Group PI

I did my PhD in the theoretical chemistry group of Prof. Ray Kapral in the University of Toronto, Canada. My career path took me into several countries and working environments, however my ultimate goal has always been understanding complex self-organized behavior of biological systems. In 2006 I joined the University of Edinburgh where I am presently a Professor of Computational Cell Biology.

For the main directions of current pursuits in our group, please see the Publications page. Here I briefly outline other areas of interest and past research exploits.

Dynamics of biological membranes

Membranes provide a quasi 2D environment that concentrates proteins and lipids so that many biochemical reactions, which hardly ever happen in the cytoplasm, can rapidly proceed on the membranes. From the biophysical point of view, description of reaction and diffusion on the membranes is complicated by many phenomena that can be neglected in the cytoplasm. For one, diffusion of most membrane lipids can no longer be seen as a motion of dilute solutes in the bulk of the solvent. Also, this motion is not purely thermal, it is affected by other physical forces, such as electrostatic interactions. Small Rho GTPases, one of the foci of research in our group, are usually attached to the membranes by one or several lipid tails and, frequently, by a so-called polybasic stretch, an unstructured sequence of several positively charged amino acids, that interacts strongly with negatively charged lipids. Much work has been done to understand how such molecules shuttle between the membrane and cytoplasm, however, little is known if their electrostatic interaction with lipids can play any role in the formation of spatial patterns on the membranes.

Pentalysine (+5) peptide overlaying the lipid lattice represents in the model the polybasic domain. Averaged demixing of phosphatidylserine (PS) and PIP3 lipids produced by the peptide in its vicinity. Difference from the expected average density of lipids is shown by color

We had a hypothesis that the polybasic stretch could sense and respond to short-living spatial gradients of charged lipids in the plane of the membrane. To test if this hypothesis had a theoretical ground, a talented PhD student in my group Vladimir Kiselev built a Monte-Carlo automaton simulating a positively charged peptide diffusing above the membrane with mobile charged lipids . One unexpected result that came early out of these efforts was a surprising finding that such positively charged proteins can diffuse within the membrane only as highly dynamic complexes with the underlying lipids. Depending on the charge of the lipids, such complexes can be either positive or negative. Moreover, we found that they indeed can sense the gradient of charged lipids and should move up or down the gradient depending on the total charge. With a biologically realistic gradient steepness, our model predicted protein velocities of up to several micrometers per second! This model prediction has potentially far reaching consequences for cell biology and still awaits experimental testing.

V. Kiselev, D. Marenduzzo, and A. Goryachev, Lateral dynamics of proteins with polybasic domoain on anionic membranes: A dynamic Monte-Carlo study, Biophys. J., 100(5), 1261 - 1270 (2011).

V. Kiselev, M. Leda, A. Lobanov, D. Marenduzzo, A. Goryachev, Lateral dynamics of charged lipids and peripheral proteins in spatially heterogeneous membranes: Comparison of continuous and Monte-Carlo approaches, J. Chem. Phys., 135, 155103 (2011).

Quorum sensing in bacteria
Ability of bacteria to sense their local population density by secreting molecules that can be recognized by the same bacteria is known as quorum sensing. This population-wide behavior is controlled by a relatively simple genetic network that encodes at least one transcription regulator and an enzyme producing the signaling molecule known as autoinducer. Quorum sensing (QS) has raised a number of interesting questions related to the ecological and evolutionary significance of this phenomenon. It also opened a tantalizing opportunity for a computational modeler to be able to describe the intracellular, cell-scale and population-wide dynamics in one multi-scale model and, for once, to be able to derive predictions on how a whole population behavior is controlled by specific molecular parameters, such as concentration of the transcription factor. Back in 2003, I, then a freshly-minted group leader in Singapore, was lucky to meet Prof. Lianhui Zhang who introduced me to the subject and challenged me to build a model for the QS system controlling cell-to-cell transfer of the pTi plasmids of the gram-negative bacterium Agrobacterium tumefaciens, a plant pathogen heavily used in biotechnology for genetic modification of plants.

