Saul H. Lapidus

Intrinsic noise, dissipation cost, and robustness of cellular networks: The underlying energy landscape of MAPK signal transduction

We develop a probabilistic method for analyzing global features of a cellular network under intrinsic statistical fluctuations, which is important when there are finite numbers of molecules. By making a self-consistent mean field approximation of splitting the variables in order to reduce the large number of degrees of freedom, which is reasonable for a not very strongly interacting network, we discovered that the underlying energy landscape of the mitogen-activated protein kinases (MAPKs) signal transduction network (with experimentally measured or inferred parameters such as chemical reaction rate coefficients in the network) is funneled toward a global minimum characterized by the nonequilibrium steady-state fixed point of the system at the end of the signal transduction process. For this system, we also show that the energy landscape is robust against intrinsic fluctuations and random perturbation to the inherent chemical reaction rates. The ratio of the slope versus the roughness of the energy landscape becomes a quantitative measure of robustness and stability of the network. Furthermore, we quantify the dissipation cost of this nonequilibrium system through entropy production, caused by the nonequilibrium flux in the system. We found that a lower dissipation cost corresponds to a more robust network. This least dissipation property might provide a design principle for robust and functional networks. Finally, we find the possibility of bistable and oscillatory-like solutions, which are important for cell fate decisions, upon perturbations. The method described here can be used in a variety of biological networks.

Extended Network Thiocyanate- and Tetracyanoethanide-Based First-Row Transition Metal Complexes

Linear chain thiocyanate complexes of M(NCS)(2)(OCMe(2))(2) (M = Fe, Mn, Cr) composition have been prepared and structurally, chemically, and magnetically characterized. Fe(NCS)(2)(OCMe(2))(2) exhibits metamagnetic-like behavior, and orders as an antiferromagnet at 6 K. The Mn and Cr compounds are antiferromagnets with T(c) of 30 and 50 K, respectively, with J/k(B) = -3.5 (-2.4 cm(-1)) and -9.9 K (-6.9 cm(-1)), respectively, when fit to one-dimensional (1-D) Fisher chain model (H = -2JS(i)·S(j)). Co(NCS)(2) was prepared by a new synthetic route, and powder diffraction was used to determine its structure to be a two-dimensional (2-D) layer with μ(N,S,S)-NCS motif, and it is an antiferromagnet (T(c) = 22 K; θ = -33 K for T > 25 K). M(NCS)(2)(OCMe(2))(2) (M = Fe, Mn) and Co(NCS)(2) react with (NBu(4))(TCNE) in dichloromethane to form M(TCNE)[C(4)(CN)(8)](1/2), and in acetone to form M[C(4)(CN)(8)](OCMe(2))(2) (M = Fe, Mn, Co). These materials possess μ(4)-[C(4)(CN)(8)](2-) that form 2-D layered structural motifs, which exhibit weak antiferromagnetic coupling. Co(TCNE)[C(4)(CN)(8)](1/2) behaves as a paramagnet with strong antiferromagnetic coupling (θ = -50 K).

Exploiting high pressures to generate porosity, polymorphism, and lattice expansion in the nonporous molecular framework Zn(CN)2.

