Egress of malaria parasites from the host cell requires the concerted rupture of its enveloping membranes. Hence, we investigated the role of the plasmodial perforin-like protein PPLP2 in the egress of Plasmodium falciparum from erythrocytes. PPLP2 is expressed in blood stage schizonts and mature gametocytes. The protein localizes in vesicular structures, which in activated gametocytes discharge PPLP2 in a calcium-dependent manner. PPLP2 comprises a MACPF domain and recombinant PPLP2 has haemolytic activities towards erythrocytes. PPLP2-deficient [PPLP2(−)] merozoites show normal egress dynamics during the erythrocytic replication cycle, but activated PPLP2(−) gametocytes were unable to leave erythrocytes and stayed trapped within these cells. While the parasitophorous vacuole membrane ruptured normally, the activated PPLP2(−) gametocytes were unable to permeabilize the erythrocyte membrane and to release the erythrocyte cytoplasm. In consequence, transmission of PPLP2(−) parasites to the Anopheles vector was reduced. Pore-forming equinatoxin II rescued both PPLP2(−) gametocyte exflagellation and parasite transmission. The pore sealant Tetronic 90R4, on the other hand, caused trapping of activated wild-type gametocytes within the enveloping erythrocytes, thus mimicking the PPLP2(−) loss-of-function phenotype. We propose that the haemolytic activity of PPLP2 is essential for gametocyte egress due to permeabilization of the erythrocyte membrane and depletion of the erythrocyte cytoplasm.

Clinical malaria is associated with proliferation of blood-stage parasites. During the blood stage, Plasmodium parasites invade host red blood cells, multiply, egress and reinvade uninfected red blood cells to continue the life cycle. Here we demonstrate that calcium-dependent permeabilization of host red blood cells is critical for egress of Plasmodium falciparum merozoites. Although perforin-like proteins have been predicted to mediate membrane perforation during egress, the expression, activity and mechanism of action of these proteins have not been demonstrated. Here, we show that two perforin-like proteins, perforin-like protein 1 and perforin-like protein 2, are expressed in the blood stage. Perforin-like protein 1 localizes to the red blood cell membrane and parasitophorous vacuolar membrane in mature schizonts following its Ca 2 þ -dependent discharge from micronemes. Furthermore, perforin-like protein 1 shows Ca 2 þ -dependent permeabilization and membranolytic activities suggesting that it may be one of the effector proteins that mediate Ca 2 þ -dependent membrane perforation during egress.

SummaryEgress of Plasmodium falciparum merozoites from host erythrocytes is a critical step in multiplication of blood-stage parasites. A cascade of proteolytic events plays a major role in degradation of membranes leading to egress of merozoites. However, the signals that regulate the temporal activation and/or secretion of proteases upon maturation of merozoites in intra-erythrocytic schizonts remain unclear. Here, we have tested the role of intracellular Ca 2+ in regulation of egress of P. falciparum merozoites from schizonts. A sharp rise in intracellular Ca 2+ just before egress, observed by timelapse video microscopy, suggested a role for intracellular Ca 2+ in this process. Chelation of intracellular Ca 2+ with chelators such as BAPTA-AM or inhibition of Ca 2+ release from intracellular stores with a phospholipase C (PLC) inhibitor blocks merozoite egress. Interestingly, chelation of intracellular Ca 2+ in schizonts was also found to block the discharge of a key protease PfSUB1 (subtilisin-like protease 1) from exonemes of P. falciparum merozoites to parasitophorous vacuole (PV). This leads to inhibition of processing of PfSERA5 (serine repeat antigen 5) and a block in parasitophorous vacuolar membrane (PVM) rupture and merozoite egress. A complete understanding of the steps regulating egress of P. falciparum merozoites may provide novel targets for development of drugs that block egress and limit parasite growth.