A. tumefaciens causes tumors of plants. Gene network reconstructed from the published data and its bistable dynamics predicted by the model. The last plot shows copy number of the transcription factor TraR as a function of extracellular autoinducer concentration.

The resulting model  predicted a bistable, truly switch-like behavior of the A. tumefaciens QS gene network. To go beyond intracellular behavior, with a group of talented software developers we built an unprecedented agent-based model of a dynamically growing spatially-distributed population in which each of the hundreds of thousands cells  was represented by an independent stochastic realization of the QS gene network that chemically communicated with its extracellular environment. This model allowed us to study gene-expression noise and transition to the quorum on a population scale. Unexpectedly, quantitative nature of the model allowed us to conclude that, specifically in A. tumefaciens, QS serves to inform the plasmid that its host bacterium is inside a biofilm, sufficiently dense to risk undertaking a cell-to-cell transfer. This first experience with QS inspired a number of later analyses of QS network architectures in several other bacterial species. Till now, many mysteries of QS networks remain still unresolved.

A. Goryachev, Understanding bacterial cell-cell communication with computational modeling, Chem. Rev., 111, 238 - 250 (2011).

A. Goryachev, Design principles of the bacterial quorum sensing gene networks. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 1(1), 45 - 60 (2009).

A. Goryachev , D.-J. Toh, T. Lee, Systems analysis of a quorum sensing network: design constraints imposed by the functional requirements, network topology and kinetic constants. BioSystems 83(2), 178 – 187 (2006).

A. Goryachev , D.-J. Toh, K. B. Wee, T. Lee, H. B. Zhang, and L. H. Zhang, Transition to quorum sensing in an Agrobacterium population: A stochastic model. PLoS Computational Biology 1(4), 265 – 275 (2005).

D.-J. Toh, F. Tang, T. Lee, D. Sarda, A. Krishnan, and A. Goryachev, Parallel computing platform for the agent-based modeling of multicellular biological systems. In: K. M. Liew, H. Shen, S. See, et al. (Eds.) Parallel and distributed computing: applications and technologies. (2004) Springer, Heidelberg.

Studying gene expression on a genomic scale

In the late 1990s, a gold rush of functional genomics swept the globe. I could not resist the temptation of its promise to reveal the inner workings of gene regulatory networks and joined one of the first in Canada microarray facilities then just established in the Toronto-based Princess Margaret Hospital. Trying to bring quantitative methodology into microarray data analysis, I focused on identifying various sources of systematic errors and estimation of random noise throughout the technology pipeline from array printing to image analysis. What came out of this effort was one of the first quantitative models  of the fluorescence intensity ratios reported by this method and a set of practical methods allowing inference of the best approximation for the true gene expression ratios hidden within the experimental measurements. Some of these methods were later implemented within commercial software during my industrial stint with GeneData AG in Basel, Switzerland.

B. Schimmer, M. Cordova, H. Cheng, A. Tsao, A. Goryachev, A. Schimmer, Q. Morris, Global profiles of gene expression induced by ACTH in Y1 mouse adrenal cells. Endocrinology, 147(5), 2357 – 2367 (2006).

L. Chen, A. Goryachev, J. Sun, P. Kim, H. Zhang, M. Phillips, P. Macgregor, S. Lebel, A. Edwards, and K. Furuya, Altered expression of genes involved in hepatic morphogenesis and fibrogenesis are identified by cDNA microarray analysis in biliary atresia. Hepatology. 38(3), 567 - 576 (2003).

A. Goryachev, P. Macgregor, and A. Edwards, Unfolding of microarray data. J. Comp. Biol. 8(4), 443 - 461 (2001).

K. Mossman, P. Macgregor, J. Rozmus, A. Goryachev, A. Edwards, and J. Smiley, Herpes simplex virus triggers and then disarms a host antiviral response. J. Virol. 75(2), 750 - 758 (2001).