Systematic exploration of the molecular framework material Zn(CN)2 at high pressure has revealed several distinct series of transitions leading to five new phases: four crystalline and one amorphous. The structures of the new crystalline phases have been resolved through ab initio structural determination, combining charge flipping and direct space methods, based on synchrotron powder diffraction data. The specific transition activated under pressure depends principally on the pressure-transmitting fluid used. Without fluid or in large molecule fluids (e.g., isopropanol, ethanol, or fluorinert), the high-pressure behavior intrinsic to Zn(CN)2 is observed; the doubly interpenetrated diamondoid framework structure transforms to a distorted, orthorhombic polymorph, Zn(CN)2-II (Pbca) at ~1.50-1.58 GPa with asymmetric displacement of the bridging CN ligand and reorientation of the Zn(C/N)4 tetrahedra. In small molecule fluids (e.g., water, methanol, methanol-ethanol-water), the nonporous interpenetrated Zn(CN)2 framework can undergo reconstructive transitions to porous, non-interpenetrated polymorphs with different topologies: diamondoid (dia-Zn(CN)2, Fd3m, P(trans) ~ 1.2 GPa), londaleite (lon-Zn(CN)2, P6(3)/mmc, P(trans) ~ 0.9 GPa), and pyrite-like (pyr-Zn(CN)2, Pa3, P(trans) ~ 1.8 GPa). Remarkably, these pressure-induced transitions are associated with near 2-fold volume expansions. While an increase in volume with pressure is counterintuitive, the resulting new phases contain large fluid-filled pores, such that the combined solid + fluid volume is reduced and the inefficiencies in space filling by the interpenetrated parent phase are eliminated. That both dia-Zn(CN)2 and lon-Zn(CN)2 phases were retained upon release to ambient pressure demonstrates the potential for application of hydrostatic pressures to interpenetrated framework systems as a novel means to generate new porous materials.

Non-Prussian Blue Structures and Magnetic Ordering of Na2MnII[MnII(CN)6] and Na2MnII[MnII(CN)6]·2H2O

The aqueous reaction of Mn(II) and NaCN leads to the isolation of the 3-D Prussian blue analogue (PBA) Na(2)Mn[Mn(CN)(6)]·2H(2)O (1·H(2)O), which under careful dehydration forms 1. 1·H(2)O is monoclinic [P2(1)/n, a = 10.66744(32) Å, b = 7.60223(23) Å, c = 7.40713(22) Å, β = 92.4379(28)°], while 1 is rhombohedral [R ̅3, a = 6.6166(2) Å, c = 19.2585(6) Å], and both structures are atypical for PBAs, which are typically face centered cubic. Most notably, the average ∠Mn-N-C angles are 165.3(3)° and 142.4(4)° for 1·H(2)O and 1, respectively, which are significantly reduced from linearity. This is attributed to the ionic nature of high-spin Mn(II) accommodating a reduced ∠Mn-N-C to minimize void space. Both 1 and 1·H(2)O magnetically order as ferrimagnets below their ordering temperature, T(c), of 58 and 30 K, respectively, as determined from the average of several independent methods. 1 and 1·H(2)O are hard magnets with 5 K coercive fields of 15,300 and 850 Oe, and remnant magnetizations of 9075 and 102 emu·Oe/mol, respectively. These data along with previous T(c)s reported for related materials reveal that T(c) increases as the ∠Mn-N-C deviates further from linearity. Hence, the bent cyanide bridges play a crucial role in the superexchange mechanism by increasing the coupling via shorter Mn(II)···Mn(II) separations, and perhaps an enhanced overlap.

Mechanochemical reactions of coordination polymers by grinding with KBr

Grinding of a one-dimensional (1-D) ladder coordination polymer (CP), [Zn(μ-CH(3)CO(2))(CF(3)CO(2))bpe] (1), and a hydrogen-bonded 1-D CP, [Cd(CH(3)CO(2))(2)bpe(H(2)O)] (2), with KBr resulted in the exchange of carboxylate by bromide ions and the formation of 1-D zigzag and 2-D CPs respectively.

Third structure determination by powder diffractometry round robin "SDPDRR-3…

The results from a third structure determination by powder diffractometry (SDPD) round robin are discussed. From the 175 potential participants having downloaded the powder data, nine sent a total of 12 solutions (8 and 4 for samples 1 and 2, respectively, a tetrahydrated calcium tartrate and a lanthanum tungstate). Participants used seven different computer programs for structure solution (ESPOIR, EXPO, FOX, PSSP, SHELXS, SUPERFLIP, and TOPAS), applying Patterson, direct methods, direct space methods, and charge flipping approach. It is concluded that solving a structure from powder data remains a challenge, at least one order of magnitude more difficult than solving a problem with similar complexity from single-crystal data. Nevertheless, a few more steps in the direction of increasing the SDPD rate of success were accomplished since the two previous round robins: this time, not only the computer program developers were successful but also some users. No result was obtained from crystal structure prediction experts.

