Stochastic Simulations of the Repressilator Circuit

The genetic repressilator circuit consists of three transcription factors, or repressors, which negatively regulate each other in a cyclic manner. This circuit was synthetically constructed on plasmids in {\it Escherichia coli} and was found to exhibit oscillations in the concentrations of the three repressors. Since the repressors and their binding sites often appear in low copy numbers, the oscillations are noisy and irregular. Therefore, the repressilator circuit cannot be fully analyzed using deterministic methods such as rate-equations. Here we perform stochastic analysis of the repressilator circuit using the master equation and Monte Carlo simulations. It is found that fluctuations modify the range of conditions in which oscillations appear as well as their amplitude and period, compared to the deterministic equations. The deterministic and stochastic approaches coincide only in the limit in which all the relevant components, including free proteins, plasmids and bound proteins, appear in high copy numbers. We also find that subtle features such as cooperative binding and bound-repressor degradation strongly affect the existence and properties of the oscillations.Comment: Accepted to PR

Measuring the sequence-affinity landscape of antibodies with massively parallel titration curves

Despite the central role that antibodies play in the adaptive immune system and in biotechnology, much remains unknown about the quantitative relationship between an antibody's amino acid sequence and its antigen binding affinity. Here we describe a new experimental approach, called Tite-Seq, that is capable of measuring binding titration curves and corresponding affinities for thousands of variant antibodies in parallel. The measurement of titration curves eliminates the confounding effects of antibody expression and stability that arise in standard deep mutational scanning assays. We demonstrate Tite-Seq on the CDR1H and CDR3H regions of a well-studied scFv antibody. Our data shed light on the structural basis for antigen binding affinity and suggests a role for secondary CDR loops in establishing antibody stability. Tite-Seq fills a large gap in the ability to measure critical aspects of the adaptive immune system, and can be readily used for studying sequence-affinity landscapes in other protein systems

The Structure of Allelic Diversity in the Presence of Purifying Selection

In the absence of selection, the structure of equilibrium allelic diversity is described by the elegant sampling formula of Ewens. This formula has helped shape our expectations of empirical patterns of molecular variation. Along with coalescent theory, it provides statistical techniques for rejecting the null model of neutrality. However, we still do not fully understand the statistics of the allelic diversity expected in the presence of natural selection. Earlier work has described the effects of strongly deleterious mutations linked to many neutral sites, and allelic variation in models where offspring fitness is unrelated to parental fitness, but it has proven difficult to understand allelic diversity in the presence of purifying selection at many linked sites. Here, we study the population genetics of infinitely many perfectly linked sites, some neutral and some deleterious. Our approach is based on studying the lineage structure within each class of individuals of similar fitness in the deleterious mutation-selection balance. Consistent with previous observations, we find that for moderate and weak selection pressures, the patterns of allelic diversity cannot be described by a neutral model for any choice of the effective population site. We compute precisely how purifying selection at many linked sites distorts the patterns of allelic diversity, by developing expressions for the likelihood of any configuration of allelic types in a sample analogous to the Ewens sampling formula.Organismic and Evolutionary Biolog

The Structure of Genealogies in the Presence of Purifying Selection: a "Fitness-Class Coalescent"

Compared to a neutral model, purifying selection distorts the structure of genealogies and hence alters the patterns of sampled genetic variation. Although these distortions may be common in nature, our understanding of how we expect purifying selection to affect patterns of molecular variation remains incomplete. Genealogical approaches such as coalescent theory have proven difficult to generalize to situations involving selection at many linked sites, unless selection pressures are extremely strong. Here, we introduce an effective coalescent theory (a "fitness-class coalescent") to describe the structure of genealogies in the presence of purifying selection at many linked sites. We use this effective theory to calculate several simple statistics describing the expected patterns of variation in sequence data, both at the sites under selection and at linked neutral sites. Our analysis combines a description of the allele frequency spectrum in the presence of purifying selection with the structured coalescent approach of Kaplan et al. (1988), to trace the ancestry of individuals through the distribution of fitnesses within the population. We also derive our results using a more direct extension of the structured coalescent approach of Hudson and Kaplan (1994). We find that purifying selection leads to patterns of genetic variation that are related but not identical to a neutrally evolving population in which population size has varied in a specific way in the past.Organismic and Evolutionary Biolog