An important result in discrepancy due to Banaszczyk states that for any set of n vectors in R m of ℓ 2 norm at most 1 and any convex body K in R m of Gaussian measure at least half, there exists a ±1 combination of these vectors which lies in 5K. This result implies the best known bounds for several problems in discrepancy. Banaszczyk's proof of this result is non-constructive and a major open problem has been to give an efficient algorithm to find such a ±1 combination of the vectors.In this paper, we resolve this question and give an efficient randomized algorithm to find a ±1 combination of the vectors which lies in cK for c > 0 an absolute constant. This leads to new efficient algorithms for several problems in discrepancy theory.

We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most t sets. We give an efficient algorithm that finds a coloring with discrepancy O ((t log n) 1/2 ), matching the best known non-constructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t 1/2 log n) bound. The result also extends to the more general Komlós setting and gives an algorithmic O(log 1/2 n) bound.

The partial coloring method is one of the most powerful and widely used method in combinatorial discrepancy problems. However, in many cases it leads to sub-optimal bounds as the partial coloring step must be iterated a logarithmic number of times, and the errors can add up in an adversarial way.We give a new and general algorithmic framework that overcomes the limitations of the partial coloring method and can be applied in a black-box manner to various problems. Using this framework, we give new improved bounds and algorithms for several classic problems in discrepancy. In particular, for Tusnady's problem, we give an improved O(log 2 n) bound for discrepancy of axis-parallel rectangles and more generally an O d (log d n) bound for d-dimensional boxes in R d . Previously, even non-constructively, the best bounds were O(log 2.5 n) and O d (log d+0.5 n) respectively. Similarly, for the Steinitz problem we give the first algorithm that matches the best known non-constructive bounds due to Banaszczyk [Ban12] in the ℓ ∞ case, and improves the previous algorithmic bounds substantially in the ℓ 2 case. Our framework is based upon a substantial generalization of the techniques developed recently in the context of the Komlós discrepancy problem [BDG16]. project no. 022.005.025. 0 Let (V, S) be a finite set system, with V = {1, . . . , n} and S = {S 1 , . . . , S m } a collection of subsets of V . For a two-coloring χ : V → {−1, 1}, the discrepancy of χ for a set S is defined as χ(S) = | j∈S χ(j)| and measures the imbalance from an even-split for S. The discrepancy of the system (V, S) is defined as disc(S) = minThat is, it is the minimum imbalance for all sets in S, over all possible two-colorings χ. More generally for any matrix A, its discrepancy is defined as disc(A) = min x∈{−1,1} n Ax ∞ . Discrepancy is a widely studied topic and has applications to many areas in mathematics and computer science. In particular in computer science, it arises naturally in computational geometry, data structure lower bounds, rounding in approximation algorithms, combinatorial optimization, communication complexity and pseudorandomness. For much more on these connections we refer the reader to the books [Cha00, Mat09, CST + 14].Partial Coloring Method: One of the most important and widely used technique in discrepancy is the partial coloring method developed in the early 80's by Beck, and its refinement by Spencer to the entropy method [Bec81b, Spe85]. An essentially similar approach, but based on ideas from convex geometry was developed independently by Gluskin [Glu89]. Besides being powerful, an important reason for its success is that it can be applied easily to many problems in a black-box manner and for most problems in discrepancy the best known bounds are achieved using this method. While these original arguments were based on the pigeonhole principle and were nonalgorithmic, in recent years several new algorithmic versions of the partial coloring method have been developed [Ban10, LM12, Rot14a, HSS14, ES14]. In particular, all ...

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We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most t sets. We give an efficient algorithm that finds a coloring with discrepancy O((t log n) 1/2 ), matching the best known non-constructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t 1/2 log n) bound. The result also extends to the more general Komlós setting and gives an algorithmic O(log 1/2 n) bound. project no. 022.005.025. 1 We assume here that t ≥ log n, otherwise the O(t) bound is better. 2 We use [n] to denote the set {1, 2, . . . , n}.