S. Hemming, D. Jansma, P. Macgregor, A. Goryachev, J. Friesen, and A. Edwards, RNA polymerase II subunit Rpb 9 regulates transcription elongation in vivo. J. Biol. Chem. 275, 35506 - 35511 (2000).

Patterns in complex-periodic systems

My strong belief in the predictive power of computational modeling dates back to my PhD days in the group of Ray Kapral at the University of Toronto. My research question was to find out if any new or unusual patterns existed in spatially-distributed systems (“media” in chemical terms) capable of complex-periodic oscillations. The notion of complex periodicity is best exemplified by the phenomenon of period-doubling. Imagine that you start with a time series describing normal periodic oscillation and then slightly increase the amplitude of every second maximum while reduce that of each previous. As a result, new oscillation pattern will repeat itself with the twice longer period. Viewed in a 3D space, such an oscillation will look not like a typical simple ring but rather as a twice-folded onto itself structure (mathematicians call it a “braid”) on which an imaginary walking observer would have to make not one (2pi) but two full turns (4pi) until he would come to the same point. We were particularly interested if such complex-periodic systems could exhibit spiral waves that are common for physical and biological systems with simple periodic dynamics. To our complete surprise, it turned out that in the period-2 system, an attempt to form a simple one-armed spiral wave inevitably results in the creation of a new, not yet reported then in the literature, structure, which we called a synchronization defect line . This is because across this line, the phase of the oscillation changes by a quantum of 2pi so that the circular walk around the spiral center amounts to the full 4pi phase increment, to match the longer period of the period-2 oscillation! Moreover, spiral waves are not necessary to have synchronization defect lines, simply, without spiral waves, these lines have to be circular  demarkating the domains with oscillation phase shifted by 2pi. Further, I demonstrated that synchronization defect lines can also exist in excitable systems exhibiting complex periodicity  (yes, such systems also exist, see below).

Does this phenomenon have anything to do with biology? It turned out, yes! Cardiologists have long known about the existence of alternating heart beats, one longer, one shorter (and smaller in amplitude). These so-called alternans formally are a period-2 complex excitable behavior. Discordant alternans, when at the same time moment in one heart location the beat is longer and in another location it is shorter, were also found with mto expoving electrodes. Thus, we suspected that synchronization defect lines should exist in the heart, but with the technology of those days their observation was, alas, impossible. Shortly after the publication of my PhD thesis that was based solely on modeling results, synchronization defect lines were observed by several experimental groups first in chemical and then biological systems. Finally, the technology of spatial optical mapping with voltage and Ca-sensitive dies  allowed to observe synchronization defect lines in experiments with whole perfused animal hearts!

A. Goryachev, R. Kapral, and H. Chate, Synchronization defect lines. Int. J. Bif. & Chaos 10, 1537 - 1564 (2000).

A. Goryachev, H. Chate, and R. Kapral, Transition to Line-Defect Mediated Turbulence in Complex Oscillatory Media. Phys. Rev. Lett. 83, 1878 - 1881 (1999).

A. Goryachev and R. Kapral, Spiral Waves in Media with Complex Excitable Dynamics. Int. J. Bif. & Chaos 9, 2243 - 2247 (1999).

A. Goryachev, H. Chate, and R. Kapral, Synchronization Defects and Broken Symmetry in Spiral Waves. Phys. Rev. Lett. 80, 873 - 876 (1998).

A. Goryachev and R. Kapral, Structure of Complex-Periodic and Chaotic Media with Spiral Waves. Phys. Rev. E 54, 5469 - 5482 (1996).

A. Goryachev and R. Kapral, Spiral Waves in Chaotic Systems. Phys. Rev. Lett. 76, 1619 - 1622 (1996).