Optimizing information flow in small genetic networks. I

In order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable randomness of individual molecular events. Here we explore how cells can maximize their control power in the presence of these physical limits; formally, we solve the theoretical problem of maximizing the information transferred from inputs to outputs when the number of available molecules is held fixed. We start with the simplest version of the problem, in which a single transcription factor protein controls the readout of one or more genes by binding to DNA. We further simplify by assuming that this regulatory network operates in steady state, that the noise is small relative to the available dynamic range, and that the target genes do not interact. Even in this simple limit, we find a surprisingly rich set of optimal solutions. Importantly, for each locally optimal regulatory network, all parameters are determined once the physical constraints on the number of available molecules are specified. Although we are solving an over--simplified version of the problem facing real cells, we see parallels between the structure of these optimal solutions and the behavior of actual genetic regulatory networks. Subsequent papers will discuss more complete versions of the problem

A mesoscopic ring as a XNOR gate: An exact result

We describe XNOR gate response in a mesoscopic ring threaded by a magnetic flux $\phi$. The ring is attached symmetrically to two semi-infinite one-dimensional metallic electrodes and two gate voltages, viz, $V_a$ and $V_b$, are applied in one arm of the ring which are treated as the inputs of the XNOR gate. The calculations are based on the tight-binding model and the Green's function method, which numerically compute the conductance-energy and current-voltage characteristics as functions of the ring-to-electrode coupling strength, magnetic flux and gate voltages. Our theoretical study shows that, for a particular value of $\phi$ ($=\phi_0/2$) ($\phi_0=ch/e$, the elementary flux-quantum), a high output current (1) (in the logical sense) appears if both the two inputs to the gate are the same, while if one but not both inputs are high (1), a low output current (0) results. It clearly exhibits the XNOR gate behavior and this aspect may be utilized in designing an electronic logic gate.Comment: 8 pages, 5 figure

An optimization of hematopoietic stem and progenitor cell isolation for scientific and clinical purposes by the application of a new parameter determining the hematopoietic graft efficacy.

The transplantation of hematopoietic stem and progenitor cells (HSPC) is an established lifesaving therapy. Bone marrow (BM), harvested from heparinized cadaveric organ donors, peripheral blood (PB) and cord blood (CB), are important sources of hematopoietic stem cells. HSPCs, which are used for transplantation purposes, are routinely evaluated in terms of number of mononuclear cells (MNCs), CD34+ MNCs count and viability. The efficacy of grafting is determined additionally in clonogenic tests in vitro. These tests deliver important information about the number of HSPCs and their proliferative potential. Unfortunately, they do not give a possibility to evaluate the functional HSPC chemotactic reactivity in the SDF-1 gradient, which is probably the key phenomenon for HSPC homing after transplantation procedure. Thus, the aim of our study was to optimize HSPC isolation according to their chemotactic reactivity in SDF-1 gradient. Using multiparameter cell sorter (FACS Aria, BD) we examined the HSPCs attracted by SDF-1 on a single cell level. The population of cells which participated in the chemotactic process was highly enriched in CXCR4+lin-AC133+CD45+ cells (referred as hematopoietic stem cells) and to our surprise in CXCR4+lin-AC133+CD45- cells (referred as pluripotent stem cells) in quantitative amounts. Since reactivity of HSPCs may depend on various factors involved in the protocol of their isolation and short-term storage, we tested the most commonly used anticoagulants (ACD, CPDA-1, EDTA and Heparin) and culture media (DME, IMDM, RPMI). HSPCs, harvested from CB, PB and BM, were subsequently investigated for clonogenic growth of CFU-GM in methylcellulose cultures and for the level of apoptosis by employing annexin V staining. Evaluating clonogenic potential, ability of chemotactic reactivity in SDF-1 gradient and intensification of apoptosis of HSPC as the most safe anticoagulant and medium were selected. This study has proved that chemotactic reactivity of HSPCs is a new but very important parameter which should be included in the procedure of their isolation

Optimizing information flow in small genetic networks. II: Feed forward interactions

Central to the functioning of a living cell is its ability to control the readout or expression of information encoded in the genome. In many cases, a single transcription factor protein activates or represses the expression of many genes. As the concentration of the transcription factor varies, the target genes thus undergo correlated changes, and this redundancy limits the ability of the cell to transmit information about input signals. We explore how interactions among the target genes can reduce this redundancy and optimize information transmission. Our discussion builds on recent work [Tkacik et al, Phys Rev E 80, 031920 (2009)], and there are connections to much earlier work on the role of lateral inhibition in enhancing the efficiency of information transmission in neural circuits; for simplicity we consider here the case where the interactions have a feed forward structure, with no loops. Even with this limitation, the networks that optimize information transmission have a structure reminiscent of the networks found in real biological systems