Role of feedback and dynamics in a gene regulatory network

Cells exhibit a diverse repertoire of dynamic behaviors. These dynamic functions are implemented by circuits of interacting biomolecules. Although these regulatory networks function deterministically by executing specific programs in response to extracellular signals, molecular interactions are inherently governed by stochastic fluctuations. This molecular noise can manifest as cell-to-cell phenotypic heterogeneity in a well-mixed environment. Single-cell variability may seem like a design flaw but the coexistence of diverse phenotypes in an isogenic population of cells can also serve a biological function by increasing the probability of survival of individual cells upon an abrupt change in environmental conditions. Decades of extensive molecular and biochemical characterization have revealed the connectivity and mechanisms that constitute regulatory networks. We are now confronted with the challenge of integrating this information to link the structure of these circuits to systems-level properties such as cellular decision making. To investigate cellular decision-making, we used the well studied galactose gene-regulatory network in \textit{Saccharomyces cerevisiae}. We analyzed the mechanism and dynamics of the coexistence of two stable on and off states for pathway activity. We demonstrate that this bimodality in the pathway activity originates from two positive feedback loops that trigger bistability in the network. By measuring the dynamics of single-cells in a mixed sugar environment, we observe that the bimodality in gene expression is a transient phenomenon. Our experiments indicate that early pathway activation in a cohort of cells prior to galactose metabolism can accelerate galactose consumption and provide a transient increase in growth rate. Together these results provide important insights into strategies implemented by cells that may have been evolutionary advantageous in competitive environments.

Isolation of the murine interleukin 2 gene and characterization of its regulatory architecture

Interleukin 2 (IL2) is the primary growth hormone used by mature T cells and this lymphokine plays an important role in the magnification of cell-mediated immune responses. Under normal circumstances its expression is limited to antigen-activated type 1 helper T cells (T_H1) and the ability to transcribe this gene is often regarded as evidence for commitment to this developmental lineage. There is, however, abundant evidence than many non-T_H1 T cells, under appropriate conditions, possess the ability to express this gene. Of paramount interest in the study of T-cell development is the mechanisms by which differentiating thymocytes are endowed with particular combinations of cell surface proteins and response repertoires. For example, why do most helper T cells express the CD4 differentiation antigen?

As a first step in understanding these developmental processes the gene encoding IL2 was isolated from a mouse genomic library by probing with a conspecific IL2 cDNA. The sequence of the 5' flanking region from + 1 to -2800 was determined and compared to the previously reported human sequence. Extensive identity exists between +1 and -580 (86%) and sites previously shown to be crucial for the proper expression of the human gene are well conserved in both sequence location in the mouse counterpart.

Transient expression assays were used to evaluate the contribution of various genomic sequences to high-level gene expression mediated by a cloned IL2 promoter fragment. Differing lengths of 5' flanking DNA, all terminating in the 5' untranslated region, were linked to a reporter gene, bacterial chloramphenicol acetyltransferase (CAT) and enzyme activity was measured after introduction into IL2-producing cell lines. No CAT was ever detected without stimulation of the recipient cells. A cloned promoter fragment containing only 321 bp of upstream DNA was expressed well in both Jurkat and EL4.El cells. Addition of intragenic or downstream DNA to these 5' IL2-CAT constructs showed that no obvious regulatory regions resided there. However, increasing the extent of 5' DNA from -321 to -2800 revealed several positive and negative regulatory elements. One negative region that was well characterized resided between -750 and -1000 and consisted almost exclusively of alternating purine and pyrimidines. There is no sequence resembling this in the human gene now, but there is evidence that there may have once been.

No region, when deleted, could relax either the stringent induction-dependence on cell-type specificity displayed by this promoter. Reagents that modulated endogenous IL2 expression, such as cAMP, cyclosporin A, and IL1, affected expression of the 5' IL2-CAT constructs also. For a given reagent, expression from all expressible constructs was suppressed or enhanced to the same extent. This suggests that these modulators affect IL2 expression through perturbation of a central inductive signal rather than by summation of the effects of discrete, independently regulated, negative and positive transcription factors.

On the distribution of the signs of the conjugates of the cyclotomic units in the maximal real subfield of the qth cyclotomic field, q A prime

Let F = Ǫ(ζ + ζ ^–1) be the maximal real subfield of the cyclotomic field Ǫ(ζ) where ζ is a primitive qth root of unity and q is an odd rational prime. The numbers u₁=-1, u_k=(ζ^k-ζ^-k)/(ζ-ζ^-1), k=2,…,p, p=(q-1)/2, are units in F and are called the cyclotomic units. In this thesis the sign distribution of the conjugates in F of the cyclotomic units is studied.

Let G(F/Ǫ) denote the Galoi's group of F over Ǫ, and let V denote the units in F. For each σϵ G(F/Ǫ) and μϵV define a mapping sgn_σ: V→GF(2) by sgn_σ(μ) = 1 iff σ(μ) ˂ 0 and sgn_σ(μ) = 0 iff σ(μ) ˃ 0. Let {σ₁, ... , σ_p} be a fixed ordering of G(F/Ǫ). The matrix M_q=(sgn_σj(v_i) ) , i, j = 1, ... , p is called the matrix of cyclotomic signatures. The rank of this matrix determines the sign distribution of the conjugates of the cyclotomic units. The matrix of cyclotomic signatures is associated with an ideal in the ring GF(2) [x] / (x^p+ 1) in such a way that the rank of the matrix equals the GF(2)-dimension of the ideal. It is shown that if p = (q-1)/ 2 is a prime and if 2 is a primitive root mod p, then M_q is non-singular. Also let p be arbitrary, let ℓ be a primitive root mod q and let L = {i | 0 ≤ i ≤ p-1, the least positive residue of defined by ℓⁱ mod q is greater than p}. Let H_q(x) ϵ GF(2)[x] be defined by H_q(x) = g. c. d. ((Σ xⁱ/I ϵ L) (x+1) + 1, x^p + 1). It is shown that the rank of M_q equals the difference p - degree H_q(x).

Further results are obtained by using the reciprocity theorem of class field theory. The reciprocity maps for a certain abelian extension of F and for the infinite primes in F are associated with the signs of conjugates. The product formula for the reciprocity maps is used to associate the signs of conjugates with the reciprocity maps at the primes which lie above (2). The case when (2) is a prime in F is studied in detail. Let T denote the group of totally positive units in F. Let U be the group generated by the cyclotomic units. Assume that (2) is a prime in F and that p is odd. Let F₍₂₎ denote the completion of F at (2) and let V₍₂₎ denote the units in F₍₂₎. The following statements are shown to be equivalent. 1) The matrix of cyclotomic signatures is non-singular. 2) U∩T = U². 3) U∩F²₍₂₎ = U². 4) V₍₂₎/ V₍₂₎² = ˂v₁ V₍₂₎²˃ ʘ…ʘ˂v_p V₍₂₎²˃ ʘ ˂3V₍₂₎²˃.

The rank of M_q was computed for 5≤q≤929 and the results appear in tables. On the basis of these results and additional calculations the following conjecture is made: If q and p = (q -1)/ 2 are both primes, then M_q is non-singular.