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Section COMPUTATIONAL NEUROSCIENCE
Competitive Learning Mechanisms for Distributed Synthetic Gene Classifiers
O.I. Kanakov1*, M.V. Ivanchenko1 and L.S. Tsimring2
1 Lobachevsky University, Nizhny Novgorod, Russia;
2 BioCircuits Institute, University of California - San Diego, La Jolla, USA. * Presenting e-mail: okanakov@rf.unn.ru
Motivation and Aims
Creating learnable classifiers based on synthetic gene circuits is one of the challenging tasks of modern synthetic biology (see references in [1,2]). A promising field where such classifiers can be applied is creation of intellectual biosensors which, in addition to sensing certain parameters of environment, produce some kind of decision based on these parameter values (e.g. whether the environment is safe or not).
Designing complicated classifier circuits within a single cell is limited by capabilities of present synthetic biology techniques (e.g. limited number of synthetic genes in a cell). A promising way of overcoming this limitation is a distributed classifier [1,2] which is essentially an ensemble of cells, where each cell is an elementary classifier, and the final decision is obtained from the overall ensemble output. Distributed classifiers are capable of solving problems which can not be solved by a single classifier cell [1,2].
If the full ensemble of cells ("master population") consists of a large number of elementary classifiers where some internal parameters are varied from cell to cell, then such distributed classifier can be trained by modifying the composition of the ensemble (by eliminating certain cells and duplicating others) without adjusting any internal parameters of each single cell. In our previous works [1,2] we considered two statements of the classification problem along with corresponding learning strategies.
The "hard" classification problem [2] assumes that the classes are separable, implying that the correct classification answer can be uniquely attributed to any classifier input (the corresponding regions in the input space do not intersect). In this case the training can consist of simply removing the incorrectly answering cells from the ensemble, which we refer to as "hard" learning strategy [2].
Conversely, the "soft" classification problem [1,2] admits inseparability of classes, which implies that the probability density functions corresponding to different classes (or to alternative a priori hypotheses) may overlap in the space of inputs. If the input falls within such overlap, then it cannot be uniquely classified, and classification error probability is necessarily non-zero. One can seek to optimize the classification rule in a certain sense. If the probability density functions of classes are known a priori, then the error probability is minimized by the Bayesian classification rule.
In [1,2] a "soft" learning strategy to address the soft classification problem was suggested and studied. It is assumed that the cell ensemble consists of "species" (or cell lines), so that the cells within each species are identical, but elementary classifier parameters are varied between different species. The "parameters" of the ensemble which are tuned in the course of learning are the sizes (the numbers of cells) of the species. The learning strategy is based on competition between the species with viabilities specifically designed in a way that the competitive dynamics produces a cell ensemble constituting a learned distributed classifier. A special mechanism to implement this competition using e.g. fluorescent-activated cell sorting was also suggested [1].
This strategy suffers from a major shortcoming which is essentially a special case of the Gause's competitive exclusion principle: only one species (having the strongest viability) remains in the limit, so the limiting state is trivial and generally can not be used as the learning outcome. States which approximate the optimum classification rule appear transiently in the course of the competitive dynamics, so a separate problem arises to stop the learning procedure at the right moment [1].
The aim of the present study is to design a competitive learning mechanism for a distributed classifier which would converge to a good approximation of the optimal classifier in the limit without the necessity of catching the correct transient state.
Methods and Results
We introduce a competition model which incorporates intra-species competition in addition to inter-species one. This produces the co-existence regime, where (generically) all species are present in the limiting equilibrium state of the ensemble. The sizes of the species in this limiting state are determined by the species viabilities.
Using the mathematical model of this competition we formulate the conditions ensuring that the limit state of the distributed classifier approximates the optimal Bayesian classification rule. We also suggest a mechanism to implement this learning strategy using standard tools like fluorescent-activated cell sorting technique.
The learning strategy based on competition with co-existence is more complicated to implement than one without coexistence, since an additional selective intra-species competition mechanism has to be organized. At the same time,
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Section COMPUTATIONAL NEUROSCIENCE
it has the following advantages: (i) classification accuracy monotonously increases in the limit, as the ensemble approaches the stable equilibrium state; (ii) the mathematical model of the competitive dynamics admits an analytical expression for species sizes in the equilibrium state, which theoretically allows to achieve the exactly optimal Bayesian classification rule as a result of learning in the limit of infinite training sequence.
Acknowledgements
This work was supported by the Russian Science Foundation (grant 16-12-00077). References
1. A. Didovyk et al., ACS synthetic biology, 2014, 4(1), 72-82.
2. O. Kanakov et al., PLOS ONE, 2015, 10(5), e0125144.
Computations with Intracellular Circuits
M.V. Ivanchenko1*, O.I. Kanakov1 and A.A. Zaikin1,2
1 Lobachevsky University, Nizhny Novgorod, Russia;
2 University College London, London, United Kingdom. * Presenting e-mail: ivanchenko.mv@gmail.com
Information processing, or computation, can be performed by natural and man-made «devices». Man-made computers are made from silicon chips, whereas natural «computers», such as the brain, use cells and molecules. At the same time there is a growing understanding that complex information processing in living systems goes beyond neurons, for example, in adaptive immune system, or in synthetically engineered bacterial cells. Even further, computation occurs on a subcellular level, that is regulatory and signaling pathways in individual cells. In fact, what we perceive as living processes originates from the remarkable ability of integrated biological «elementary» circuits to perform sophisticated computations. For neuronal systems it follows that their information processing abilities may substantially involve similar mechanisms. In our talk we will introduce the key concepts and discuss recent progress that has been made in biomolecular computing. As a proop of principle we present our recent results on a scheme of a synthetically engineered distributed genetic circuit capable of solving classification tasks for quite generic input vectors of chemical signals.
Acknowledgements
The authors acknowledge support of the Russian Science Foundation (grant No. 16-12-00077).
Synaptic Origins of Working Memory Capacity
M. Tsodyks*
Weizmann Institute of Science, Israel. * Presenting e-mail: misha@weizmann.ac.il
Working memory plays a fundamental role in many cognitive tasks. It is thus puzzling that its capacity is extremely limited, averaging just 4 items for most of the people. The origins of this limit are not clear. I will consider this issue in the framework of synaptic theory of working memory. I will derive an analytical estimate for capacity in terms of basic parameters of short-term synaptic plasticity and neuronal spike-generation dynamics. The obtained expression indicates that capacity can be tuned to the desired level by modulating the average excitation in the network. If time permits, I will show how this process could account for spontaneous chunking of word lists in free recall experiments.