First Row Transition Metal(II) Thiocyanate Complexes, and Formation of 1-, 2-, and 3-Dimensional Extended Network Structures of M(NCS)2(Solvent)2 (M = Cr, Mn, Co) Composition

The reaction of first row transition M(II) ions with KSCN in various solvents form tetrahedral (NMe4)2[M(II)(NCS)4] (M = Fe, Co), octahedral trans-M(II)(NCS)2(Sol)4 (M = Fe, V, Ni; Sol = MeCN, THF), and K4[M(II)(NCS)6] (M = V, Ni). The reaction of M(NCS)2(OCMe2)2 (M = Cr, Mn) in MeCN and [Co(NCMe)6](BF4)2 and KSCN in acetone and after diffusion of diethyl ether form M(NCS)2(Sol)2 that structurally differ as they form one-dimensional (1-D) (M = Co; Sol = THF), two-dimensional (2-D) (M = Mn; Sol = MeCN), and three-dimensional (3-D) (M = Cr; Sol = MeCN) extended structures. 1-D Co(NCS)2(THF)2 has trans-THFs, while the acetonitriles have a cis geometry for 2- and 3-D M(NCS)2(NCMe)2 (M = Cr, Mn). 2-D Mn(NCS)2(NCMe)2 is best described as Mn(II)(μ(N,N)-NCS)(μ(N,S)-NCS)(NCMe)2 [= Mn2(μ(N,N)-NCS)2(μ(N,S)-NCS)2(NCMe)4] with the latter μ(N,S)-NCS providing the 2-D connectivity. In addition, the reaction of Fe(NCS)2(OCMe2)2 and 7,7,8,8-tetracyanoquino-p-dimethane (TCNQ) forms 2-D structured Fe(II)(NCS)2TCNQ. The magnetic behavior of 1-D Co(NCS)2(THF)2 can be modeled by a 1-D Fisher expression (H = -2JS(i)·S(j)) with g = 2.4 and J/kB = 0.68 K (0.47 cm(-1)) and exhibit weak ferromagnetic coupling. Cr(NCS)2(NCMe)2 and Fe(II)(NCS)2TCNQ magnetically order as antiferromagnets with Tcs of 37 and 29 K, respectively, while Mn(NCS)2(NCMe)2 exhibits strong antiferromagnetic coupling. M(NCS)2(THF)4 and K4[M(NCS)6] (M = V, Ni) are paramagnets with weak coupling between the octahedral metal centers.

Implementation and use of robust refinement in powder diffraction in the presence of impurities

A modification to the usual least-squares analysis is implemented for the robust refinement of structural parameters from powder diffraction data in the presence of unmodeled impurities. This is accomplished in the program TOPAS-Academic by an iterative reweighting of the data as the model is refined. The method is tested and characterized using mixtures of known materials, acetaminophen and ibuprofen. The technique is also used to refine two previously unknown structures.

Evidence for Multicenter Bonding in Dianionic Tetracyanoethylene Dimers by Raman Spectroscopy

Raman spectroscopic studies have the potential to pro-vide a deeper insight into the properties of long bonds byexploring the shape of the intradimer C···C stretching vibra-tionalmode.ThismodeisexpectedtobeRaman-activebasedon symmetry considerations, and its observation unequivo-cally characterizes the presence of the long, multicenter bondin p-[TCNE]

Structure and magnetic ordering of a 2-D MnII(TCNE)I(OH2) (TCNE = tetracyanoethylene) organic-based magnet (Tc = 171 K)

Mn(II)(TCNE)I(OH(2)) was isolated from the reaction of tetracyanoethylene (TCNE) and MnI(2)(THF)(3), and has a 2-D structure possessing an unusual, asymmetric bonded μ(4)-[TCNE]˙(-). Direct antiferromagnetic coupling between the S = 5/2 Mn(II) and S = 1/2 [TCNE]˙(-) leads to magnetic ordering as a canted antiferrimagnet at a T(c) of 171 K.