.K. Brojen Singh a,∗ , R. Ramaswamy b , Sonu Chand Thakur a , B. Indrajit Sharma c a Centre for Interdisciplinary Research in Basic Sciences, Jamia Millia Islamia, New Delhi 110025, India b School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India c Department of Physics, Assam University, Silchar 788 011, Assam, India a r t i c l e i n f o Article history: Received 24 January 2012 Received in revised form 13 July 2012 Accepted 5 August 2012 Keywords: Cell signaling Synchronization Coupling Intercellular communication Intracellular communication a b s t r a c t We examine the possibilities of various coupling mechanisms among a group of identical stochastic oscillators via Chemical Langevin formalism where each oscillator is modeled by stochastic model of testosterone (T) releasing pathway. Our results show that the rate of synchrony among the coupled oscil- lators depends on various parameters namely fluctuating factor, coupling constants , and interestingly on system size. The results show that synchronization is achieved much faster in classical deterministic system rather than stochastic system. Then we do large scale simulation of such coupled pathways using stochastic simulation algorithm and the detection of synchrony is measured by various order parameters such as synchronization manifolds, phase plots etc and found that the proper synchrony of the oscillators is maintained in different coupling mechanisms and support our theoretical claims. We also found that the coupling constant follows power law behavior with the systems size (V) by  ∼ AV - , where  = 1 and A is a constant. We also examine the phase transition like behavior in all coupling mechanisms that we have considered for simulation. The behavior of the system is also investigated at thermodynamic limit; where V→ ∞, molecular population, N→ ∞ but N V → finite, to see the role of noise in information processing and found the destructive role in the rate of synchronization. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction The experimental observation of oscillation in testosterone level in men (Murray, 2002) in the pathway of hypothalamic, pituitary and leydig cells, is believed to be originated due to var- ious feedback mechanisms involved in the pathway (Yen et al., 1999). Following a central neuron system signal, the hypothal- amic cells in the hypothalamus secret gonadotropin releasing hormone (GnRH) and travel to reach pituitary gland via tuberoin- fundibular pathway to activate the releasing of luteinizing hormone (LH) from the pituitary cells (Heuett and Qian, 2006). The LH diffuses through blood to activate testosterone (T) production by the leydig cells in testes. Excess production of T is con- trolled by a feedback mechanism which inhibits the secretion of GnRH. There have been various mathematical models (both determi- nistic as well as stochastic) (Cartwright and Husain, 1986; Keenan and Veldhuis, 1998; Keenan et al., 2000; Heuett and Qian, 2006) to investigate and understand the origin of the oscillatory behaviour of the testosterone level in male reproductive organ in human being. Extensive study on the possibilities of oscillation in T without ∗ Corresponding author. Tel.: +91 11 2698 17171/4492; fax: +91 11 26983409. E-mail addresses: brojen2k@yahoo.com, rk.brojen@gmail.com (R.K.B. Singh). using experimental parameters, is also been done deterministi- cally. The stochastic model to study various mechanisms involved in this pathway gives us important insights, for example the oscil- lation of T can be obtained with the experimental values of the interacting or secreting hormones in the pathway etc and it is a realistic model which consider various interaction events along the pathway (Gillespie, 1977, 2007). Further, these models takes into account the noise fluctuation systematically in the system dynamics which enable to study the constructive role of noise such as detection and amplification of weak signal which is known as stochastic resonance (Hanggi, 2002). The Chemical Langevin Equa- tion (CLE) formalism is a simple stochastic formalism which is derived from the Chemical Master Equation (CME) under certain realistic approaximations (Gillespie, 2000) and can describe well the importance of noise (Gonze et al., 2003) associated with the dynamics with order V -1/2 . A pathway which consists of a hypothalamic cell which release GnRH, then a pituitary cell secreting LH activated by GnRH, a Leydig cell which release T and control of T population by feedback mech- anism, gives rise an oscillatory behaviour of T and therefore the pathway can be taken as an oscillator. There are a number of such identical pathways or oscillators which do the identical function in releasing T hormone in testes. The basic issue we raise in this work is the interaction of such identical pathways provided a central neu- ron stimulus signal, to do the synchronous function of releasing T 1476-9271/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compbiolchem.2012.08.001